|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return( cos(c(x)) );
> end;
exact_soln_y1 := proc(x) return cos(c(x)) end proc
> exact_soln_y2 := proc(x)
> return( sin(c(x)) + c(10.0) * c(x) + c(10.0));
> end;
exact_soln_y2 := proc(x) return sin(c(x)) + c(10.0)*c(x) + c(10.0) end proc
> exact_soln_y2p := proc(x)
> return( cos(c(x)) + c(10.0));
> end;
exact_soln_y2p := proc(x) return cos(c(x)) + c(10.0) end proc
> exact_soln_y2pp := proc(x)
> return( neg(sin(c(x))));
> end;
exact_soln_y2pp := proc(x) return neg(sin(c(x))) end proc
> exact_soln_y2ppp := proc(x)
> return( neg(cos(c(x))));
> end;
exact_soln_y2ppp := proc(x) return neg(cos(c(x))) end proc
> exact_soln_y2pppp := proc(x)
> return( sin(c(x)));
> end;
exact_soln_y2pppp := proc(x) return sin(c(x)) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[2,1] + array_given_rad_poles[2,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 4
> glob_least_given_sing := rad_given;
> fi;# end if 4;
> elif
> (glob_type_given_pole = 3) then # if number 4
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> elif
> (glob_type_given_pole = 5) then # if number 5
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 5;
> if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," ");
> if ((float_abs(array_rad_test_poles[2,1]) < glob_least_ratio_sing)) then # if number 6
> glob_least_ratio_sing := array_rad_test_poles[2,1];
> fi;# end if 6;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," ");
> if ((float_abs(array_rad_test_poles[2,2]) < glob_least_3_sing)) then # if number 6
> glob_least_3_sing := array_rad_test_poles[2,2];
> fi;# end if 6;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," ");
> if ((float_abs(array_rad_test_poles[2,3]) < glob_least_6_sing)) then # if number 6
> glob_least_6_sing := array_rad_test_poles[2,3];
> fi;# end if 6;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 5
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[2, 1]
- array_given_rad_poles[2, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 2")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_rad_test_poles[2, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_rad_test_poles[2, 1], 4, " ");
if float_abs(array_rad_test_poles[2, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[2, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[2, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 2] and
array_rad_test_poles[2, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_rad_test_poles[2, 2], 4, " ");
if float_abs(array_rad_test_poles[2, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[2, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 3] and
array_rad_test_poles[2, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_rad_test_poles[2, 3], 4, " ");
if float_abs(array_rad_test_poles[2, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[2, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[2, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 5
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 5;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y2[1]) < min_size) then # if number 5
> min_size := float_abs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_y1[1]) < min_size) then # if number 5
> min_size := float_abs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (min_size < glob__1) then # if number 5
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y2[1]) < min_size then
min_size := float_abs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if float_abs(array_y1[1]) < min_size then
min_size := float_abs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> est_tmp := float_abs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := float_abs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 5
> ;
> est_tmp := c(float_abs(array_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
> array_max_est_error[2] := c(est_tmp);
> fi;# end if 5
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y2[no_terms - 3]))
+ c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if;
est_tmp := c(float_abs(array_y1[no_terms - 3]))
+ c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
end if;
if c(array_max_est_error[2]) <= c(est_tmp) then
array_max_est_error[2] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 5
> ret := true;
> else
> ret := false;
> fi;# end if 5;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y2(ind_var));
> omniout_complex(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 6;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> ;
> term_no := 1;
> numeric_val := array_y1[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y1(ind_var));
> omniout_complex(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 6;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y2(ind_var));
omniout_complex(ALWAYS, "y2[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
term_no := 1;
numeric_val := array_y1[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y1(ind_var));
omniout_complex(ALWAYS, "y1[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 5
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 5;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 5 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,1]) then # if number 8
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,1] := glob_larger_float;
> array_ord_test_poles[2,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[2,1]) then # if number 10
> array_rad_test_poles[2,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[2,1] := rad_c;
> array_ord_test_poles[2,1] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 5 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 9;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 10
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 11
> found_sing := 0;
> fi;# end if 11;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 11
> if (rad_c < array_rad_test_poles[1,2]) then # if number 12
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 13
> glob_min_pole_est := rad_c;
> fi;# end if 13;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 12;
> fi;# end if 11;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,2] := glob_larger_float;
> array_ord_test_poles[2,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 11;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 12
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 13
> found_sing := 0;
> fi;# end if 13;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 13
> if (rad_c < array_rad_test_poles[2,2]) then # if number 14
> array_rad_test_poles[2,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[2,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 15
> glob_min_pole_est := rad_c;
> fi;# end if 15;
> array_ord_test_poles[2,2] := tmp_ord;
> fi;# end if 14;
> fi;# end if 13;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 5 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 13;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 14
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 15
> found_sing := 0;
> fi;# end if 15;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 15
> if (rad_c < array_rad_test_poles[1,3]) then # if number 16
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 17
> glob_min_pole_est := rad_c;
> fi;# end if 17;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 16;
> fi;# end if 15;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,3] := glob_larger_float;
> array_ord_test_poles[2,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 15;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 16
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 17
> found_sing := 0;
> fi;# end if 17;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 17
> if (rad_c < array_rad_test_poles[2,3]) then # if number 18
> array_rad_test_poles[2,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[2,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 19
> glob_min_pole_est := rad_c;
> fi;# end if 19;
> array_ord_test_poles[2,3] := tmp_ord;
> fi;# end if 18;
> fi;# end if 17;
> #BOTTOM general radius test2
> ;
> if (true) then # if number 17
> display_poles();
> fi;# end if 17
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 15;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 1] := glob_larger_float;
array_ord_test_poles[2, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 1] then
array_rad_test_poles[2, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[2, 1] := rad_c;
array_ord_test_poles[2, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 15;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 2] := glob_larger_float;
array_ord_test_poles[2, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 2] then
array_rad_test_poles[2, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[2, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 15;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 3] := glob_larger_float;
array_ord_test_poles[2, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 3] then
array_rad_test_poles[2, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[2, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_y1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp1[1]) * (expt((glob_h) , c(5))) * c(factorial_3(0,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[2,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[3,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[4,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[5,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[6,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1 order_d = 4
> array_tmp3[1] := array_y2_higher[5,1];
> #emit pre neg FULL $eq_no = 2
> array_tmp4[1] := neg(array_tmp3[1]);
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[2,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y1_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp1[2] := array_y1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,7]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp1[2]) * (expt((glob_h) , c(5))) * c(factorial_3(1,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[3,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[4,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[5,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[6,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2 order_d = 4
> array_tmp3[2] := array_y2_higher[5,2];
> #emit pre neg FULL $eq_no = 2
> array_tmp4[2] := neg(array_tmp3[2]);
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[2,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y1_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp1[3] := array_y1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,8]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp1[3]) * (expt((glob_h) , c(5))) * c(factorial_3(2,7));
> if (8 <= ATS_MAX_TERMS) then # if number 3
> array_y2[8] := temporary;
> array_y2_higher[1,8] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y2_higher[2,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[3,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[4,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[5,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[6,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3 order_d = 4
> array_tmp3[3] := array_y2_higher[5,3];
> #emit pre neg FULL $eq_no = 2
> array_tmp4[3] := neg(array_tmp3[3]);
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[2,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y1_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp1[4] := array_y1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,9]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp1[4]) * (expt((glob_h) , c(5))) * c(factorial_3(3,8));
> if (9 <= ATS_MAX_TERMS) then # if number 3
> array_y2[9] := temporary;
> array_y2_higher[1,9] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(8);
> array_y2_higher[2,8] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y2_higher[3,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[4,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[5,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[6,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4 order_d = 4
> array_tmp3[4] := array_y2_higher[5,4];
> #emit pre neg FULL $eq_no = 2
> array_tmp4[4] := neg(array_tmp3[4]);
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[2,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y1_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp1[5] := array_y1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,10]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp1[5]) * (expt((glob_h) , c(5))) * c(factorial_3(4,9));
> if (10 <= ATS_MAX_TERMS) then # if number 3
> array_y2[10] := temporary;
> array_y2_higher[1,10] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(9);
> array_y2_higher[2,9] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(8);
> array_y2_higher[3,8] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y2_higher[4,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[5,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[6,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5 order_d = 4
> array_tmp3[5] := array_y2_higher[5,5];
> #emit pre neg FULL $eq_no = 2
> array_tmp4[5] := neg(array_tmp3[5]);
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[2,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y1_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp1[kkk] := array_y1[kkk];
> #emit assign $eq_no = 1
> order_d := 5;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp1[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y2[kkk + order_d] := c(temporary);
> array_y2_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y2_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit diff $eq_no = 2
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp3[kkk] := array_y2_higher[5,kkk];
> fi;# end if 1;
> #emit neg FULL $eq_no = 2
> array_tmp4[kkk] := neg(array_tmp3[kkk]);
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2
> temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y1[kkk + order_d] := c(temporary);
> array_y1_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y1_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_0D0[1] + array_y1[1];
if not array_y2_set_initial[1, 6] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp1[1])*expt(glob_h, c(5))*c(factorial_3(0, 5));
if 6 <= ATS_MAX_TERMS then
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[2, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[3, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[4, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[5, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[6, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp3[1] := array_y2_higher[5, 1];
array_tmp4[1] := neg(array_tmp3[1]);
if not array_y1_set_initial[2, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_y1[2];
if not array_y2_set_initial[1, 7] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp1[2])*expt(glob_h, c(5))*c(factorial_3(1, 6));
if 7 <= ATS_MAX_TERMS then
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[3, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[4, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[5, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[6, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[2] := array_y2_higher[5, 2];
array_tmp4[2] := neg(array_tmp3[2]);
if not array_y1_set_initial[2, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_y1[3];
if not array_y2_set_initial[1, 8] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp1[3])*expt(glob_h, c(5))*c(factorial_3(2, 7));
if 8 <= ATS_MAX_TERMS then
array_y2[8] := temporary;
array_y2_higher[1, 8] := temporary
end if;
temporary := c(temporary)*c(7)/c(glob_h);
array_y2_higher[2, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[3, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[4, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[5, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[6, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[3] := array_y2_higher[5, 3];
array_tmp4[3] := neg(array_tmp3[3]);
if not array_y1_set_initial[2, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_y1[4];
if not array_y2_set_initial[1, 9] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp1[4])*expt(glob_h, c(5))*c(factorial_3(3, 8));
if 9 <= ATS_MAX_TERMS then
array_y2[9] := temporary;
array_y2_higher[1, 9] := temporary
end if;
temporary := c(temporary)*c(8)/c(glob_h);
array_y2_higher[2, 8] := c(temporary);
temporary := c(temporary)*c(7)/c(glob_h);
array_y2_higher[3, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[4, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[5, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[6, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[4] := array_y2_higher[5, 4];
array_tmp4[4] := neg(array_tmp3[4]);
if not array_y1_set_initial[2, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_y1[5];
if not array_y2_set_initial[1, 10] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp1[5])*expt(glob_h, c(5))*c(factorial_3(4, 9));
if 10 <= ATS_MAX_TERMS then
array_y2[10] := temporary;
array_y2_higher[1, 10] := temporary
end if;
temporary := c(temporary)*c(9)/c(glob_h);
array_y2_higher[2, 9] := c(temporary);
temporary := c(temporary)*c(8)/c(glob_h);
array_y2_higher[3, 8] := c(temporary);
temporary := c(temporary)*c(7)/c(glob_h);
array_y2_higher[4, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[5, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[6, 5] := c(temporary)
end if
end if;
kkk := 6;
array_tmp3[5] := array_y2_higher[5, 5];
array_tmp4[5] := neg(array_tmp3[5]);
if not array_y1_set_initial[2, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y1_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_y1[kkk];
order_d := 5;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := c(array_tmp1[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y2[kkk + order_d] := c(temporary);
array_y2_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y2_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
if kkk <= ATS_MAX_TERMS then
array_tmp3[kkk] := array_y2_higher[5, kkk]
end if;
array_tmp4[kkk] := neg(array_tmp3[kkk]);
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y1[kkk + order_d] := c(temporary);
array_y1_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y1_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_0D0,
> array_const_1,
> array_const_4,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y2_init:= Array(0..(40),[]);
> array_y1_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_y2:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_y1:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y2_higher := Array(0..(6) ,(0..40+ 1),[]);
> array_y2_higher_work := Array(0..(6) ,(0..40+ 1),[]);
> array_y2_higher_work2 := Array(0..(6) ,(0..40+ 1),[]);
> array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> array_y1_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y2_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y1_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=6) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=6) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=6) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y2);
> zero_ats_ar(array_x);
> zero_ats_ar(array_y1);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_5);
> array_const_5[1] := c(5);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_4);
> array_const_4[1] := c(4);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := true;
> array_y2_set_initial[1,3] := true;
> array_y2_set_initial[1,4] := true;
> array_y2_set_initial[1,5] := true;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y2_set_initial[1,31] := false;
> array_y2_set_initial[1,32] := false;
> array_y2_set_initial[1,33] := false;
> array_y2_set_initial[1,34] := false;
> array_y2_set_initial[1,35] := false;
> array_y2_set_initial[1,36] := false;
> array_y2_set_initial[1,37] := false;
> array_y2_set_initial[1,38] := false;
> array_y2_set_initial[1,39] := false;
> array_y2_set_initial[1,40] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> array_y1_set_initial[2,31] := false;
> array_y1_set_initial[2,32] := false;
> array_y1_set_initial[2,33] := false;
> array_y1_set_initial[2,34] := false;
> array_y1_set_initial[2,35] := false;
> array_y1_set_initial[2,36] := false;
> array_y1_set_initial[2,37] := false;
> array_y1_set_initial[2,38] := false;
> array_y1_set_initial[2,39] := false;
> array_y1_set_initial[2,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest7postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 5 ) = y1 ; ");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
> omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);");
> omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.1);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return( cos(c(x)) );");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return( sin(c(x)) + c(10.0) * c(x) + c(10.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return( cos(c(x)) + c(10.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"return( neg(sin(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)");
> omniout_str(ALWAYS,"return( neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)");
> omniout_str(ALWAYS,"return( sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
> array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);
> array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.1);
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 18;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 17;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 17
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 17;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 17
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 5;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 18
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 18
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 19;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 18;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 18
> omniout_str(INFO," ");
> fi;# end if 18;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 19;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 18;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> if (glob_subiter_method = 1 ) then # if number 18
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 19
> subiter := 1;
> while (subiter <= 6) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 6 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 19;
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 19
> display_alot(current_iter);
> fi;# end if 19;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 19
> check_for_pole();
> fi;# end if 19;
> if (true) then # if number 19
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 19;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2;
> order_diff := 6;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 6;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[6,iii] := array_y2_higher[6,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 6;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 5;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 5;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 5;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 5;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 4;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 4;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 4;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 3;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 3;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 3;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 5;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 5;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 6;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 6;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 5;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 5;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 19
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 19;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 19
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 19;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y2 , x , 5 ) = y1 ; ");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 19
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T15:50:21-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest7")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 5 ) = y1 ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 20
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> if (glob_min_good_digits <> -16) then # if number 20
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> if (glob_good_digits <> -16) then # if number 20
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 20
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 21
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 22
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 23
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 24
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 25
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 25;
> if (glob_least_ratio_sing < glob_large_float) then # if number 25
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> if (glob_least_3_sing < glob_large_float) then # if number 25
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> if (glob_least_6_sing < glob_large_float) then # if number 25
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 25
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 25;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"mtest7 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest7 maple results")
> ;
> logitem_str(html_log_file,"Poor Accuracy - Not sure of algorithm for multiple equations")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ; ")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logditto(html_log_file)
> ;
> if (array_est_digits[2] <> -16) then # if number 25
> logitem_integer(html_log_file,array_est_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> if (glob_min_good_digits <> -16) then # if number 25
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> if (glob_good_digits <> -16) then # if number 25
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logditto(html_log_file)
> ;
> if (glob_type_given_pole = 0) then # if number 25
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 4) then # if number 26
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 5) then # if number 27
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 3) then # if number 28
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 1) then # if number 29
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 30
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_ratio_sing < glob_large_float) then # if number 30
> glob_least_ratio_sing := 0;
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_3_sing < glob_large_float) then # if number 30
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_6_sing < glob_large_float) then # if number 30
> glob_least_6_sing := 0.0;
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (c(glob_percent_done) < glob__100) then # if number 30
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 30;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 29;
> if (glob_html_log) then # if number 29
> fclose(html_log_file);
> fi;# end if 29
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_5, array_const_0D0, array_const_1,
array_const_4, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y2_higher, array_y2_higher_work, array_y2_higher_work2,
array_y2_set_initial, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 40;
Digits := 64;
max_terms := 40;
glob_html_log := true;
array_y2_init := Array(0 .. 40, []);
array_y1_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_y2 := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_y1 := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y2_higher := Array(0 .. 6, 0 .. 41, []);
array_y2_higher_work := Array(0 .. 6, 0 .. 41, []);
array_y2_higher_work2 := Array(0 .. 6, 0 .. 41, []);
array_y2_set_initial := Array(0 .. 3, 0 .. 41, []);
array_y1_higher := Array(0 .. 2, 0 .. 41, []);
array_y1_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y1_set_initial := Array(0 .. 3, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y2_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_y1_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_y1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= 40 do
array_y2_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= 40 do
array_y2_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= 40 do
array_y2_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_y2_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y1_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y1_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y1_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_y1_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y2);
zero_ats_ar(array_x);
zero_ats_ar(array_y1);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_5);
array_const_5[1] := c(5);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_4);
array_const_4[1] := c(4);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := true;
array_y2_set_initial[1, 3] := true;
array_y2_set_initial[1, 4] := true;
array_y2_set_initial[1, 5] := true;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y2_set_initial[1, 31] := false;
array_y2_set_initial[1, 32] := false;
array_y2_set_initial[1, 33] := false;
array_y2_set_initial[1, 34] := false;
array_y2_set_initial[1, 35] := false;
array_y2_set_initial[1, 36] := false;
array_y2_set_initial[1, 37] := false;
array_y2_set_initial[1, 38] := false;
array_y2_set_initial[1, 39] := false;
array_y2_set_initial[1, 40] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 30] := false;
array_y1_set_initial[2, 31] := false;
array_y1_set_initial[2, 32] := false;
array_y1_set_initial[2, 33] := false;
array_y1_set_initial[2, 34] := false;
array_y1_set_initial[2, 35] := false;
array_y1_set_initial[2, 36] := false;
array_y1_set_initial[2, 37] := false;
array_y1_set_initial[2, 38] := false;
array_y1_set_initial[2, 39] := false;
array_y1_set_initial[2, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest7postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ; ");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( diff ( y2\
, x , 4 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
;
omniout_str(ALWAYS,
"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);");
omniout_str(ALWAYS,
"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.1);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(\t cos(c(x)) );");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(\tsin(c(x)) + c(10.0) * c(x) + c(10.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return(\tcos(c(x)) + c(10.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "return( neg(sin(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)");
omniout_str(ALWAYS, "return(\tneg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)");
omniout_str(ALWAYS, "return( sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(x_start);
array_y2_init[3] := exact_soln_y2pp(x_start);
array_y2_init[4] := exact_soln_y2ppp(x_start);
array_y2_init[5] := exact_soln_y2pppp(x_start);
glob_look_poles := true;
glob_max_h := c(0.1);
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 5;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] :=
array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] :=
array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 6 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 6 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 6;
ord := 6;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 6;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 5;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 5;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 5;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 5;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 4;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 4;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 4;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 4;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 4;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 4;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 3;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 3;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 3;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 3;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 3;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 3;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 5;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 5;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 6;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 6;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 5;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 5;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y2 , x , 5 ) = y1 ; ");
omniout_str(INFO, "diff ( y1 , x , 1 ) = neg ( diff ( \
y2 , x , 4 ) ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T15:50:21-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest7");
logitem_str(html_log_file,
"diff ( y2 , x , 5 ) = y1 ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"mtest7 diffeq.mxt");
logitem_str(html_log_file, "mtest7 maple results");
logitem_str(html_log_file, "Poor Accuracy - Not sure of algor\
ithm for multiple equations");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = n\
eg ( diff ( y2 , x , 4 ) ) ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
glob_desired_digits_correct := 0.;
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0; logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_3_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.; logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if c(glob_percent_done) < glob__100 then
logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.5MB, alloc=40.3MB, time=0.07
##############ECHO OF PROBLEM#################
##############temp/mtest7postcpx.cpx#################
diff ( y2 , x , 5 ) = y1 ;
diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);
array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);
glob_look_poles := true;
glob_max_h := c(0.1);
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return( cos(c(x)) );
end;
exact_soln_y2 := proc(x)
return( sin(c(x)) + c(10.0) * c(x) + c(10.0));
end;
exact_soln_y2p := proc(x)
return( cos(c(x)) + c(10.0));
end;
exact_soln_y2pp := proc(x)
return( neg(sin(c(x))));
end;
exact_soln_y2ppp := proc(x)
return( neg(cos(c(x))));
end;
exact_soln_y2pppp := proc(x)
return( sin(c(x)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
memory used=53.5MB, alloc=40.3MB, time=0.66
memory used=100.0MB, alloc=40.3MB, time=1.20
x[1] = 0.1 0.1
h = 0.0001 0.005
y2[1] (numeric) = 11.1003329998 1.09966633349
y2[1] (closed_form) = 11.1003329998 1.09966633349
absolute error = 0
relative error = 0 %
Correct digits = 62
h = 0.0001 0.005
y1[1] (numeric) = 0.999983333337 -0.00999998888889
y1[1] (closed_form) = 0.999983333337 -0.00999998888889
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1414
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1414
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=145.8MB, alloc=40.3MB, time=1.74
memory used=192.3MB, alloc=40.3MB, time=2.29
x[1] = 0.1001 0.105
h = 0.0001 0.003
y2[1] (numeric) = 11.1014738411 1.14366603417
y2[1] (closed_form) = 11.1014843031 1.15466646612
absolute error = 0.011
relative error = 0.09856 %
Correct digits = 3
h = 0.0001 0.003
y1[1] (numeric) = 1.00048412347 -0.0105122476776
y1[1] (closed_form) = 1.00048412347 -0.0105122476776
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1452
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1452
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=238.0MB, alloc=40.3MB, time=2.82
memory used=284.7MB, alloc=40.3MB, time=3.38
x[1] = 0.1002 0.108
h = 0.001 0.001
y2[1] (numeric) = 11.1026163718 1.18766731208
y2[1] (closed_form) = 11.1026163718 1.18766731208
absolute error = 5.369e-13
relative error = 4.808e-12 %
Correct digits = 13
h = 0.001 0.001
y1[1] (numeric) = 1.00079256889 -0.0108245151295
y1[1] (closed_form) = 1.00079256889 -0.0108245151295
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1475
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1475
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=330.6MB, alloc=40.3MB, time=3.93
memory used=377.0MB, alloc=40.3MB, time=4.48
x[1] = 0.1012 0.109
h = 0.001 0.003
y2[1] (numeric) = 11.1037605975 1.23167023111
y2[1] (closed_form) = 11.1136280969 1.19865717918
absolute error = 0.03446
relative error = 0.3082 %
Correct digits = 3
h = 0.001 0.003
y1[1] (numeric) = 1.00079960894 -0.0110337996083
y1[1] (closed_form) = 1.00079960894 -0.0110337996083
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1489
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1489
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=422.8MB, alloc=40.3MB, time=5.02
memory used=469.3MB, alloc=40.3MB, time=5.57
memory used=515.8MB, alloc=40.3MB, time=6.12
x[1] = 0.1022 0.112
h = 0.0001 0.004
y2[1] (numeric) = 11.1049065238 1.27567485514
y2[1] (closed_form) = 11.1246627347 1.23164867691
absolute error = 0.04826
relative error = 0.4311 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.00102792236 -0.0114503883919
y1[1] (closed_form) = 1.00102792236 -0.0114503883919
absolute error = 1e-63
relative error = 9.989e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1518
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1518
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=561.6MB, alloc=40.3MB, time=6.65
memory used=608.1MB, alloc=40.3MB, time=7.20
x[1] = 0.1023 0.116
h = 0.003 0.006
y2[1] (numeric) = 11.106054156 1.31968124811
y2[1] (closed_form) = 11.1258095055 1.27565250577
absolute error = 0.04826
relative error = 0.4309 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.00147225055 -0.0118726973391
y1[1] (closed_form) = 1.00147225055 -0.0118726973391
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.155
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.155
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=653.8MB, alloc=40.3MB, time=7.73
memory used=700.2MB, alloc=40.3MB, time=8.28
x[1] = 0.1053 0.122
h = 0.0001 0.005
y2[1] (numeric) = 11.1072034999 1.36368947394
y2[1] (closed_form) = 11.1588886778 1.34162544034
absolute error = 0.0562
relative error = 0.5 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.00187103916 -0.0128547054021
y1[1] (closed_form) = 1.00187103916 -0.0128547054021
absolute error = 1e-65
relative error = 9.981e-64 %
Correct digits = 65
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1616
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1616
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=746.0MB, alloc=40.3MB, time=8.82
memory used=792.7MB, alloc=40.3MB, time=9.37
x[1] = 0.1054 0.127
h = 0.0001 0.003
y2[1] (numeric) = 11.108354561 1.40769959662
y2[1] (closed_form) = 11.1600545238 1.39663499766
absolute error = 0.05287
relative error = 0.4701 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.00248109187 -0.0133969752478
y1[1] (closed_form) = 1.00248109187 -0.0133969752478
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1656
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1656
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=838.6MB, alloc=44.3MB, time=9.91
memory used=885.2MB, alloc=44.3MB, time=10.48
x[1] = 0.1055 0.13
h = 0.001 0.001
y2[1] (numeric) = 11.1095073449 1.45171168014
y2[1] (closed_form) = 11.1611954781 1.42964164314
absolute error = 0.0562
relative error = 0.4995 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.00285489407 -0.0137281638158
y1[1] (closed_form) = 1.00285489407 -0.0137281638158
absolute error = 1e-65
relative error = 9.971e-64 %
Correct digits = 65
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1681
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1681
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=931.5MB, alloc=44.3MB, time=11.02
memory used=977.4MB, alloc=44.3MB, time=11.57
memory used=1023.9MB, alloc=44.3MB, time=12.12
x[1] = 0.1065 0.131
h = 0.001 0.003
y2[1] (numeric) = 11.1106618573 1.49572578851
y2[1] (closed_form) = 11.1722121911 1.44063066333
absolute error = 0.08261
relative error = 0.7333 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.00287832643 -0.0139650037997
y1[1] (closed_form) = 1.00287832643 -0.0139650037997
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1695
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1695
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1069.8MB, alloc=44.3MB, time=12.65
memory used=1116.3MB, alloc=44.3MB, time=13.20
x[1] = 0.1075 0.134
h = 0.0001 0.004
y2[1] (numeric) = 11.111818104 1.53974198577
y2[1] (closed_form) = 11.1832577896 1.47362553714
absolute error = 0.09734
relative error = 0.8629 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.00316697577 -0.014420336423
y1[1] (closed_form) = 1.00316697577 -0.014420336423
absolute error = 1.000e-63
relative error = 9.968e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1725
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1725
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1162.0MB, alloc=44.3MB, time=13.73
memory used=1208.4MB, alloc=44.3MB, time=14.28
x[1] = 0.1076 0.138
h = 0.003 0.006
y2[1] (numeric) = 11.1129760906 1.58376033597
y2[1] (closed_form) = 11.1844167075 1.51763779872
absolute error = 0.09734
relative error = 0.8625 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.00369866804 -0.014867247953
y1[1] (closed_form) = 1.00369866804 -0.014867247953
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1759
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1759
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1254.1MB, alloc=44.3MB, time=14.81
memory used=1300.5MB, alloc=44.3MB, time=15.36
x[1] = 0.1106 0.144
h = 0.0001 0.005
y2[1] (numeric) = 11.114135823 1.62778090319
y2[1] (closed_form) = 11.2175209979 1.58361530388
absolute error = 0.1124
relative error = 0.9924 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.00421252288 -0.015948936748
y1[1] (closed_form) = 1.00421252288 -0.015948936748
absolute error = 1e-63
relative error = 9.957e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1826
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1826
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1346.6MB, alloc=44.3MB, time=15.90
memory used=1392.9MB, alloc=44.3MB, time=16.45
memory used=1439.4MB, alloc=44.3MB, time=17.00
x[1] = 0.1107 0.149
h = 0.0001 0.003
y2[1] (numeric) = 11.1152973069 1.67180375151
y2[1] (closed_form) = 11.2187026307 1.63863653119
absolute error = 0.1086
relative error = 0.9578 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.00493198983 -0.0165216071589
y1[1] (closed_form) = 1.00493198983 -0.0165216071589
absolute error = 1e-63
relative error = 9.950e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1869
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1869
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1485.6MB, alloc=44.3MB, time=17.54
memory used=1532.3MB, alloc=44.3MB, time=18.12
x[1] = 0.1108 0.152
h = 0.001 0.001
y2[1] (numeric) = 11.1164605484 1.71582894507
y2[1] (closed_form) = 11.219853236 1.67165031411
absolute error = 0.1124
relative error = 0.9912 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.005371242 -0.0168719550168
y1[1] (closed_form) = 1.005371242 -0.0168719550168
absolute error = 1e-63
relative error = 9.945e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1895
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1895
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1578.1MB, alloc=44.3MB, time=18.66
memory used=1624.4MB, alloc=44.3MB, time=19.20
x[1] = 0.1118 0.153
h = 0.001 0.003
y2[1] (numeric) = 11.1176255533 1.75985654798
y2[1] (closed_form) = 11.2308756312 1.6826387012
absolute error = 0.1371
relative error = 1.207 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.00541102212 -0.0171364639514
y1[1] (closed_form) = 1.00541102212 -0.0171364639514
absolute error = 1e-63
relative error = 9.945e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1909
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1909
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1670.2MB, alloc=44.3MB, time=19.74
memory used=1716.8MB, alloc=44.3MB, time=20.29
x[1] = 0.1128 0.156
h = 0.0001 0.004
y2[1] (numeric) = 11.1187923275 1.80388662438
y2[1] (closed_form) = 11.2419333654 1.71563807267
absolute error = 0.1515
relative error = 1.332 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.00576003279 -0.0176308153291
y1[1] (closed_form) = 1.00576003279 -0.0176308153291
absolute error = 1e-63
relative error = 9.941e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.194
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.194
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1762.6MB, alloc=44.3MB, time=20.82
memory used=1809.0MB, alloc=44.3MB, time=21.37
x[1] = 0.1129 0.16
h = 0.003 0.006
y2[1] (numeric) = 11.1199608772 1.84791923845
y2[1] (closed_form) = 11.2431054388 1.75966055917
absolute error = 0.1515
relative error = 1.331 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.00637922732 -0.0181026571991
y1[1] (closed_form) = 1.00637922732 -0.0181026571991
absolute error = 1e-63
relative error = 9.935e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1975
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1975
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1855.2MB, alloc=44.3MB, time=21.91
memory used=1901.3MB, alloc=44.3MB, time=22.45
memory used=1947.7MB, alloc=44.3MB, time=23.00
x[1] = 0.1159 0.166
h = 0.0001 0.005
y2[1] (numeric) = 11.1211312084 1.89195445434
y2[1] (closed_form) = 11.2762376567 1.82564463623
absolute error = 0.1687
relative error = 1.477 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.0070081304 -0.0192846397327
y1[1] (closed_form) = 1.0070081304 -0.0192846397327
absolute error = 1.000e-63
relative error = 9.929e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2044
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2044
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1993.6MB, alloc=44.3MB, time=23.54
memory used=2040.2MB, alloc=44.3MB, time=24.09
x[1] = 0.116 0.171
h = 0.0001 0.003
y2[1] (numeric) = 11.1223033272 1.93599233625
y2[1] (closed_form) = 11.2774363301 1.88067978046
absolute error = 0.1647
relative error = 1.441 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.00783720606 -0.0198881395948
y1[1] (closed_form) = 1.00783720606 -0.0198881395948
absolute error = 1.000e-63
relative error = 9.921e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2088
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2088
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2086.1MB, alloc=44.3MB, time=24.63
memory used=2132.8MB, alloc=44.3MB, time=25.19
x[1] = 0.1161 0.174
h = 0.001 0.001
y2[1] (numeric) = 11.1234772398 1.98003294839
y2[1] (closed_form) = 11.2785973579 1.91370203975
absolute error = 0.1687
relative error = 1.475 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.00834202675 -0.0202579089155
y1[1] (closed_form) = 1.00834202675 -0.0202579089155
absolute error = 1e-65
relative error = 9.915e-64 %
Correct digits = 65
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2116
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2116
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2178.7MB, alloc=44.3MB, time=25.73
memory used=2225.1MB, alloc=44.3MB, time=26.28
x[1] = 0.1171 0.175
h = 0.001 0.003
y2[1] (numeric) = 11.1246529525 2.02407635497
y2[1] (closed_form) = 11.2896261318 1.92469000593
absolute error = 0.1926
relative error = 1.682 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.00839811108 -0.0205502166739
y1[1] (closed_form) = 1.00839811108 -0.0205502166739
absolute error = 1.000e-63
relative error = 9.917e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.213
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.213
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2270.9MB, alloc=44.3MB, time=26.82
memory used=2317.4MB, alloc=44.3MB, time=27.36
memory used=2363.7MB, alloc=44.3MB, time=27.91
x[1] = 0.1181 0.178
h = 0.0001 0.004
y2[1] (numeric) = 11.1258304716 2.0681226202
y2[1] (closed_form) = 11.3006971836 1.95769499587
absolute error = 0.2068
relative error = 1.803 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.00880752691 -0.0210838935875
y1[1] (closed_form) = 1.00880752691 -0.0210838935875
absolute error = 1.000e-63
relative error = 9.913e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2162
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2162
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2409.4MB, alloc=44.3MB, time=28.44
memory used=2455.7MB, alloc=44.3MB, time=28.99
x[1] = 0.1182 0.182
h = 0.003 0.006
y2[1] (numeric) = 11.1270098035 2.11217180832
y2[1] (closed_form) = 11.301883429 2.0017295011
absolute error = 0.2068
relative error = 1.802 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.00951439597 -0.0215810253281
y1[1] (closed_form) = 1.00951439597 -0.0215810253281
absolute error = 1.000e-63
relative error = 9.905e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2198
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2198
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2501.4MB, alloc=44.3MB, time=29.52
memory used=2547.8MB, alloc=44.3MB, time=30.07
x[1] = 0.1212 0.188
h = 0.0001 0.005
y2[1] (numeric) = 11.1281909546 2.15622398357
y2[1] (closed_form) = 11.3350463981 2.06772214785
absolute error = 0.225
relative error = 1.953 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.01025835835 -0.0228639871644
y1[1] (closed_form) = 1.01025835835 -0.0228639871644
absolute error = 1.000e-63
relative error = 9.896e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2268
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2268
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2593.5MB, alloc=44.3MB, time=30.60
memory used=2640.1MB, alloc=44.3MB, time=31.15
x[1] = 0.1213 0.193
h = 0.0001 0.003
y2[1] (numeric) = 11.1293739313 2.20027921021
y2[1] (closed_form) = 11.3362633769 2.12277345831
absolute error = 0.2209
relative error = 1.916 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.01119727997 -0.0234987849821
y1[1] (closed_form) = 1.01119727997 -0.0234987849821
absolute error = 1.000e-63
relative error = 9.887e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2314
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2314
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2686.1MB, alloc=44.3MB, time=31.70
memory used=2732.8MB, alloc=44.3MB, time=32.26
x[1] = 0.1214 0.196
h = 0.001 0.001
y2[1] (numeric) = 11.1305587404 2.2443375525
y2[1] (closed_form) = 11.3374356055 2.15580553433
absolute error = 0.225
relative error = 1.95 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.01176781311 -0.0238882620851
y1[1] (closed_form) = 1.01176781311 -0.0238882620851
absolute error = 1.000e-63
relative error = 9.881e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2343
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2343
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2779.3MB, alloc=44.3MB, time=32.81
memory used=2825.5MB, alloc=44.3MB, time=33.35
memory used=2872.1MB, alloc=44.3MB, time=33.91
x[1] = 0.1224 0.197
h = 0.0001 0.004
y2[1] (numeric) = 11.1317453883 2.2883990747
y2[1] (closed_form) = 11.3484714577 2.1667932901
absolute error = 0.2485
relative error = 2.151 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.01184015904 -0.0242085150168
y1[1] (closed_form) = 1.01184015904 -0.0242085150168
absolute error = 1e-63
relative error = 9.880e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2357
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2357
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2917.9MB, alloc=44.3MB, time=34.44
memory used=2964.3MB, alloc=44.3MB, time=34.99
x[1] = 0.1225 0.201
h = 0.003 0.006
y2[1] (numeric) = 11.1329338818 2.33246384108
y2[1] (closed_form) = 11.3496705507 2.21083976422
absolute error = 0.2485
relative error = 2.149 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.01262296704 -0.0247266799437
y1[1] (closed_form) = 1.01262296704 -0.0247266799437
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2394
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2394
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3010.1MB, alloc=44.3MB, time=35.52
memory used=3056.7MB, alloc=44.3MB, time=36.07
x[1] = 0.1255 0.207
h = 0.0001 0.005
y2[1] (numeric) = 11.1341242278 2.37653191592
y2[1] (closed_form) = 11.3828621282 2.27684179712
absolute error = 0.268
relative error = 2.308 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.01346721491 -0.0260957947093
y1[1] (closed_form) = 1.01346721491 -0.0260957947093
absolute error = 1e-63
relative error = 9.864e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2465
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2465
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3102.5MB, alloc=44.3MB, time=36.60
memory used=3149.0MB, alloc=44.3MB, time=37.15
x[1] = 0.1256 0.212
h = 0.0001 0.003
y2[1] (numeric) = 11.1353164329 2.42060336349
y2[1] (closed_form) = 11.3840956568 2.33190906523
absolute error = 0.2641
relative error = 2.273 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.01450129208 -0.0267566252526
y1[1] (closed_form) = 1.01450129208 -0.0267566252526
absolute error = 1.000e-63
relative error = 9.854e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2513
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2513
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3195.1MB, alloc=44.3MB, time=37.68
memory used=3241.6MB, alloc=44.3MB, time=38.24
memory used=3288.2MB, alloc=44.3MB, time=38.81
x[1] = 0.1257 0.215
h = 0.001 0.001
y2[1] (numeric) = 11.1365105043 2.46467824809
y2[1] (closed_form) = 11.3852780167 2.36495081209
absolute error = 0.268
relative error = 2.305 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.01512876276 -0.0271625284212
y1[1] (closed_form) = 1.01512876276 -0.0271625284212
absolute error = 1e-63
relative error = 9.847e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2542
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2542
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3334.1MB, alloc=44.3MB, time=39.34
memory used=3380.5MB, alloc=44.3MB, time=39.90
x[1] = 0.1267 0.216
h = 0.001 0.003
y2[1] (numeric) = 11.1377064488 2.50875663398
y2[1] (closed_form) = 11.3963205233 2.3759386497
absolute error = 0.2907
relative error = 2.497 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.01521540828 -0.0275067724077
y1[1] (closed_form) = 1.01521540828 -0.0275067724077
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2556
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2556
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3426.2MB, alloc=44.3MB, time=40.43
memory used=3472.6MB, alloc=44.3MB, time=40.98
x[1] = 0.1277 0.219
h = 0.0001 0.004
y2[1] (numeric) = 11.1389042737 2.55283858545
y2[1] (closed_form) = 11.4074194286 2.40895726787
absolute error = 0.3046
relative error = 2.613 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.01573788214 -0.0281138296284
y1[1] (closed_form) = 1.01573788214 -0.0281138296284
absolute error = 1e-63
relative error = 9.841e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.259
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.259
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3518.4MB, alloc=44.3MB, time=41.51
memory used=3564.7MB, alloc=44.3MB, time=42.06
x[1] = 0.1278 0.223
h = 0.003 0.006
y2[1] (numeric) = 11.140103986 2.59692416679
y2[1] (closed_form) = 11.4086345891 2.4530191172
absolute error = 0.3047
relative error = 2.611 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.01660878108 -0.0286580356999
y1[1] (closed_form) = 1.01660878108 -0.0286580356999
absolute error = 1e-63
relative error = 9.833e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2629
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2629
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3610.5MB, alloc=44.3MB, time=42.59
memory used=3657.1MB, alloc=44.3MB, time=43.14
x[1] = 0.1308 0.229
h = 0.0001 0.005
y2[1] (numeric) = 11.141305593 2.64101344227
y2[1] (closed_form) = 11.4418621922 2.51903346283
absolute error = 0.3244
relative error = 2.769 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.01756819591 -0.0301295987246
y1[1] (closed_form) = 1.01756819591 -0.0301295987246
absolute error = 1e-63
relative error = 9.823e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2701
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2701
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3703.5MB, alloc=44.3MB, time=43.68
memory used=3749.6MB, alloc=44.3MB, time=44.22
memory used=3796.2MB, alloc=44.3MB, time=44.77
x[1] = 0.1309 0.234
h = 0.0001 0.003
y2[1] (numeric) = 11.1425091022 2.68510647617
y2[1] (closed_form) = 11.443116386 2.57412110684
absolute error = 0.3204
relative error = 2.732 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.01871268108 -0.0308227013598
y1[1] (closed_form) = 1.01871268108 -0.0308227013598
absolute error = 1e-63
relative error = 9.812e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.275
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.275
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3842.3MB, alloc=44.3MB, time=45.32
memory used=3889.1MB, alloc=44.3MB, time=45.89
x[1] = 0.131 0.237
h = 0.001 0.001
y2[1] (numeric) = 11.1437145208 2.72920333278
y2[1] (closed_form) = 11.4443113991 2.60717517931
absolute error = 0.3244
relative error = 2.764 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.01940620362 -0.0312489074978
y1[1] (closed_form) = 1.01940620362 -0.0312489074978
absolute error = 1e-63
relative error = 9.805e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.278
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.278
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3935.0MB, alloc=44.3MB, time=46.43
memory used=3981.5MB, alloc=44.3MB, time=46.98
x[1] = 0.132 0.238
h = 0.001 0.003
y2[1] (numeric) = 11.1449218565 2.77330407636
y2[1] (closed_form) = 11.4553622917 2.61816320194
absolute error = 0.347
relative error = 2.953 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.01950903603 -0.0316214135167
y1[1] (closed_form) = 1.01950903603 -0.0316214135167
absolute error = 1.000e-63
relative error = 9.804e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2794
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2794
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4027.2MB, alloc=44.3MB, time=47.52
memory used=4073.8MB, alloc=44.3MB, time=48.06
x[1] = 0.133 0.241
h = 0.0001 0.004
y2[1] (numeric) = 11.1461311169 2.81740877119
y2[1] (closed_form) = 11.4664779254 2.65119065712
absolute error = 0.3609
relative error = 3.067 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.02009214664 -0.0322688500487
y1[1] (closed_form) = 1.02009214664 -0.0322688500487
absolute error = 1.000e-63
relative error = 9.799e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2828
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2828
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4119.7MB, alloc=44.3MB, time=48.60
memory used=4166.0MB, alloc=44.3MB, time=49.15
memory used=4212.5MB, alloc=44.3MB, time=49.70
x[1] = 0.1331 0.245
h = 0.003 0.006
y2[1] (numeric) = 11.1473423097 2.86151748151
y2[1] (closed_form) = 11.4677101988 2.69526968339
absolute error = 0.3609
relative error = 3.064 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.02105140668 -0.0328395484898
y1[1] (closed_form) = 1.02105140668 -0.0328395484898
absolute error = 1.000e-63
relative error = 9.789e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2869
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2869
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4258.3MB, alloc=44.3MB, time=50.23
memory used=4304.9MB, alloc=44.3MB, time=50.79
x[1] = 0.1361 0.251
h = 0.0001 0.005
y2[1] (numeric) = 11.1485554426 2.90563027159
y2[1] (closed_form) = 11.5009767016 2.76129833109
absolute error = 0.3808
relative error = 3.22 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.02212608268 -0.0344144544453
y1[1] (closed_form) = 1.02212608268 -0.0344144544453
absolute error = 1e-63
relative error = 9.778e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2942
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2942
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4350.7MB, alloc=44.3MB, time=51.32
memory used=4397.2MB, alloc=44.3MB, time=51.88
x[1] = 0.1362 0.256
h = 0.0001 0.003
y2[1] (numeric) = 11.1497705237 2.94974720569
y2[1] (closed_form) = 11.5022528632 2.81640861127
absolute error = 0.3769
relative error = 3.182 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.023381336 -0.035140412088
y1[1] (closed_form) = 1.023381336 -0.035140412088
absolute error = 1.000e-63
relative error = 9.766e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2993
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2993
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4443.0MB, alloc=44.3MB, time=52.41
memory used=4489.8MB, alloc=44.3MB, time=52.97
x[1] = 0.1363 0.259
h = 0.001 0.001
y2[1] (numeric) = 11.1509875608 2.99386834803
y2[1] (closed_form) = 11.5034613305 2.84947635629
absolute error = 0.3809
relative error = 3.214 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.02414112719 -0.0355872772541
y1[1] (closed_form) = 1.02414112719 -0.0355872772541
absolute error = 2.000e-63
relative error = 1.952e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3024
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3024
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4535.8MB, alloc=44.3MB, time=53.52
memory used=4582.4MB, alloc=44.3MB, time=54.08
x[1] = 0.1373 0.26
h = 0.001 0.003
y2[1] (numeric) = 11.1522065622 3.03799376286
y2[1] (closed_form) = 11.5145213187 2.86046476933
absolute error = 0.4035
relative error = 3.401 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.0242601065 -0.0359882391217
y1[1] (closed_form) = 1.0242601065 -0.0359882391217
absolute error = 2e-63
relative error = 1.951e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3038
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3038
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4628.4MB, alloc=44.3MB, time=54.61
memory used=4674.8MB, alloc=44.3MB, time=55.16
memory used=4721.3MB, alloc=44.3MB, time=55.71
x[1] = 0.1383 0.263
h = 0.0001 0.004
y2[1] (numeric) = 11.1534275359 3.08212351439
y2[1] (closed_form) = 11.5256548956 2.89350218162
absolute error = 0.4173
relative error = 3.512 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.02490396873 -0.0366764861378
y1[1] (closed_form) = 1.02490396873 -0.0366764861378
absolute error = 1.000e-63
relative error = 9.751e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3073
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3073
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4767.1MB, alloc=44.3MB, time=56.25
memory used=4813.6MB, alloc=44.3MB, time=56.80
x[1] = 0.1384 0.267
h = 0.003 0.006
y2[1] (numeric) = 11.1546504904 3.12625766683
y2[1] (closed_form) = 11.5269053391 2.93760019037
absolute error = 0.4173
relative error = 3.508 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.02595189411 -0.0372741608594
y1[1] (closed_form) = 1.02595189411 -0.0372741608594
absolute error = 1e-63
relative error = 9.741e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3114
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3114
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4859.5MB, alloc=44.3MB, time=57.33
memory used=4906.1MB, alloc=44.3MB, time=57.88
x[1] = 0.1414 0.273
h = 0.0001 0.005
y2[1] (numeric) = 11.1558754341 3.17039628438
y2[1] (closed_form) = 11.5602136369 3.00364512693
absolute error = 0.4374
relative error = 3.662 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.02714195396 -0.0389533784147
y1[1] (closed_form) = 1.02714195396 -0.0389533784147
absolute error = 1e-63
relative error = 9.729e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3189
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3189
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4952.0MB, alloc=44.3MB, time=58.42
memory used=4998.6MB, alloc=44.3MB, time=58.97
x[1] = 0.1415 0.278
h = 0.0001 0.003
y2[1] (numeric) = 11.1571023754 3.21453943123
y2[1] (closed_form) = 11.5615130838 3.05878030878
absolute error = 0.4334
relative error = 3.624 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.02850837843 -0.0397128147928
y1[1] (closed_form) = 1.02850837843 -0.0397128147928
absolute error = 1.000e-63
relative error = 9.716e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3242
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3242
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5044.5MB, alloc=44.3MB, time=59.50
memory used=5091.2MB, alloc=44.3MB, time=60.07
x[1] = 0.1416 0.281
h = 0.001 0.001
y2[1] (numeric) = 11.158331323 3.25868717156
y2[1] (closed_form) = 11.5627358159 3.0918630764
absolute error = 0.4375
relative error = 3.655 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.02933468047 -0.0401807199198
y1[1] (closed_form) = 1.02933468047 -0.0401807199198
absolute error = 1.000e-63
relative error = 9.708e-62 %
Correct digits = 63
memory used=5137.9MB, alloc=44.3MB, time=60.62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3273
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3273
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5184.0MB, alloc=44.3MB, time=61.17
memory used=5230.5MB, alloc=44.3MB, time=61.72
x[1] = 0.1426 0.282
h = 0.001 0.003
y2[1] (numeric) = 11.1595622858 3.30283956951
y2[1] (closed_form) = 11.5738056135 3.10285208326
absolute error = 0.46
relative error = 3.839 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.0294697674 -0.0406103481919
y1[1] (closed_form) = 1.0294697674 -0.0406103481919
absolute error = 1.000e-63
relative error = 9.707e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3288
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3288
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5276.2MB, alloc=44.3MB, time=62.25
memory used=5322.7MB, alloc=44.3MB, time=62.80
x[1] = 0.1436 0.285
h = 0.0001 0.004
y2[1] (numeric) = 11.1607952724 3.34699668924
y2[1] (closed_form) = 11.5849583587 3.13590057312
absolute error = 0.4738
relative error = 3.948 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.0301745143 -0.0413398696397
y1[1] (closed_form) = 1.0301745143 -0.0413398696397
absolute error = 1.000e-63
relative error = 9.701e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3324
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3324
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5368.5MB, alloc=44.3MB, time=63.34
memory used=5414.9MB, alloc=44.3MB, time=63.88
x[1] = 0.1437 0.289
h = 0.003 0.006
y2[1] (numeric) = 11.1620302919 3.39115859486
y2[1] (closed_form) = 11.5862280422 3.18001937432
absolute error = 0.4738
relative error = 3.944 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.0313114434 -0.04196503753
y1[1] (closed_form) = 1.0313114434 -0.04196503753
absolute error = 1.000e-63
relative error = 9.690e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3367
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3367
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5460.7MB, alloc=44.3MB, time=64.42
memory used=5507.2MB, alloc=44.3MB, time=64.97
x[1] = 0.1467 0.295
h = 0.0001 0.005
y2[1] (numeric) = 11.1632673535 3.43532535049
y2[1] (closed_form) = 11.6195810531 3.24608258421
absolute error = 0.494
relative error = 4.095 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.03261703805 -0.0437496098217
y1[1] (closed_form) = 1.03261703805 -0.0437496098217
absolute error = 1.000e-63
relative error = 9.680e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3443
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3443
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5553.4MB, alloc=44.3MB, time=65.50
memory used=5599.6MB, alloc=44.3MB, time=66.05
memory used=5646.2MB, alloc=44.3MB, time=66.60
x[1] = 0.1468 0.3
h = 0.0001 0.003
y2[1] (numeric) = 11.1645064662 3.47949702023
y2[1] (closed_form) = 11.6209051196 3.30124493914
absolute error = 0.49
relative error = 4.056 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.03409507953 -0.0445431898539
y1[1] (closed_form) = 1.03409507953 -0.0445431898539
absolute error = 1.000e-63
relative error = 9.666e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3497
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3497
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5692.2MB, alloc=44.3MB, time=67.14
memory used=5738.7MB, alloc=44.3MB, time=67.71
x[1] = 0.1469 0.303
h = 0.001 0.001
y2[1] (numeric) = 11.1657476395 3.52367366814
y2[1] (closed_form) = 11.622142937 3.33434408291
absolute error = 0.4941
relative error = 4.087 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.03498816002 -0.0450325409788
y1[1] (closed_form) = 1.03498816002 -0.0450325409788
absolute error = 1.000e-63
relative error = 9.657e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.353
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.353
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5784.6MB, alloc=44.3MB, time=68.25
memory used=5831.3MB, alloc=44.3MB, time=68.80
x[1] = 0.1479 0.304
h = 0.0001 0.004
y2[1] (numeric) = 11.1669908828 3.56785535827
y2[1] (closed_form) = 11.6332232624 3.34533388502
absolute error = 0.5166
relative error = 4.268 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.03513931598 -0.0454910630373
y1[1] (closed_form) = 1.03513931598 -0.0454910630373
absolute error = 3e-65
relative error = 2.895e-63 %
Correct digits = 65
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3544
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3544
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5877.2MB, alloc=44.3MB, time=69.33
memory used=5923.6MB, alloc=44.3MB, time=69.88
x[1] = 0.148 0.308
h = 0.003 0.006
y2[1] (numeric) = 11.1682362057 3.61204215465
y2[1] (closed_form) = 11.6345100971 3.38947228362
absolute error = 0.5167
relative error = 4.264 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.03635349007 -0.04613926912
y1[1] (closed_form) = 1.03635349007 -0.04613926912
absolute error = 1.000e-63
relative error = 9.644e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3588
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3588
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5969.3MB, alloc=44.3MB, time=70.41
memory used=6015.8MB, alloc=44.3MB, time=70.96
x[1] = 0.151 0.314
h = 0.0001 0.005
y2[1] (numeric) = 11.1694836179 3.6562341213
y2[1] (closed_form) = 11.6679037013 3.45555339047
absolute error = 0.5373
relative error = 4.415 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.03775994886 -0.0480140405886
y1[1] (closed_form) = 1.03775994886 -0.0480140405886
absolute error = 1.001e-63
relative error = 9.634e-62 %
Correct digits = 63
memory used=6062.3MB, alloc=44.3MB, time=71.51
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3666
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3666
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6108.3MB, alloc=44.3MB, time=72.05
memory used=6154.8MB, alloc=44.3MB, time=72.60
x[1] = 0.1511 0.319
h = 0.0001 0.003
y2[1] (numeric) = 11.1707331293 3.70043132221
y2[1] (closed_form) = 11.6692496806 3.51074127424
absolute error = 0.5334
relative error = 4.377 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.03933487464 -0.0488362369329
y1[1] (closed_form) = 1.03933487464 -0.0488362369329
absolute error = 1.000e-63
relative error = 9.615e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3721
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3721
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6200.8MB, alloc=44.3MB, time=73.14
memory used=6247.5MB, alloc=44.3MB, time=73.70
x[1] = 0.1512 0.322
h = 0.001 0.001
y2[1] (numeric) = 11.1719847497 3.74463382132
y2[1] (closed_form) = 11.670500931 3.54385579414
absolute error = 0.5374
relative error = 4.406 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.04028593203 -0.049343592276
y1[1] (closed_form) = 1.04028593203 -0.049343592276
absolute error = 1.001e-63
relative error = 9.610e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3755
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3755
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6293.4MB, alloc=44.3MB, time=74.25
memory used=6339.8MB, alloc=44.3MB, time=74.80
x[1] = 0.1522 0.323
h = 0.001 0.003
y2[1] (numeric) = 11.1732384894 3.78884168257
y2[1] (closed_form) = 11.6815908847 3.55484657762
absolute error = 0.5596
relative error = 4.583 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.04045123738 -0.0498269893422
y1[1] (closed_form) = 1.04045123738 -0.0498269893422
absolute error = 1.000e-63
relative error = 9.605e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.377
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.377
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6385.6MB, alloc=44.3MB, time=75.33
memory used=6432.0MB, alloc=44.3MB, time=75.88
x[1] = 0.1532 0.326
h = 0.0001 0.004
y2[1] (numeric) = 11.1744943585 3.83305496987
y2[1] (closed_form) = 11.6927824345 3.58791892786
absolute error = 0.5733
relative error = 4.688 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.04127019884 -0.0506339311263
y1[1] (closed_form) = 1.04127019884 -0.0506339311263
absolute error = 1.000e-63
relative error = 9.597e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3807
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3807
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6478.0MB, alloc=44.3MB, time=76.41
memory used=6524.3MB, alloc=44.3MB, time=76.96
memory used=6570.8MB, alloc=44.3MB, time=77.51
x[1] = 0.1533 0.33
h = 0.003 0.006
y2[1] (numeric) = 11.1757523675 3.8772737471
y2[1] (closed_form) = 11.6940905152 3.63208151371
absolute error = 0.5734
relative error = 4.683 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.04257410438 -0.0513106760591
y1[1] (closed_form) = 1.04257410438 -0.0513106760591
absolute error = 1.001e-63
relative error = 9.588e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3853
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3853
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6616.5MB, alloc=44.3MB, time=78.04
memory used=6663.1MB, alloc=44.3MB, time=78.59
x[1] = 0.1563 0.336
h = 0.0001 0.005
y2[1] (numeric) = 11.1770125268 3.92149807811
y2[1] (closed_form) = 11.7275343059 3.6981846166
absolute error = 0.5941
relative error = 4.831 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.04409646806 -0.0532929406906
y1[1] (closed_form) = 1.04409646806 -0.0532929406906
absolute error = 1.001e-63
relative error = 9.573e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3932
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3932
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6709.0MB, alloc=44.3MB, time=79.13
memory used=6755.5MB, alloc=44.3MB, time=79.68
x[1] = 0.1564 0.341
h = 0.0001 0.003
y2[1] (numeric) = 11.1782748471 3.96572802673
y2[1] (closed_form) = 11.7289074076 3.75340393466
absolute error = 0.5902
relative error = 4.792 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.04578396391 -0.0541506224751
y1[1] (closed_form) = 1.04578396391 -0.0541506224751
absolute error = 1.001e-63
relative error = 9.561e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3989
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3989
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6801.4MB, alloc=44.3MB, time=80.22
memory used=6848.1MB, alloc=44.3MB, time=80.78
x[1] = 0.1565 0.344
h = 0.001 0.001
y2[1] (numeric) = 11.1795393392 4.00996365675
y2[1] (closed_form) = 11.7301752828 3.78653737029
absolute error = 0.5942
relative error = 4.821 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.046802371 -0.0546802431283
y1[1] (closed_form) = 1.046802371 -0.0546802431283
absolute error = 1.001e-63
relative error = 9.552e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4024
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4024
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6894.1MB, alloc=44.3MB, time=81.32
memory used=6940.7MB, alloc=44.3MB, time=81.88
x[1] = 0.1575 0.345
h = 0.001 0.003
y2[1] (numeric) = 11.180806014 4.05420503193
y2[1] (closed_form) = 11.7412771123 3.79752932687
absolute error = 0.6164
relative error = 4.995 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.04698367824 -0.0551930026442
y1[1] (closed_form) = 1.04698367824 -0.0551930026442
absolute error = 2.001e-63
relative error = 1.908e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4039
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4039
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6987.0MB, alloc=44.3MB, time=82.42
memory used=7033.3MB, alloc=44.3MB, time=82.96
memory used=7080.0MB, alloc=44.3MB, time=83.52
x[1] = 0.1585 0.348
h = 0.0001 0.004
y2[1] (numeric) = 11.1820748827 4.098452216
y2[1] (closed_form) = 11.7524913874 3.83061597909
absolute error = 0.6302
relative error = 5.098 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.04786401178 -0.0560427270402
y1[1] (closed_form) = 1.04786401178 -0.0560427270402
absolute error = 1.002e-63
relative error = 9.547e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4077
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4077
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7125.8MB, alloc=44.3MB, time=84.05
memory used=7172.2MB, alloc=44.3MB, time=84.60
x[1] = 0.1586 0.352
h = 0.003 0.006
y2[1] (numeric) = 11.1833459565 4.14270527265
y2[1] (closed_form) = 11.7538218255 3.87480457816
absolute error = 0.6302
relative error = 5.092 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.04925808543 -0.0567486234603
y1[1] (closed_form) = 1.04925808543 -0.0567486234603
absolute error = 1.002e-63
relative error = 9.534e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4124
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4124
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7218.2MB, alloc=44.3MB, time=85.13
memory used=7264.7MB, alloc=44.3MB, time=85.68
x[1] = 0.1616 0.358
h = 0.0001 0.005
y2[1] (numeric) = 11.1846192467 4.18696426555
y2[1] (closed_form) = 11.787318796 3.94093165648
absolute error = 0.651
relative error = 5.238 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.05089658578 -0.0588396400566
y1[1] (closed_form) = 1.05089658578 -0.0588396400566
absolute error = 1.002e-63
relative error = 9.518e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4205
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4205
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7310.7MB, alloc=44.3MB, time=86.22
memory used=7357.4MB, alloc=44.3MB, time=86.77
x[1] = 0.1617 0.363
h = 0.0001 0.003
y2[1] (numeric) = 11.1858947649 4.23122925832
y2[1] (closed_form) = 11.7887204075 3.99618470143
absolute error = 0.647
relative error = 5.198 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.05269722104 -0.0597335918718
y1[1] (closed_form) = 1.05269722104 -0.0597335918718
absolute error = 1.002e-63
relative error = 9.507e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4264
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4264
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7403.4MB, alloc=44.3MB, time=87.30
memory used=7450.0MB, alloc=44.3MB, time=87.86
memory used=7496.8MB, alloc=44.3MB, time=88.43
x[1] = 0.1618 0.366
h = 0.001 0.001
y2[1] (numeric) = 11.1871725227 4.27550031457
y2[1] (closed_form) = 11.7900057605 4.02933841892
absolute error = 0.6512
relative error = 5.226 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.05378331863 -0.0602859568118
y1[1] (closed_form) = 1.05378331863 -0.0602859568118
absolute error = 1.002e-63
relative error = 9.491e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.43
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.43
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7542.7MB, alloc=44.3MB, time=88.96
memory used=7589.0MB, alloc=44.3MB, time=89.52
x[1] = 0.1628 0.367
h = 0.001 0.003
y2[1] (numeric) = 11.1884525322 4.31977749784
y2[1] (closed_form) = 11.8011201995 4.0403317439
absolute error = 0.6734
relative error = 5.399 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.05398059082 -0.0608283548403
y1[1] (closed_form) = 1.05398059082 -0.0608283548403
absolute error = 2.001e-63
relative error = 1.895e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4316
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4316
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7634.9MB, alloc=44.3MB, time=90.05
memory used=7681.5MB, alloc=44.3MB, time=90.60
x[1] = 0.1638 0.37
h = 0.0001 0.004
y2[1] (numeric) = 11.1897348051 4.36406087166
y2[1] (closed_form) = 11.8123584734 4.07343382218
absolute error = 0.6871
relative error = 5.499 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.05492249965 -0.0617214545662
y1[1] (closed_form) = 1.05492249965 -0.0617214545662
absolute error = 1.002e-63
relative error = 9.486e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4355
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4355
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7727.3MB, alloc=44.3MB, time=91.14
memory used=7773.7MB, alloc=44.3MB, time=91.68
x[1] = 0.1639 0.374
h = 0.003 0.006
y2[1] (numeric) = 11.1910193537 4.40835049948
y2[1] (closed_form) = 11.8137123963 4.11765026708
absolute error = 0.6872
relative error = 5.493 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.05640721236 -0.0624571494307
y1[1] (closed_form) = 1.05640721236 -0.0624571494307
absolute error = 2.001e-63
relative error = 1.891e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4403
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4403
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7819.5MB, alloc=44.3MB, time=92.22
memory used=7866.0MB, alloc=44.3MB, time=92.77
x[1] = 0.1669 0.38
h = 0.0001 0.005
y2[1] (numeric) = 11.1923061904 4.45264644477
y2[1] (closed_form) = 11.84726557 4.18380329876
absolute error = 0.708
relative error = 5.635 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.05816210876 -0.0646582534612
y1[1] (closed_form) = 1.05816210876 -0.0646582534612
absolute error = 1.003e-63
relative error = 9.463e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4486
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4486
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7912.5MB, alloc=44.3MB, time=93.31
memory used=7958.9MB, alloc=44.3MB, time=93.86
memory used=8005.4MB, alloc=44.3MB, time=94.40
x[1] = 0.167 0.385
h = 0.0001 0.003
y2[1] (numeric) = 11.1935953275 4.49694877091
y2[1] (closed_form) = 11.8486970995 4.23909237191
absolute error = 0.704
relative error = 5.595 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.0600764959 -0.0655893028202
y1[1] (closed_form) = 1.0600764959 -0.0655893028202
absolute error = 2.002e-63
relative error = 1.885e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4548
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4548
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8051.3MB, alloc=44.3MB, time=94.95
memory used=8098.0MB, alloc=44.3MB, time=95.51
x[1] = 0.1671 0.388
h = 0.001 0.001
y2[1] (numeric) = 11.1948867779 4.54125754127
y2[1] (closed_form) = 11.8500007958 4.27226774256
absolute error = 0.7082
relative error = 5.622 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.06123065034 -0.0661649171799
y1[1] (closed_form) = 1.06123065034 -0.0661649171799
absolute error = 1.003e-63
relative error = 9.435e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4585
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4585
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8144.0MB, alloc=44.3MB, time=96.06
memory used=8190.5MB, alloc=44.3MB, time=96.61
x[1] = 0.1681 0.389
h = 0.001 0.003
y2[1] (numeric) = 11.1961805541 4.58557281916
y2[1] (closed_form) = 11.861128584 4.28326262891
absolute error = 0.7304
relative error = 5.792 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.06144385093 -0.06673724702
y1[1] (closed_form) = 1.06144385093 -0.06673724702
absolute error = 1.003e-63
relative error = 9.433e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.46
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.46
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8236.3MB, alloc=44.3MB, time=97.14
memory used=8282.9MB, alloc=44.3MB, time=97.70
x[1] = 0.1691 0.392
h = 0.0001 0.004
y2[1] (numeric) = 11.1974766693 4.62989466784
y2[1] (closed_form) = 11.8723921447 4.31638125878
absolute error = 0.7442
relative error = 5.891 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.06244755619 -0.0676743489303
y1[1] (closed_form) = 1.06244755619 -0.0676743489303
absolute error = 1.003e-63
relative error = 9.423e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4641
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4641
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8328.8MB, alloc=44.3MB, time=98.23
memory used=8375.3MB, alloc=44.3MB, time=98.78
x[1] = 0.1692 0.396
h = 0.003 0.006
y2[1] (numeric) = 11.1987751367 4.67422315054
y2[1] (closed_form) = 11.8737706972 4.36062738934
absolute error = 0.7443
relative error = 5.884 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.0640234133 -0.0684405239204
y1[1] (closed_form) = 1.0640234133 -0.0684405239204
absolute error = 1.003e-63
relative error = 9.409e-62 %
Correct digits = 63
memory used=8421.7MB, alloc=44.3MB, time=99.33
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4691
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4691
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8467.6MB, alloc=44.3MB, time=99.86
memory used=8514.1MB, alloc=44.3MB, time=100.42
x[1] = 0.1722 0.402
h = 0.0001 0.005
y2[1] (numeric) = 11.2000759694 4.71855833044
y2[1] (closed_form) = 11.9073831291 4.42680835101
absolute error = 0.7651
relative error = 6.023 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.06589499251 -0.0707531281916
y1[1] (closed_form) = 1.06589499251 -0.0707531281916
absolute error = 1.004e-63
relative error = 9.399e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4776
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4776
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8560.0MB, alloc=44.3MB, time=100.95
memory used=8606.5MB, alloc=44.3MB, time=101.50
x[1] = 0.1723 0.407
h = 0.0001 0.003
y2[1] (numeric) = 11.2013791811 4.76290027068
y2[1] (closed_form) = 11.9088460068 4.48213576314
absolute error = 0.7611
relative error = 5.982 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.06792378719 -0.0717221460499
y1[1] (closed_form) = 1.06792378719 -0.0717221460499
absolute error = 1.004e-63
relative error = 9.381e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4839
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4839
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8652.5MB, alloc=44.3MB, time=102.05
memory used=8699.2MB, alloc=44.3MB, time=102.61
x[1] = 0.1724 0.41
h = 0.001 0.001
y2[1] (numeric) = 11.2026847854 4.80724903434
y2[1] (closed_form) = 11.9101689254 4.51533416384
absolute error = 0.7653
relative error = 6.009 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.06914639045 -0.0723215414344
y1[1] (closed_form) = 1.06914639045 -0.0723215414344
absolute error = 1.004e-63
relative error = 9.370e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4877
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4877
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8745.2MB, alloc=44.3MB, time=103.15
memory used=8791.7MB, alloc=44.3MB, time=103.70
x[1] = 0.1734 0.411
h = 0.0001 0.004
y2[1] (numeric) = 11.2039927961 4.85160468446
y2[1] (closed_form) = 11.921310809 4.52633080214
absolute error = 0.7876
relative error = 6.177 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.06937548317 -0.0729241137464
y1[1] (closed_form) = 1.06937548317 -0.0729241137464
absolute error = 1.004e-63
relative error = 9.367e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4893
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4893
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8838.0MB, alloc=44.3MB, time=104.24
memory used=8884.3MB, alloc=44.3MB, time=104.78
memory used=8930.7MB, alloc=44.3MB, time=105.33
x[1] = 0.1735 0.415
h = 0.003 0.006
y2[1] (numeric) = 11.2053032273 4.89596728403
y2[1] (closed_form) = 11.9227111087 4.57060427663
absolute error = 0.7877
relative error = 6.169 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.07103060008 -0.0737160031704
y1[1] (closed_form) = 1.07103060008 -0.0737160031704
absolute error = 1.004e-63
relative error = 9.352e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4945
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4945
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8976.5MB, alloc=44.3MB, time=105.86
memory used=9023.0MB, alloc=44.3MB, time=106.41
x[1] = 0.1765 0.421
h = 0.0001 0.005
y2[1] (numeric) = 11.2066160932 4.94033689598
y2[1] (closed_form) = 11.9563766553 4.63681161755
absolute error = 0.8089
relative error = 6.307 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.0730042189 -0.076124378964
y1[1] (closed_form) = 1.0730042189 -0.076124378964
absolute error = 1.005e-63
relative error = 9.343e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5032
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5032
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9069.0MB, alloc=44.3MB, time=106.94
memory used=9115.6MB, alloc=44.3MB, time=107.50
x[1] = 0.1766 0.426
h = 0.0001 0.003
y2[1] (numeric) = 11.2079314082 4.9847135832
y2[1] (closed_form) = 11.9578671852 4.69217428577
absolute error = 0.805
relative error = 6.267 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.07513251711 -0.0771254355981
y1[1] (closed_form) = 1.07513251711 -0.0771254355981
absolute error = 1.004e-63
relative error = 9.315e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5097
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5097
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9161.5MB, alloc=44.3MB, time=108.03
memory used=9208.2MB, alloc=44.3MB, time=108.59
x[1] = 0.1767 0.429
h = 0.001 0.001
y2[1] (numeric) = 11.2092491869 5.02909740851
y2[1] (closed_form) = 11.9592070676 4.72539386063
absolute error = 0.8091
relative error = 6.292 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.07641466469 -0.0777449248564
y1[1] (closed_form) = 1.07641466469 -0.0777449248564
absolute error = 1.004e-63
relative error = 9.303e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5136
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5136
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9254.3MB, alloc=44.3MB, time=109.14
memory used=9300.8MB, alloc=44.3MB, time=109.69
x[1] = 0.1777 0.43
h = 0.001 0.003
y2[1] (numeric) = 11.210569444 5.07348843469
y2[1] (closed_form) = 11.970361663 4.73639233778
absolute error = 0.8312
relative error = 6.457 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.07665777353 -0.0783736022804
y1[1] (closed_form) = 1.07665777353 -0.0783736022804
absolute error = 1.005e-63
relative error = 9.310e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5153
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5153
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9347.1MB, alloc=44.3MB, time=110.23
memory used=9393.3MB, alloc=44.3MB, time=110.78
memory used=9439.9MB, alloc=44.3MB, time=111.33
x[1] = 0.1787 0.433
h = 0.0001 0.004
y2[1] (numeric) = 11.2118921945 5.11788672446
y2[1] (closed_form) = 11.9816755291 4.76954510587
absolute error = 0.8449
relative error = 6.552 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.07777766086 -0.0793936255503
y1[1] (closed_form) = 1.07777766086 -0.0793936255503
absolute error = 1.005e-63
relative error = 9.299e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5195
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5195
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9485.7MB, alloc=44.3MB, time=111.86
memory used=9532.0MB, alloc=44.3MB, time=112.40
x[1] = 0.1788 0.437
h = 0.003 0.006
y2[1] (numeric) = 11.2132174536 5.16229234048
y2[1] (closed_form) = 11.9831026153 4.81385172486
absolute error = 0.8451
relative error = 6.544 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.07952496334 -0.0802173504665
y1[1] (closed_form) = 1.07952496334 -0.0802173504665
absolute error = 1.005e-63
relative error = 9.284e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5248
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5248
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9577.8MB, alloc=44.3MB, time=112.94
memory used=9624.3MB, alloc=44.3MB, time=113.49
x[1] = 0.1818 0.443
h = 0.0001 0.005
y2[1] (numeric) = 11.2145452366 5.20670534535
y2[1] (closed_form) = 12.0168331717 4.88009070846
absolute error = 0.8662
relative error = 6.679 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.08161588983 -0.0827400595285
y1[1] (closed_form) = 1.08161588983 -0.0827400595285
absolute error = 1.005e-63
relative error = 9.264e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5338
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5338
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9670.0MB, alloc=44.3MB, time=114.02
memory used=9716.6MB, alloc=44.3MB, time=114.57
x[1] = 0.1819 0.448
h = 0.0001 0.003
y2[1] (numeric) = 11.2158755591 5.25112580163
y2[1] (closed_form) = 12.0183577461 4.93549606078
absolute error = 0.8623
relative error = 6.637 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.08385994262 -0.0837808138071
y1[1] (closed_form) = 1.08385994262 -0.0837808138071
absolute error = 1.004e-63
relative error = 9.236e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5405
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5405
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9762.9MB, alloc=44.3MB, time=115.11
memory used=9809.4MB, alloc=44.3MB, time=115.66
memory used=9856.2MB, alloc=44.3MB, time=116.23
x[1] = 0.182 0.451
h = 0.001 0.001
y2[1] (numeric) = 11.2172084368 5.2955537718
y2[1] (closed_form) = 12.0197185082 4.968741255
absolute error = 0.8665
relative error = 6.662 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.0852113438 -0.0844251395041
y1[1] (closed_form) = 1.0852113438 -0.0844251395041
absolute error = 1.005e-63
relative error = 9.233e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5446
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5446
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9901.9MB, alloc=44.3MB, time=116.76
memory used=9948.2MB, alloc=44.3MB, time=117.31
x[1] = 0.183 0.452
h = 0.001 0.003
y2[1] (numeric) = 11.2185438857 5.33998931829
y2[1] (closed_form) = 12.0308886037 4.9797418411
absolute error = 0.8886
relative error = 6.825 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.0854702819 -0.085084684565
y1[1] (closed_form) = 1.0854702819 -0.085084684565
absolute error = 2.002e-63
relative error = 1.839e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5463
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5463
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9994.1MB, alloc=44.3MB, time=117.86
memory used=10040.9MB, alloc=44.3MB, time=118.41
x[1] = 0.184 0.455
h = 0.0001 0.004
y2[1] (numeric) = 11.2198819218 5.38443250345
y2[1] (closed_form) = 12.0422315158 5.01291440645
absolute error = 0.9024
relative error = 6.918 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.08665270596 -0.0861506915662
y1[1] (closed_form) = 1.08665270596 -0.0861506915662
absolute error = 2.002e-63
relative error = 1.837e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5507
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5507
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10086.8MB, alloc=44.3MB, time=118.94
memory used=10133.3MB, alloc=44.3MB, time=119.49
x[1] = 0.1841 0.459
h = 0.003 0.006
y2[1] (numeric) = 11.2212225615 5.42888338959
y2[1] (closed_form) = 12.0436865877 5.05725603382
absolute error = 0.9025
relative error = 6.909 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.08849279854 -0.0870070350314
y1[1] (closed_form) = 1.08849279854 -0.0870070350314
absolute error = 1.006e-63
relative error = 9.213e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5562
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5562
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10179.1MB, alloc=44.3MB, time=120.02
memory used=10225.7MB, alloc=44.3MB, time=120.57
x[1] = 0.1871 0.465
h = 0.0001 0.005
y2[1] (numeric) = 11.2225658215 5.47334203895
y2[1] (closed_form) = 12.0774853098 5.12352863456
absolute error = 0.9237
relative error = 7.041 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.09070139764 -0.0896457151636
y1[1] (closed_form) = 1.09070139764 -0.0896457151636
absolute error = 1.006e-63
relative error = 9.193e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5653
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5653
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10272.1MB, alloc=44.3MB, time=121.11
memory used=10318.3MB, alloc=44.3MB, time=121.66
memory used=10364.8MB, alloc=44.3MB, time=122.22
x[1] = 0.1872 0.47
h = 0.0001 0.003
y2[1] (numeric) = 11.2239117183 5.51780851371
y2[1] (closed_form) = 12.0790454286 5.17897901307
absolute error = 0.9198
relative error = 6.999 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.0930619854 -0.0907271649432
y1[1] (closed_form) = 1.0930619854 -0.0907271649432
absolute error = 1.007e-63
relative error = 9.183e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5723
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5723
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10410.8MB, alloc=44.3MB, time=122.76
memory used=10457.5MB, alloc=44.3MB, time=123.32
x[1] = 0.1873 0.473
h = 0.001 0.001
y2[1] (numeric) = 11.2252602691 5.56228287597
y2[1] (closed_form) = 12.0804279915 5.21225122207
absolute error = 0.924
relative error = 7.023 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.09448310605 -0.0913969360123
y1[1] (closed_form) = 1.09448310605 -0.0913969360123
absolute error = 1.007e-63
relative error = 9.170e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5766
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5766
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10503.4MB, alloc=44.3MB, time=123.86
memory used=10549.8MB, alloc=44.3MB, time=124.41
x[1] = 0.1883 0.474
h = 0.001 0.003
y2[1] (numeric) = 11.226611491 5.60676518777
y2[1] (closed_form) = 12.0916143542 5.22325410042
absolute error = 0.9462
relative error = 7.184 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.09475783765 -0.0920877098006
y1[1] (closed_form) = 1.09475783765 -0.0920877098006
absolute error = 1.007e-63
relative error = 9.168e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5783
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5783
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10595.6MB, alloc=44.3MB, time=124.94
memory used=10642.1MB, alloc=44.3MB, time=125.50
x[1] = 0.1893 0.477
h = 0.0001 0.004
y2[1] (numeric) = 11.2279654013 5.65125551108
y2[1] (closed_form) = 12.1029876644 5.25644759628
absolute error = 0.96
relative error = 7.275 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.09600308892 -0.0932004623123
y1[1] (closed_form) = 1.09600308892 -0.0932004623123
absolute error = 2.004e-63
relative error = 1.822e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5828
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5828
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10688.2MB, alloc=44.3MB, time=126.03
memory used=10734.8MB, alloc=44.3MB, time=126.58
memory used=10781.3MB, alloc=44.3MB, time=127.13
x[1] = 0.1894 0.481
h = 0.003 0.006
y2[1] (numeric) = 11.2293220177 5.6957539078
y2[1] (closed_form) = 12.1044719418 5.30082610534
absolute error = 0.9601
relative error = 7.266 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.09793661082 -0.0940902438952
y1[1] (closed_form) = 1.09793661082 -0.0940902438952
absolute error = 1.008e-63
relative error = 9.151e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5885
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5885
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10827.2MB, alloc=44.3MB, time=127.67
memory used=10873.7MB, alloc=44.3MB, time=128.21
x[1] = 0.1924 0.487
h = 0.0001 0.005
y2[1] (numeric) = 11.230681358 5.74026043978
y2[1] (closed_form) = 12.1383420246 5.36713429713
absolute error = 0.9814
relative error = 7.394 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.10026327411 -0.0968466132164
y1[1] (closed_form) = 1.10026327411 -0.0968466132164
absolute error = 2.004e-63
relative error = 1.815e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.598
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.598
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10919.7MB, alloc=44.3MB, time=128.75
memory used=10966.3MB, alloc=44.3MB, time=129.31
x[1] = 0.1925 0.492
h = 0.0001 0.003
y2[1] (numeric) = 11.2320434402 5.78477516876
y2[1] (closed_form) = 12.1399392142 5.42263205615
absolute error = 0.9775
relative error = 7.352 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.10274122087 -0.0979698020854
y1[1] (closed_form) = 1.10274122087 -0.0979698020854
absolute error = 1.008e-63
relative error = 9.109e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6052
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6052
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11012.3MB, alloc=44.3MB, time=129.84
memory used=11059.1MB, alloc=44.3MB, time=130.41
x[1] = 0.1926 0.495
h = 0.001 0.001
y2[1] (numeric) = 11.2334082826 5.82929815646
y2[1] (closed_form) = 12.1413445156 5.45593268258
absolute error = 0.9817
relative error = 7.375 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.10423255271 -0.0986656553211
y1[1] (closed_form) = 1.10423255271 -0.0986656553211
absolute error = 1.007e-63
relative error = 9.085e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6096
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6096
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11105.0MB, alloc=44.3MB, time=130.95
memory used=11151.5MB, alloc=44.3MB, time=131.50
x[1] = 0.1936 0.496
h = 0.001 0.003
y2[1] (numeric) = 11.2347759037 5.87382946447
y2[1] (closed_form) = 12.15254792 5.46693803373
absolute error = 1.004
relative error = 7.534 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.10452304197 -0.0993880368486
y1[1] (closed_form) = 1.10452304197 -0.0993880368486
absolute error = 1.3e-64
relative error = 1.172e-62 %
Correct digits = 64
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6113
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6113
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11197.5MB, alloc=44.3MB, time=132.03
memory used=11243.8MB, alloc=44.3MB, time=132.58
memory used=11290.2MB, alloc=44.3MB, time=133.13
x[1] = 0.1946 0.499
h = 0.0001 0.004
y2[1] (numeric) = 11.2361463222 5.91836915434
y2[1] (closed_form) = 12.1639529993 5.50015359581
absolute error = 1.018
relative error = 7.623 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.10583142866 -0.100548332615
y1[1] (closed_form) = 1.10583142866 -0.100548332615
absolute error = 1.020e-63
relative error = 9.184e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.616
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.616
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11335.9MB, alloc=44.3MB, time=133.66
memory used=11382.4MB, alloc=44.3MB, time=134.21
x[1] = 0.1947 0.503
h = 0.003 0.006
y2[1] (numeric) = 11.2375195569 5.96291728754
y2[1] (closed_form) = 12.1654677243 5.54457086989
absolute error = 1.018
relative error = 7.614 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.10785905392 -0.101472408919
y1[1] (closed_form) = 1.10785905392 -0.101472408919
absolute error = 1.020e-63
relative error = 9.167e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6219
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6219
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11428.2MB, alloc=44.3MB, time=134.74
memory used=11474.9MB, alloc=44.3MB, time=135.30
x[1] = 0.1977 0.509
h = 0.0001 0.005
y2[1] (numeric) = 11.2388956271 6.00747392546
y2[1] (closed_form) = 12.1994124033 5.61091662619
absolute error = 1.039
relative error = 7.739 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.11030419934 -0.10434826674
y1[1] (closed_form) = 1.11030419934 -0.10434826674
absolute error = 1.020e-63
relative error = 9.145e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6317
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6317
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11520.7MB, alloc=44.3MB, time=135.83
memory used=11567.3MB, alloc=44.3MB, time=136.38
x[1] = 0.1978 0.514
h = 0.0001 0.003
y2[1] (numeric) = 11.2402745522 6.05203912942
y2[1] (closed_form) = 12.2010482181 5.66646413299
absolute error = 1.035
relative error = 7.696 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.1129003729 -0.105514284687
y1[1] (closed_form) = 1.1129003729 -0.105514284687
absolute error = 2.010e-63
relative error = 1.798e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6392
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6392
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11613.4MB, alloc=44.3MB, time=136.91
memory used=11660.1MB, alloc=44.3MB, time=137.48
x[1] = 0.1979 0.517
h = 0.001 0.001
y2[1] (numeric) = 11.2416563517 6.09661296064
y2[1] (closed_form) = 12.2024772125 5.69979458717
absolute error = 1.04
relative error = 7.719 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.11446243357 -0.106236885149
y1[1] (closed_form) = 1.11446243357 -0.106236885149
absolute error = 2.010e-63
relative error = 1.795e-61 %
Correct digits = 63
memory used=11706.6MB, alloc=44.3MB, time=138.03
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6437
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6437
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11752.6MB, alloc=44.3MB, time=138.58
memory used=11799.2MB, alloc=44.3MB, time=139.13
x[1] = 0.1989 0.518
h = 0.0001 0.004
y2[1] (numeric) = 11.2430410455 6.14119548029
y2[1] (closed_form) = 12.213698442 5.71080258884
absolute error = 1.062
relative error = 7.875 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.11476864446 -0.106991271513
y1[1] (closed_form) = 1.11476864446 -0.106991271513
absolute error = 2.010e-63
relative error = 1.795e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6455
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6455
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11845.0MB, alloc=44.3MB, time=139.66
memory used=11891.4MB, alloc=44.3MB, time=140.21
x[1] = 0.199 0.522
h = 0.003 0.006
y2[1] (numeric) = 11.2444286538 6.18578674943
y2[1] (closed_form) = 12.2152398948 5.75525512996
absolute error = 1.062
relative error = 7.865 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.11687826023 -0.107944449662
y1[1] (closed_form) = 1.11687826023 -0.107944449662
absolute error = 2.010e-63
relative error = 1.791e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6516
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6516
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11937.2MB, alloc=44.3MB, time=140.74
memory used=11983.8MB, alloc=44.3MB, time=141.29
x[1] = 0.202 0.528
h = 0.0001 0.005
y2[1] (numeric) = 11.2458191967 6.23038682906
y2[1] (closed_form) = 12.2492509279 5.82163574248
absolute error = 1.083
relative error = 7.989 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.11942719981 -0.110923244089
y1[1] (closed_form) = 1.11942719981 -0.110923244089
absolute error = 2.022e-63
relative error = 1.798e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6616
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6616
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12029.8MB, alloc=44.3MB, time=141.82
memory used=12076.3MB, alloc=44.3MB, time=142.37
x[1] = 0.2021 0.533
h = 0.0001 0.003
y2[1] (numeric) = 11.247212695 6.27499578008
y2[1] (closed_form) = 12.2509206258 5.87722846243
absolute error = 1.08
relative error = 7.946 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.12212639623 -0.112125613455
y1[1] (closed_form) = 1.12212639623 -0.112125613455
absolute error = 2.010e-63
relative error = 1.782e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6694
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6694
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12122.5MB, alloc=44.3MB, time=142.92
memory used=12169.0MB, alloc=44.3MB, time=143.47
memory used=12215.7MB, alloc=44.3MB, time=144.04
x[1] = 0.2022 0.536
h = 0.001 0.001
y2[1] (numeric) = 11.2486091693 6.31961366333
y2[1] (closed_form) = 12.252370414 5.91058602486
absolute error = 1.084
relative error = 7.968 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.12375010223 -0.112870940099
y1[1] (closed_form) = 1.12375010223 -0.112870940099
absolute error = 1.044e-63
relative error = 9.244e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6741
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6741
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12261.5MB, alloc=44.3MB, time=144.57
memory used=12308.0MB, alloc=44.3MB, time=145.12
x[1] = 0.2032 0.537
h = 0.001 0.003
y2[1] (numeric) = 11.2500086408 6.36424053952
y2[1] (closed_form) = 12.2636075859 5.92159667324
absolute error = 1.106
relative error = 8.122 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.12407020471 -0.113653020395
y1[1] (closed_form) = 1.12407020471 -0.113653020395
absolute error = 2.010e-63
relative error = 1.779e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6759
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6759
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12353.8MB, alloc=44.3MB, time=145.66
memory used=12400.5MB, alloc=44.3MB, time=146.21
x[1] = 0.2042 0.54
h = 0.0001 0.004
y2[1] (numeric) = 11.2514111308 6.4088764693
y2[1] (closed_form) = 12.2750752016 5.95485674528
absolute error = 1.12
relative error = 8.208 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.12549754312 -0.114903269739
y1[1] (closed_form) = 1.12549754312 -0.114903269739
absolute error = 2.010e-63
relative error = 1.777e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6809
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6809
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12446.3MB, alloc=44.3MB, time=146.74
memory used=12492.8MB, alloc=44.3MB, time=147.29
x[1] = 0.2043 0.544
h = 0.003 0.006
y2[1] (numeric) = 11.2528166607 6.45352151324
y2[1] (closed_form) = 12.276649452 5.99935159987
absolute error = 1.12
relative error = 8.197 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.1277026207 -0.115892427998
y1[1] (closed_form) = 1.1277026207 -0.115892427998
absolute error = 2.010e-63
relative error = 1.773e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6872
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6872
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12538.5MB, alloc=44.3MB, time=147.82
memory used=12585.2MB, alloc=44.3MB, time=148.38
x[1] = 0.2073 0.55
h = 0.0001 0.005
y2[1] (numeric) = 11.2542252525 6.4981757318
y2[1] (closed_form) = 12.3107411939 6.06577348825
absolute error = 1.142
relative error = 8.318 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.1303709133 -0.118994272584
y1[1] (closed_form) = 1.1303709133 -0.118994272584
absolute error = 2.010e-63
relative error = 1.768e-61 %
Correct digits = 63
memory used=12631.5MB, alloc=44.3MB, time=148.92
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6975
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6975
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12677.6MB, alloc=44.3MB, time=149.46
memory used=12724.2MB, alloc=44.3MB, time=150.02
x[1] = 0.2074 0.555
h = 0.0001 0.003
y2[1] (numeric) = 11.2556369281 6.54283918536
y2[1] (closed_form) = 12.3124524597 6.12142041724
absolute error = 1.138
relative error = 8.274 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.13319008261 -0.120241613581
y1[1] (closed_form) = 1.13319008261 -0.120241613581
absolute error = 2.010e-63
relative error = 1.764e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7056
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7056
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12770.2MB, alloc=44.3MB, time=150.56
memory used=12817.0MB, alloc=44.3MB, time=151.12
x[1] = 0.2075 0.558
h = 0.001 0.001
y2[1] (numeric) = 11.2570517099 6.58751193421
y2[1] (closed_form) = 12.3139277479 6.15481046536
absolute error = 1.142
relative error = 8.296 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.13488555869 -0.121014994772
y1[1] (closed_form) = 1.13488555869 -0.121014994772
absolute error = 3.002e-63
relative error = 2.630e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7105
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7105
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12863.1MB, alloc=44.3MB, time=151.66
memory used=12909.4MB, alloc=44.3MB, time=152.22
x[1] = 0.2085 0.559
h = 0.001 0.003
y2[1] (numeric) = 11.2584696204 6.63219403855
y2[1] (closed_form) = 12.3251842236 6.16582409658
absolute error = 1.164
relative error = 8.448 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.13522132013 -0.121829867983
y1[1] (closed_form) = 1.13522132013 -0.121829867983
absolute error = 3.007e-63
relative error = 2.633e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7123
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7123
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12955.3MB, alloc=44.3MB, time=152.75
memory used=13001.8MB, alloc=44.3MB, time=153.30
x[1] = 0.2095 0.562
h = 0.0001 0.004
y2[1] (numeric) = 11.2598906824 6.67688555846
y2[1] (closed_form) = 12.336687628 6.19910951629
absolute error = 1.178
relative error = 8.532 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.13671278427 -0.123130140954
y1[1] (closed_form) = 1.13671278427 -0.123130140954
absolute error = 3.007e-63
relative error = 2.630e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7175
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7175
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13047.8MB, alloc=44.3MB, time=153.83
memory used=13094.3MB, alloc=44.3MB, time=154.38
memory used=13140.7MB, alloc=44.3MB, time=154.93
x[1] = 0.2096 0.566
h = 0.003 0.006
y2[1] (numeric) = 11.2613149191 6.72158655395
y2[1] (closed_form) = 12.338295986 6.24364859973
absolute error = 1.178
relative error = 8.521 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.13901409833 -0.124156244567
y1[1] (closed_form) = 1.13901409833 -0.124156244567
absolute error = 3.007e-63
relative error = 2.624e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7241
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7241
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13186.6MB, alloc=44.3MB, time=155.46
memory used=13233.1MB, alloc=44.3MB, time=156.01
x[1] = 0.2126 0.572
h = 0.0001 0.005
y2[1] (numeric) = 11.2627423537 6.76629708494
y2[1] (closed_form) = 12.3724718 6.31011373758
absolute error = 1.2
relative error = 8.639 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.14180223707 -0.127383175806
y1[1] (closed_form) = 1.14180223707 -0.127383175806
absolute error = 3.007e-63
relative error = 2.617e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7347
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7347
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13278.9MB, alloc=44.3MB, time=156.55
memory used=13325.6MB, alloc=44.3MB, time=157.10
x[1] = 0.2127 0.577
h = 0.0001 0.003
y2[1] (numeric) = 11.2641730099 6.81101721123
y2[1] (closed_form) = 12.3742262749 6.3658172843
absolute error = 1.196
relative error = 8.595 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.1447423737 -0.128676714606
y1[1] (closed_form) = 1.1447423737 -0.128676714606
absolute error = 3.002e-63
relative error = 2.606e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7431
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7431
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13371.3MB, alloc=44.3MB, time=157.64
memory used=13418.0MB, alloc=44.3MB, time=158.20
x[1] = 0.2128 0.58
h = 0.001 0.001
y2[1] (numeric) = 11.2656069115 6.85574699253
y2[1] (closed_form) = 12.3757280704 6.39924125286
absolute error = 1.2
relative error = 8.615 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.14651021251 -0.129478898361
y1[1] (closed_form) = 1.14651021251 -0.129478898361
absolute error = 3.007e-63
relative error = 2.606e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7482
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7482
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13464.2MB, alloc=44.3MB, time=158.74
memory used=13510.8MB, alloc=44.3MB, time=159.30
x[1] = 0.2138 0.581
h = 0.001 0.003
y2[1] (numeric) = 11.2670440827 6.90048648846
y2[1] (closed_form) = 12.3870046591 6.41025803602
absolute error = 1.223
relative error = 8.765 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.14686159593 -0.130327014312
y1[1] (closed_form) = 1.14686159593 -0.130327014312
absolute error = 3.002e-63
relative error = 2.601e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7501
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7501
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13556.9MB, alloc=44.3MB, time=159.84
memory used=13603.2MB, alloc=44.3MB, time=160.39
memory used=13649.7MB, alloc=44.3MB, time=160.94
x[1] = 0.2148 0.584
h = 0.0001 0.004
y2[1] (numeric) = 11.2684845479 6.94523575852
y2[1] (closed_form) = 12.3985453039 6.44356995069
absolute error = 1.236
relative error = 8.849 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.14841756257 -0.131678251571
y1[1] (closed_form) = 1.14841756257 -0.131678251571
absolute error = 3.007e-63
relative error = 2.601e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7554
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7554
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13695.4MB, alloc=44.3MB, time=161.48
memory used=13741.8MB, alloc=44.3MB, time=162.02
x[1] = 0.2149 0.588
h = 0.003 0.006
y2[1] (numeric) = 11.2699283317 6.98999486211
y2[1] (closed_form) = 12.4001891055 6.48815519056
absolute error = 1.237
relative error = 8.836 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.150815923 -0.132742305069
y1[1] (closed_form) = 1.150815923 -0.132742305069
absolute error = 3.007e-63
relative error = 2.595e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7622
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7622
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13787.7MB, alloc=44.3MB, time=162.55
memory used=13834.3MB, alloc=44.3MB, time=163.11
x[1] = 0.2179 0.594
h = 0.0001 0.005
y2[1] (numeric) = 11.2713754592 7.03476385856
y2[1] (closed_form) = 12.4344524032 6.55466555163
absolute error = 1.258
relative error = 8.952 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.15372442649 -0.136096444436
y1[1] (closed_form) = 1.15372442649 -0.136096444436
absolute error = 3.015e-63
relative error = 2.595e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7733
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7733
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13880.0MB, alloc=44.3MB, time=163.64
memory used=13926.6MB, alloc=44.3MB, time=164.19
x[1] = 0.218 0.599
h = 0.0001 0.003
y2[1] (numeric) = 11.2728259555 7.07954280705
y2[1] (closed_form) = 12.4362517613 6.61042814049
absolute error = 1.254
relative error = 8.907 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.15678656924 -0.137437456484
y1[1] (closed_form) = 1.15678656924 -0.137437456484
absolute error = 3.007e-63
relative error = 2.581e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.782
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.782
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13972.7MB, alloc=44.3MB, time=164.73
memory used=14019.5MB, alloc=44.3MB, time=165.29
x[1] = 0.2181 0.602
h = 0.001 0.001
y2[1] (numeric) = 11.2742798461 7.12433176668
y2[1] (closed_form) = 12.4377810915 6.64388747353
absolute error = 1.259
relative error = 8.927 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.15862738968 -0.138269220829
y1[1] (closed_form) = 1.15862738968 -0.138269220829
absolute error = 3.007e-63
relative error = 2.577e-61 %
Correct digits = 63
memory used=14066.2MB, alloc=44.3MB, time=165.85
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7872
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7872
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14112.2MB, alloc=44.3MB, time=166.39
memory used=14158.7MB, alloc=44.3MB, time=166.94
x[1] = 0.2191 0.603
h = 0.001 0.003
y2[1] (numeric) = 11.2757371569 7.16913079645
y2[1] (closed_form) = 12.4490786123 6.65490757448
absolute error = 1.281
relative error = 9.075 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.1589943575 -0.139151048143
y1[1] (closed_form) = 1.1589943575 -0.139151048143
absolute error = 3.007e-63
relative error = 2.576e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7892
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7892
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14204.6MB, alloc=44.3MB, time=167.48
memory used=14251.2MB, alloc=44.3MB, time=168.03
x[1] = 0.2201 0.606
h = 0.0001 0.004
y2[1] (numeric) = 11.2771979139 7.21393995521
y2[1] (closed_form) = 12.4606579723 6.68824713478
absolute error = 1.295
relative error = 9.157 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.16061522089 -0.140554228629
y1[1] (closed_form) = 1.16061522089 -0.140554228629
absolute error = 3.007e-63
relative error = 2.572e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7947
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7947
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14297.0MB, alloc=44.3MB, time=168.56
memory used=14343.3MB, alloc=44.3MB, time=169.12
x[1] = 0.2202 0.61
h = 0.003 0.006
y2[1] (numeric) = 11.2786621434 7.25875930175
y2[1] (closed_form) = 12.4623385804 6.73288047146
absolute error = 1.295
relative error = 9.144 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.16311147303 -0.141657276478
y1[1] (closed_form) = 1.16311147303 -0.141657276478
absolute error = 3.007e-63
relative error = 2.566e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8018
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8018
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14389.2MB, alloc=44.3MB, time=169.65
memory used=14435.8MB, alloc=44.3MB, time=170.20
x[1] = 0.2232 0.616
h = 0.0001 0.005
y2[1] (numeric) = 11.2801298722 7.30358889473
y2[1] (closed_form) = 12.4966928238 6.79943802968
absolute error = 1.317
relative error = 9.256 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.16614088506 -0.145140831516
y1[1] (closed_form) = 1.16614088506 -0.145140831516
absolute error = 4.005e-63
relative error = 3.408e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8133
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8133
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14482.0MB, alloc=44.3MB, time=170.74
memory used=14528.3MB, alloc=44.3MB, time=171.29
memory used=14574.8MB, alloc=44.3MB, time=171.83
x[1] = 0.2233 0.621
h = 0.0001 0.003
y2[1] (numeric) = 11.281601127 7.34842879269
y2[1] (closed_form) = 12.4985387736 6.85526210156
absolute error = 1.313
relative error = 9.211 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.16932611729 -0.146530642357
y1[1] (closed_form) = 1.16932611729 -0.146530642357
absolute error = 4.005e-63
relative error = 3.398e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8223
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8223
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14620.9MB, alloc=44.3MB, time=172.38
memory used=14667.6MB, alloc=44.3MB, time=172.94
x[1] = 0.2234 0.624
h = 0.001 0.001
y2[1] (numeric) = 11.2830759351 7.39327905407
y2[1] (closed_form) = 12.5000966865 6.88875825282
absolute error = 1.317
relative error = 9.231 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.17124056466 -0.147392795823
y1[1] (closed_form) = 1.17124056466 -0.147392795823
absolute error = 3.007e-63
relative error = 2.547e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8278
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8278
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14713.7MB, alloc=44.3MB, time=173.48
memory used=14760.2MB, alloc=44.3MB, time=174.03
x[1] = 0.2244 0.625
h = 0.0001 0.004
y2[1] (numeric) = 11.2845543241 7.4381397372
y2[1] (closed_form) = 12.5114159689 6.89978183405
absolute error = 1.34
relative error = 9.377 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.17162307852 -0.14830882213
y1[1] (closed_form) = 1.17162307852 -0.14830882213
absolute error = 4.011e-63
relative error = 3.397e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8298
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8298
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14806.1MB, alloc=44.3MB, time=174.57
memory used=14852.4MB, alloc=44.3MB, time=175.11
x[1] = 0.2245 0.629
h = 0.003 0.006
y2[1] (numeric) = 11.2860363217 7.48301090026
y2[1] (closed_form) = 12.513128767 6.94445859588
absolute error = 1.34
relative error = 9.364 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.17420477878 -0.149445121938
y1[1] (closed_form) = 1.17420477878 -0.149445121938
absolute error = 3.015e-63
relative error = 2.547e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8372
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8372
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14898.1MB, alloc=44.3MB, time=175.64
memory used=14944.8MB, alloc=44.3MB, time=176.19
x[1] = 0.2275 0.635
h = 0.0001 0.005
y2[1] (numeric) = 11.287521956 7.52789260136
y2[1] (closed_form) = 12.5475635115 7.01105950119
absolute error = 1.362
relative error = 9.475 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.17734029839 -0.153040458423
y1[1] (closed_form) = 1.17734029839 -0.153040458423
absolute error = 4.011e-63
relative error = 3.379e-61 %
Correct digits = 62
memory used=14991.4MB, alloc=44.3MB, time=176.74
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8489
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8489
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15037.5MB, alloc=44.3MB, time=177.28
memory used=15084.1MB, alloc=44.3MB, time=177.83
x[1] = 0.2276 0.64
h = 0.0001 0.003
y2[1] (numeric) = 11.2890112554 7.57278489845
y2[1] (closed_form) = 12.5494501887 7.06693904662
absolute error = 1.358
relative error = 9.43 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.18063298733 -0.154471889345
y1[1] (closed_form) = 1.18063298733 -0.154471889345
absolute error = 3.015e-63
relative error = 2.532e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8583
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8583
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15130.1MB, alloc=44.3MB, time=178.38
memory used=15176.9MB, alloc=44.3MB, time=178.94
x[1] = 0.2277 0.643
h = 0.001 0.001
y2[1] (numeric) = 11.2905042486 7.6176878494
y2[1] (closed_form) = 12.5510330982 7.10046841948
absolute error = 1.363
relative error = 9.449 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.18261172293 -0.155359983885
y1[1] (closed_form) = 1.18261172293 -0.155359983885
absolute error = 3.015e-63
relative error = 2.528e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8639
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8639
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15222.8MB, alloc=44.3MB, time=179.48
memory used=15269.3MB, alloc=44.3MB, time=180.03
x[1] = 0.2287 0.644
h = 0.001 0.003
y2[1] (numeric) = 11.2920009646 7.66260151192
y2[1] (closed_form) = 12.5623717407 7.11149539674
absolute error = 1.385
relative error = 9.593 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.18300800258 -0.156305668146
y1[1] (closed_form) = 1.18300800258 -0.156305668146
absolute error = 3.007e-63
relative error = 2.520e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.866
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.866
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15315.1MB, alloc=44.3MB, time=180.57
memory used=15361.7MB, alloc=44.3MB, time=181.12
x[1] = 0.2297 0.647
h = 0.0001 0.004
y2[1] (numeric) = 11.2935014327 7.70752594362
y2[1] (closed_form) = 12.5740267873 7.14488997781
absolute error = 1.399
relative error = 9.671 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.18475138096 -0.157807456753
y1[1] (closed_form) = 1.18475138096 -0.157807456753
absolute error = 3.015e-63
relative error = 2.523e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.872
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.872
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15407.7MB, alloc=44.3MB, time=181.65
memory used=15453.9MB, alloc=44.3MB, time=182.20
memory used=15500.3MB, alloc=44.3MB, time=182.74
x[1] = 0.2298 0.651
h = 0.003 0.006
y2[1] (numeric) = 11.2950056825 7.75246120197
y2[1] (closed_form) = 12.5757789797 7.18961850002
absolute error = 1.399
relative error = 9.658 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.18743265414 -0.158984791963
y1[1] (closed_form) = 1.18743265414 -0.158984791963
absolute error = 3.007e-63
relative error = 2.510e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8796
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8796
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15546.2MB, alloc=44.3MB, time=183.28
memory used=15592.8MB, alloc=44.3MB, time=183.83
x[1] = 0.2328 0.657
h = 0.0001 0.005
y2[1] (numeric) = 11.2965137439 7.79740734432
y2[1] (closed_form) = 12.6103112298 7.25627031918
absolute error = 1.421
relative error = 9.766 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.19069018914 -0.162713877657
y1[1] (closed_form) = 1.19069018914 -0.162713877657
absolute error = 4.005e-63
relative error = 3.333e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8918
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8918
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15638.8MB, alloc=44.3MB, time=184.36
memory used=15685.3MB, alloc=44.3MB, time=184.92
x[1] = 0.2329 0.662
h = 0.0001 0.003
y2[1] (numeric) = 11.2980256472 7.84236442792
y2[1] (closed_form) = 12.6122477437 7.31221595712
absolute error = 1.417
relative error = 9.721 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.19410811989 -0.164196696031
y1[1] (closed_form) = 1.19410811989 -0.164196696031
absolute error = 3.007e-63
relative error = 2.494e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9015
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9015
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15731.3MB, alloc=44.3MB, time=185.45
memory used=15778.0MB, alloc=44.3MB, time=186.02
x[1] = 0.233 0.665
h = 0.001 0.001
y2[1] (numeric) = 11.2995414228 7.88733250987
y2[1] (closed_form) = 12.6138612267 7.34578489363
absolute error = 1.422
relative error = 9.738 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.19616176422 -0.165116758738
y1[1] (closed_form) = 1.19616176422 -0.165116758738
absolute error = 4.005e-63
relative error = 3.317e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9074
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9074
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15824.2MB, alloc=44.3MB, time=186.56
memory used=15870.6MB, alloc=44.3MB, time=187.11
x[1] = 0.234 0.666
h = 0.001 0.003
y2[1] (numeric) = 11.3010611017 7.93231164712
y2[1] (closed_form) = 12.6252232014 7.35681565432
absolute error = 1.444
relative error = 9.881 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.19657352245 -0.166097601157
y1[1] (closed_form) = 1.19657352245 -0.166097601157
absolute error = 4.005e-63
relative error = 3.315e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9096
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9096
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15916.9MB, alloc=44.3MB, time=187.65
memory used=15963.1MB, alloc=44.3MB, time=188.20
memory used=16009.6MB, alloc=44.3MB, time=188.75
x[1] = 0.235 0.669
h = 0.0001 0.004
y2[1] (numeric) = 11.302584715 7.97730189653
y2[1] (closed_form) = 12.6369213047 7.39024121175
absolute error = 1.458
relative error = 9.958 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.19838303506 -0.167654344407
y1[1] (closed_form) = 1.19838303506 -0.167654344407
absolute error = 3.007e-63
relative error = 2.485e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9157
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9157
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16055.4MB, alloc=44.3MB, time=189.28
memory used=16101.8MB, alloc=44.3MB, time=189.83
x[1] = 0.2351 0.673
h = 0.003 0.006
y2[1] (numeric) = 11.3041122942 8.02230331479
y2[1] (closed_form) = 12.6387143372 7.43502347474
absolute error = 1.458
relative error = 9.944 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.20116482903 -0.168873877114
y1[1] (closed_form) = 1.20116482903 -0.168873877114
absolute error = 3.015e-63
relative error = 2.486e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9236
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9236
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16147.6MB, alloc=44.3MB, time=190.36
memory used=16194.1MB, alloc=44.3MB, time=190.92
x[1] = 0.2381 0.679
h = 0.0001 0.005
y2[1] (numeric) = 11.3056438711 8.0673159585
y2[1] (closed_form) = 12.6733477105 7.50172818346
absolute error = 1.48
relative error = 10.05 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.20454499492 -0.172739171907
y1[1] (closed_form) = 1.20454499492 -0.172739171907
absolute error = 3.015e-63
relative error = 2.478e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9363
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9363
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16240.1MB, alloc=44.3MB, time=191.45
memory used=16286.8MB, alloc=44.3MB, time=192.01
x[1] = 0.2382 0.684
h = 0.0001 0.003
y2[1] (numeric) = 11.3071794779 8.11233988409
y2[1] (closed_form) = 12.6753358747 7.55774240625
absolute error = 1.476
relative error = 10 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.20808937996 -0.174274850906
y1[1] (closed_form) = 1.20808937996 -0.174274850906
absolute error = 3.015e-63
relative error = 2.470e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9464
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9464
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16332.9MB, alloc=44.3MB, time=192.54
memory used=16379.5MB, alloc=44.3MB, time=193.10
x[1] = 0.2383 0.687
h = 0.001 0.001
y2[1] (numeric) = 11.3087191469 8.15737514788
y2[1] (closed_form) = 12.6769810434 7.5913523905
absolute error = 1.481
relative error = 10.02 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.21021865477 -0.175227780203
y1[1] (closed_form) = 1.21021865477 -0.175227780203
absolute error = 3.015e-63
relative error = 2.466e-61 %
Correct digits = 63
memory used=16426.4MB, alloc=44.3MB, time=193.67
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9525
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9525
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16472.3MB, alloc=44.3MB, time=194.20
memory used=16518.8MB, alloc=44.3MB, time=194.76
x[1] = 0.2393 0.688
h = 0.001 0.003
y2[1] (numeric) = 11.310262911 8.20242180603
y2[1] (closed_form) = 12.6883672116 7.60238708693
absolute error = 1.503
relative error = 10.16 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.21064585055 -0.176244323998
y1[1] (closed_form) = 1.21064585055 -0.176244323998
absolute error = 3.027e-63
relative error = 2.474e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9548
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9548
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16564.6MB, alloc=44.3MB, time=195.30
memory used=16611.2MB, alloc=44.3MB, time=195.84
x[1] = 0.2403 0.691
h = 0.0001 0.004
y2[1] (numeric) = 11.3118108034 8.24747991458
y2[1] (closed_form) = 12.7001099448 7.63584478647
absolute error = 1.517
relative error = 10.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.21252195933 -0.177857153656
y1[1] (closed_form) = 1.21252195933 -0.177857153656
absolute error = 3.027e-63
relative error = 2.470e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9612
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9612
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16657.0MB, alloc=44.3MB, time=196.38
memory used=16703.3MB, alloc=44.3MB, time=196.92
x[1] = 0.2404 0.695
h = 0.003 0.006
y2[1] (numeric) = 11.3133628574 8.29254952942
y2[1] (closed_form) = 12.7019452942 7.68068278566
absolute error = 1.517
relative error = 10.22 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.21540525796 -0.179120088638
y1[1] (closed_form) = 1.21540525796 -0.179120088638
absolute error = 3.027e-63
relative error = 2.464e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9694
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9694
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16749.1MB, alloc=44.3MB, time=197.46
memory used=16795.7MB, alloc=44.3MB, time=198.01
x[1] = 0.2434 0.701
h = 0.0001 0.005
y2[1] (numeric) = 11.3149191068 8.33763070631
y2[1] (closed_form) = 12.7366834669 7.74744236017
absolute error = 1.539
relative error = 10.33 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.21890869438 -0.18312414312
y1[1] (closed_form) = 1.21890869438 -0.18312414312
absolute error = 3.027e-63
relative error = 2.455e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9825
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9825
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16842.0MB, alloc=44.3MB, time=198.55
memory used=16888.3MB, alloc=44.3MB, time=199.09
memory used=16935.0MB, alloc=44.3MB, time=199.65
x[1] = 0.2435 0.706
h = 0.0001 0.003
y2[1] (numeric) = 11.3164795857 8.38272350087
y2[1] (closed_form) = 12.7387251346 7.80352767938
absolute error = 1.536
relative error = 10.28 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.22258079154 -0.184714209508
y1[1] (closed_form) = 1.22258079154 -0.184714209508
absolute error = 3.027e-63
relative error = 2.448e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9931
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9931
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16981.1MB, alloc=44.3MB, time=200.19
memory used=17027.8MB, alloc=44.3MB, time=200.76
x[1] = 0.2436 0.709
h = 0.001 0.001
y2[1] (numeric) = 11.3180443286 8.42782796855
y2[1] (closed_form) = 12.7404031249 7.83718020678
absolute error = 1.54
relative error = 10.3 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.22478644535 -0.185700936442
y1[1] (closed_form) = 1.22478644535 -0.185700936442
absolute error = 3.027e-63
relative error = 2.443e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9995
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9995
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17073.8MB, alloc=44.3MB, time=201.30
memory used=17120.1MB, alloc=44.3MB, time=201.84
x[1] = 0.2446 0.71
h = 0.001 0.003
y2[1] (numeric) = 11.3196133703 8.47294416469
y2[1] (closed_form) = 12.7518143599 7.84821898741
absolute error = 1.563
relative error = 10.44 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.22522903638 -0.186753744708
y1[1] (closed_form) = 1.22522903638 -0.186753744708
absolute error = 3.027e-63
relative error = 2.442e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.002
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.002
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17166.1MB, alloc=44.3MB, time=202.38
memory used=17212.7MB, alloc=44.3MB, time=202.93
x[1] = 0.2456 0.713
h = 0.0001 0.004
y2[1] (numeric) = 11.3211867459 8.51807214447
y2[1] (closed_form) = 12.7636033239 7.88170999908
absolute error = 1.577
relative error = 10.51 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.22717222056 -0.188423833642
y1[1] (closed_form) = 1.22717222056 -0.188423833642
absolute error = 3.015e-63
relative error = 2.428e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.008
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17258.6MB, alloc=44.3MB, time=203.47
memory used=17304.9MB, alloc=44.3MB, time=204.02
x[1] = 0.2457 0.717
h = 0.003 0.006
y2[1] (numeric) = 11.3227644908 8.56321196292
y2[1] (closed_form) = 12.7654824994 7.92660574538
absolute error = 1.577
relative error = 10.49 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.23015804386 -0.189731419135
y1[1] (closed_form) = 1.23015804386 -0.189731419135
absolute error = 3.015e-63
relative error = 2.422e-61 %
Correct digits = 63
memory used=17351.4MB, alloc=44.3MB, time=204.56
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.017
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.017
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17397.3MB, alloc=44.3MB, time=205.10
memory used=17443.9MB, alloc=44.3MB, time=205.65
x[1] = 0.2487 0.723
h = 0.0001 0.005
y2[1] (numeric) = 11.324346641 8.60836367491
y2[1] (closed_form) = 12.8003292082 7.99342216251
absolute error = 1.599
relative error = 10.6 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.2337854143 -0.19387687591
y1[1] (closed_form) = 1.2337854143 -0.19387687591
absolute error = 3.027e-63
relative error = 2.423e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.031
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.031
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17489.8MB, alloc=44.3MB, time=206.19
memory used=17536.3MB, alloc=44.3MB, time=206.74
x[1] = 0.2488 0.728
h = 0.0001 0.003
y2[1] (numeric) = 11.3259332325 8.6535273352
y2[1] (closed_form) = 12.8024262734 8.04958110964
absolute error = 1.595
relative error = 10.55 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.23758652693 -0.195522911033
y1[1] (closed_form) = 1.23758652693 -0.195522911033
absolute error = 3.027e-63
relative error = 2.416e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.042
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.042
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17582.3MB, alloc=44.3MB, time=207.28
memory used=17629.0MB, alloc=44.3MB, time=207.84
x[1] = 0.2489 0.731
h = 0.001 0.001
y2[1] (numeric) = 11.3275243018 8.69870299836
y2[1] (closed_form) = 12.8041382465 8.08327768734
absolute error = 1.6
relative error = 10.56 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.23986933524 -0.196544399873
y1[1] (closed_form) = 1.23986933524 -0.196544399873
absolute error = 3.027e-63
relative error = 2.411e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.048
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.048
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17675.0MB, alloc=44.3MB, time=208.38
memory used=17721.6MB, alloc=44.3MB, time=208.93
x[1] = 0.2499 0.732
h = 0.0001 0.004
y2[1] (numeric) = 11.3291198859 8.74389071882
y2[1] (closed_form) = 12.8155754338 8.09432069665
absolute error = 1.622
relative error = 10.7 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.24032727777 -0.197634055829
y1[1] (closed_form) = 1.24032727777 -0.197634055829
absolute error = 4.031e-63
relative error = 3.210e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.051
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17767.8MB, alloc=44.3MB, time=209.47
memory used=17814.0MB, alloc=44.3MB, time=210.02
memory used=17860.4MB, alloc=44.3MB, time=210.56
x[1] = 0.25 0.736
h = 0.003 0.006
y2[1] (numeric) = 11.330720022 8.78909055087
y2[1] (closed_form) = 12.8174928466 8.13926831948
absolute error = 1.623
relative error = 10.69 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.24340274838 -0.198979869842
y1[1] (closed_form) = 1.24340274838 -0.198979869842
absolute error = 4.020e-63
relative error = 3.192e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.06
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17906.4MB, alloc=44.3MB, time=211.10
memory used=17953.1MB, alloc=44.3MB, time=211.66
x[1] = 0.253 0.742
h = 0.0001 0.005
y2[1] (numeric) = 11.3323247476 8.83430254861
y2[1] (closed_form) = 12.8524353105 8.20613660291
absolute error = 1.645
relative error = 10.79 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.24713907531 -0.203247740885
y1[1] (closed_form) = 1.24713907531 -0.203247740885
absolute error = 4.020e-63
relative error = 3.181e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.074
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17999.1MB, alloc=44.3MB, time=212.20
memory used=18045.6MB, alloc=44.3MB, time=212.75
x[1] = 0.2531 0.747
h = 0.0001 0.003
y2[1] (numeric) = 11.3339341006 8.87952676602
y2[1] (closed_form) = 12.8545806908 8.26236166079
absolute error = 1.641
relative error = 10.74 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.25105301216 -0.204941701948
y1[1] (closed_form) = 1.25105301216 -0.204941701948
absolute error = 4.020e-63
relative error = 3.171e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.085
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.085
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18091.6MB, alloc=44.3MB, time=213.29
memory used=18138.3MB, alloc=44.3MB, time=213.85
x[1] = 0.2532 0.75
h = 0.001 0.001
y2[1] (numeric) = 11.3355481194 8.9247632569
y2[1] (closed_form) = 12.8563223149 8.29609779576
absolute error = 1.646
relative error = 10.76 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.25340330449 -0.205992978524
y1[1] (closed_form) = 1.25340330449 -0.205992978524
absolute error = 5.009e-63
relative error = 3.943e-61 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.092
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18184.4MB, alloc=44.3MB, time=214.39
memory used=18230.7MB, alloc=44.3MB, time=214.94
x[1] = 0.2542 0.751
h = 0.001 0.003
y2[1] (numeric) = 11.3371668426 8.97001207489
y2[1] (closed_form) = 12.8677825076 8.30714488128
absolute error = 1.668
relative error = 10.89 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.2538748736 -0.207114652195
y1[1] (closed_form) = 1.2538748736 -0.207114652195
absolute error = 4.011e-63
relative error = 3.156e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.094
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.094
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18276.9MB, alloc=44.3MB, time=215.48
memory used=18323.2MB, alloc=44.3MB, time=216.03
memory used=18369.8MB, alloc=44.3MB, time=216.58
x[1] = 0.2552 0.754
h = 0.0001 0.004
y2[1] (numeric) = 11.3387903092 9.01527327347
y2[1] (closed_form) = 12.8796614271 8.34070160535
absolute error = 1.682
relative error = 10.96 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.25594492087 -0.208893739119
y1[1] (closed_form) = 1.25594492087 -0.208893739119
absolute error = 4.011e-63
relative error = 3.151e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.102
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.102
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18415.7MB, alloc=44.3MB, time=217.12
memory used=18462.3MB, alloc=44.3MB, time=217.67
x[1] = 0.2553 0.758
h = 0.0001 0.004
y2[1] (numeric) = 11.3404185587 9.06054690595
y2[1] (closed_form) = 12.8816255397 8.38571077941
absolute error = 1.682
relative error = 10.95 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.25912492715 -0.210286631604
y1[1] (closed_form) = 1.25912492715 -0.210286631604
absolute error = 4.011e-63
relative error = 3.142e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.111
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.111
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18508.1MB, alloc=44.3MB, time=218.20
memory used=18554.5MB, alloc=44.3MB, time=218.75
x[1] = 0.2554 0.762
h = 0.003 0.006
y2[1] (numeric) = 11.3420516307 9.10583302549
y2[1] (closed_form) = 12.8835955516 8.43073257391
absolute error = 1.683
relative error = 10.93 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.26232489863 -0.211683893879
y1[1] (closed_form) = 1.26232489863 -0.211683893879
absolute error = 4.005e-63
relative error = 3.129e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.12
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.12
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18600.3MB, alloc=44.3MB, time=219.29
memory used=18647.0MB, alloc=44.3MB, time=219.84
x[1] = 0.2584 0.768
h = 0.0001 0.005
y2[1] (numeric) = 11.3436895655 9.15113168509
y2[1] (closed_form) = 12.9186717368 8.49767648463
absolute error = 1.705
relative error = 11.03 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.26621372943 -0.216119287686
y1[1] (closed_form) = 1.26621372943 -0.216119287686
absolute error = 4.005e-63
relative error = 3.118e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.135
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.135
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18693.1MB, alloc=44.3MB, time=220.37
memory used=18739.6MB, alloc=44.3MB, time=220.92
memory used=18786.4MB, alloc=44.3MB, time=221.48
x[1] = 0.2585 0.773
h = 0.0001 0.003
y2[1] (numeric) = 11.3453324036 9.19644293757
y2[1] (closed_form) = 12.9208835513 8.55399601698
absolute error = 1.701
relative error = 10.98 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.27028437459 -0.21787775553
y1[1] (closed_form) = 1.27028437459 -0.21787775553
absolute error = 4.011e-63
relative error = 3.112e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.147
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.147
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18832.3MB, alloc=44.3MB, time=222.02
memory used=18879.1MB, alloc=44.3MB, time=222.58
x[1] = 0.2586 0.776
h = 0.001 0.001
y2[1] (numeric) = 11.3469801857 9.24176683559
y2[1] (closed_form) = 12.9226659715 8.58778869102
absolute error = 1.706
relative error = 11 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.2727284224 -0.21896916811
y1[1] (closed_form) = 1.2727284224 -0.21896916811
absolute error = 3.015e-63
relative error = 2.335e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.154
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.154
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18925.0MB, alloc=44.3MB, time=223.12
memory used=18971.4MB, alloc=44.3MB, time=223.68
x[1] = 0.2596 0.777
h = 0.001 0.003
y2[1] (numeric) = 11.3486329531 9.28710343165
y2[1] (closed_form) = 12.9341584973 8.59884211311
absolute error = 1.728
relative error = 11.13 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.27321932576 -0.220134895664
y1[1] (closed_form) = 1.27321932576 -0.220134895664
absolute error = 3.015e-63
relative error = 2.333e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.157
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.157
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19017.3MB, alloc=44.3MB, time=224.21
memory used=19063.9MB, alloc=44.3MB, time=224.76
x[1] = 0.2606 0.78
h = 0.0001 0.004
y2[1] (numeric) = 11.3502907476 9.33245277807
y2[1] (closed_form) = 12.9460959666 8.63244393995
absolute error = 1.743
relative error = 11.2 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.2753721271 -0.221982918078
y1[1] (closed_form) = 1.2753721271 -0.221982918078
absolute error = 3.015e-63
relative error = 2.329e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.164
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.164
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19109.6MB, alloc=44.3MB, time=225.29
memory used=19156.0MB, alloc=44.3MB, time=225.84
x[1] = 0.2607 0.784
h = 0.003 0.006
y2[1] (numeric) = 11.351953611 9.377814927
y2[1] (closed_form) = 12.9481144909 8.67752976293
absolute error = 1.743
relative error = 11.18 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.27867800967 -0.223428835531
y1[1] (closed_form) = 1.27867800967 -0.223428835531
absolute error = 3.015e-63
relative error = 2.323e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.174
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.174
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19202.2MB, alloc=44.3MB, time=226.38
memory used=19248.4MB, alloc=44.3MB, time=226.92
memory used=19294.8MB, alloc=44.3MB, time=227.48
x[1] = 0.2637 0.79
h = 0.0001 0.005
y2[1] (numeric) = 11.3536215859 9.42318993042
y2[1] (closed_form) = 12.9833108439 8.74453671147
absolute error = 1.765
relative error = 11.28 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.28269307582 -0.228014188885
y1[1] (closed_form) = 1.28269307582 -0.228014188885
absolute error = 3.015e-63
relative error = 2.314e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.189
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19340.8MB, alloc=44.3MB, time=228.02
memory used=19387.6MB, alloc=44.3MB, time=228.57
x[1] = 0.2638 0.795
h = 0.0001 0.003
y2[1] (numeric) = 11.3552947148 9.46857784015
y2[1] (closed_form) = 12.98558394 8.80093778119
absolute error = 1.762
relative error = 11.23 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.2868970587 -0.22983369543
y1[1] (closed_form) = 1.2868970587 -0.22983369543
absolute error = 3.015e-63
relative error = 2.306e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.202
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.202
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19433.6MB, alloc=44.3MB, time=229.12
memory used=19480.4MB, alloc=44.3MB, time=229.68
x[1] = 0.2639 0.798
h = 0.001 0.001
y2[1] (numeric) = 11.3569730411 9.51397870782
y2[1] (closed_form) = 12.98740395 8.83477921536
absolute error = 1.766
relative error = 11.24 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.28942083297 -0.230962962143
y1[1] (closed_form) = 1.28942083297 -0.230962962143
absolute error = 2.022e-63
relative error = 1.544e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.209
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.209
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19526.4MB, alloc=44.3MB, time=230.22
memory used=19572.9MB, alloc=44.3MB, time=230.77
x[1] = 0.2649 0.799
h = 0.001 0.003
y2[1] (numeric) = 11.3586566083 9.55939258488
y2[1] (closed_form) = 12.998925189 8.84583732432
absolute error = 1.789
relative error = 11.38 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.28992697687 -0.232167434898
y1[1] (closed_form) = 1.28992697687 -0.232167434898
absolute error = 2.040e-63
relative error = 1.556e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.212
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19618.8MB, alloc=44.3MB, time=231.31
memory used=19665.4MB, alloc=44.3MB, time=231.86
x[1] = 0.2659 0.802
h = 0.0001 0.004
y2[1] (numeric) = 11.3603454603 9.60481952261
y2[1] (closed_form) = 13.0109155917 8.87947731425
absolute error = 1.803
relative error = 11.45 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.29214902791 -0.234077851003
y1[1] (closed_form) = 1.29214902791 -0.234077851003
absolute error = 2.040e-63
relative error = 1.553e-61 %
Correct digits = 63
memory used=19711.9MB, alloc=44.3MB, time=232.40
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.22
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.22
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19757.6MB, alloc=44.3MB, time=232.94
memory used=19803.9MB, alloc=44.3MB, time=233.48
x[1] = 0.266 0.806
h = 0.003 0.006
y2[1] (numeric) = 11.3620396415 9.65025957212
y2[1] (closed_form) = 13.0129842789 8.92462924691
absolute error = 1.803
relative error = 11.43 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.29556199159 -0.235573853852
y1[1] (closed_form) = 1.29556199159 -0.235573853852
absolute error = 2.040e-63
relative error = 1.549e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.23
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.23
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19849.8MB, alloc=44.3MB, time=234.02
memory used=19896.3MB, alloc=44.3MB, time=234.57
x[1] = 0.269 0.812
h = 0.0001 0.005
y2[1] (numeric) = 11.3637391965 9.69571278431
y2[1] (closed_form) = 13.048304803 8.99170121603
absolute error = 1.826
relative error = 11.52 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.29970405426 -0.240312193705
y1[1] (closed_form) = 1.29970405426 -0.240312193705
absolute error = 2.040e-63
relative error = 1.543e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.246
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19942.2MB, alloc=44.3MB, time=235.10
memory used=19988.8MB, alloc=44.3MB, time=235.66
x[1] = 0.2691 0.817
h = 0.0001 0.003
y2[1] (numeric) = 11.3654441706 9.74117920994
y2[1] (closed_form) = 13.0506412538 9.0481864446
absolute error = 1.822
relative error = 11.47 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.30404286723 -0.242194548948
y1[1] (closed_form) = 1.30404286723 -0.242194548948
absolute error = 2.062e-63
relative error = 1.554e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.259
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.259
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20034.8MB, alloc=44.3MB, time=236.19
memory used=20081.5MB, alloc=44.3MB, time=236.75
x[1] = 0.2692 0.82
h = 0.001 0.001
y2[1] (numeric) = 11.3671546092 9.78665889956
y2[1] (closed_form) = 13.0525001235 9.08207819905
absolute error = 1.827
relative error = 11.49 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.30664725523 -0.243362773241
y1[1] (closed_form) = 1.30664725523 -0.243362773241
absolute error = 2.040e-63
relative error = 1.535e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.267
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.267
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20127.8MB, alloc=44.3MB, time=237.30
memory used=20174.0MB, alloc=44.3MB, time=237.85
memory used=20220.6MB, alloc=44.3MB, time=238.41
x[1] = 0.2702 0.821
h = 0.001 0.003
y2[1] (numeric) = 11.3688705583 9.83215190353
y2[1] (closed_form) = 13.0640510159 9.09314112251
absolute error = 1.849
relative error = 11.62 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.30716858953 -0.244606658384
y1[1] (closed_form) = 1.30716858953 -0.244606658384
absolute error = 2.062e-63
relative error = 1.550e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.269
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.269
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20266.4MB, alloc=44.3MB, time=238.94
memory used=20313.1MB, alloc=44.3MB, time=239.49
x[1] = 0.2712 0.824
h = 0.0001 0.004
y2[1] (numeric) = 11.3705920642 9.87765827203
y2[1] (closed_form) = 13.0760961085 9.12682047089
absolute error = 1.863
relative error = 11.69 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.30946045781 -0.246580857406
y1[1] (closed_form) = 1.30946045781 -0.246580857406
absolute error = 3.041e-63
relative error = 2.283e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.277
Order of pole (three term test) = 31.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20359.0MB, alloc=44.3MB, time=240.02
memory used=20405.4MB, alloc=44.3MB, time=240.57
x[1] = 0.2713 0.828
h = 0.003 0.006
y2[1] (numeric) = 11.3723191736 9.92317805507
y2[1] (closed_form) = 13.0782166474 9.17204061288
absolute error = 1.864
relative error = 11.67 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.31298170976 -0.248128423675
y1[1] (closed_form) = 1.31298170976 -0.248128423675
absolute error = 3.041e-63
relative error = 2.276e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.288
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.288
Order of pole (three term test) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20451.1MB, alloc=44.3MB, time=241.10
memory used=20497.6MB, alloc=44.3MB, time=241.65
x[1] = 0.2743 0.834
h = 0.0001 0.005
y2[1] (numeric) = 11.3740519337 9.96871130243
y2[1] (closed_form) = 13.1136654175 9.239179586
absolute error = 1.886
relative error = 11.76 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.31725155233 -0.253022876346
y1[1] (closed_form) = 1.31725155233 -0.253022876346
absolute error = 2.062e-63
relative error = 1.537e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.305
Order of pole (three term test) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20543.5MB, alloc=44.3MB, time=242.18
memory used=20590.1MB, alloc=44.3MB, time=242.74
memory used=20636.6MB, alloc=44.3MB, time=243.29
x[1] = 0.2744 0.839
h = 0.0001 0.003
y2[1] (numeric) = 11.3757903921 10.0142580637
y2[1] (closed_form) = 13.116067345 9.29575161851
absolute error = 1.883
relative error = 11.71 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.32172673455 -0.254969950384
y1[1] (closed_form) = 1.32172673455 -0.254969950384
absolute error = 3.041e-63
relative error = 2.259e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.318
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.318
Order of pole (three term test) = 31.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20682.7MB, alloc=44.3MB, time=243.83
memory used=20729.5MB, alloc=44.3MB, time=244.39
x[1] = 0.2745 0.842
h = 0.001 0.001
y2[1] (numeric) = 11.3775345967 10.0598183884
y2[1] (closed_form) = 13.1179663734 9.32969526727
absolute error = 1.887
relative error = 11.72 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.32441265124 -0.256178272267
y1[1] (closed_form) = 1.32441265124 -0.256178272267
absolute error = 3.027e-63
relative error = 2.244e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.326
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.326
Order of pole (three term test) = 31.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20775.4MB, alloc=44.3MB, time=244.93
memory used=20821.9MB, alloc=44.3MB, time=245.48
x[1] = 0.2755 0.843
h = 0.001 0.003
y2[1] (numeric) = 11.3792845959 10.1053923257
y2[1] (closed_form) = 13.1295478744 9.34076312815
absolute error = 1.91
relative error = 11.85 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.32494912353 -0.257462258499
y1[1] (closed_form) = 1.32494912353 -0.257462258499
absolute error = 3.027e-63
relative error = 2.242e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.329
Order of pole (three term test) = 31.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20867.7MB, alloc=44.3MB, time=246.02
memory used=20914.5MB, alloc=44.3MB, time=246.57
x[1] = 0.2765 0.846
h = 0.0001 0.004
y2[1] (numeric) = 11.3810404386 10.1509799246
y2[1] (closed_form) = 13.1416494473 9.37448303553
absolute error = 1.924
relative error = 11.92 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.32731139356 -0.259501675023
y1[1] (closed_form) = 1.32731139356 -0.259501675023
absolute error = 3.027e-63
relative error = 2.238e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.338
Order of pole (three term test) = 31.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20960.4MB, alloc=44.3MB, time=247.10
memory used=21006.8MB, alloc=44.3MB, time=247.65
x[1] = 0.2766 0.85
h = 0.003 0.006
y2[1] (numeric) = 11.3828021738 10.196581234
y2[1] (closed_form) = 13.1438235661 9.41977350551
absolute error = 1.925
relative error = 11.9 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.33094217826 -0.261102331502
y1[1] (closed_form) = 1.33094217826 -0.261102331502
absolute error = 3.027e-63
relative error = 2.231e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.349
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.349
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21052.9MB, alloc=44.3MB, time=248.18
memory used=21099.3MB, alloc=44.3MB, time=248.73
memory used=21145.9MB, alloc=44.3MB, time=249.28
x[1] = 0.2796 0.856
h = 0.0001 0.005
y2[1] (numeric) = 11.3845698513 10.2421963024
y2[1] (closed_form) = 13.1794047314 9.4869814667
absolute error = 1.947
relative error = 11.99 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.33534060599 -0.266156124286
y1[1] (closed_form) = 1.33534060599 -0.266156124286
absolute error = 3.027e-63
relative error = 2.223e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.366
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.366
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21192.0MB, alloc=44.3MB, time=249.82
memory used=21238.6MB, alloc=44.3MB, time=250.37
x[1] = 0.2797 0.861
h = 0.0001 0.003
y2[1] (numeric) = 11.3863435212 10.2878251784
y2[1] (closed_form) = 13.1818743075 9.54364297253
absolute error = 1.944
relative error = 11.94 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.3399537437 -0.268169848527
y1[1] (closed_form) = 1.3399537437 -0.268169848527
absolute error = 3.027e-63
relative error = 2.215e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.38
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.38
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21284.6MB, alloc=44.3MB, time=250.92
memory used=21331.3MB, alloc=44.3MB, time=251.48
x[1] = 0.2798 0.864
h = 0.001 0.001
y2[1] (numeric) = 11.3881232339 10.3334679102
y2[1] (closed_form) = 13.1838148243 9.57764010393
absolute error = 1.948
relative error = 11.96 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.34272213184 -0.269419445304
y1[1] (closed_form) = 1.34272213184 -0.269419445304
absolute error = 3.027e-63
relative error = 2.210e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.389
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.389
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21377.3MB, alloc=44.3MB, time=252.02
memory used=21423.9MB, alloc=44.3MB, time=252.57
x[1] = 0.2808 0.865
h = 0.0001 0.004
y2[1] (numeric) = 11.3899090403 10.3791245457
y2[1] (closed_form) = 13.1954279039 9.58871302026
absolute error = 1.971
relative error = 12.08 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.34327368726 -0.270744243139
y1[1] (closed_form) = 1.34327368726 -0.270744243139
absolute error = 3.027e-63
relative error = 2.209e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.392
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.392
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21469.7MB, alloc=44.3MB, time=253.10
memory used=21516.2MB, alloc=44.3MB, time=253.65
x[1] = 0.2809 0.869
h = 0.003 0.006
y2[1] (numeric) = 11.3917009918 10.4247951329
y2[1] (closed_form) = 13.1976486852 9.63406640472
absolute error = 1.971
relative error = 12.07 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.34700043743 -0.272390532846
y1[1] (closed_form) = 1.34700043743 -0.272390532846
absolute error = 3.027e-63
relative error = 2.202e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.403
Order of pole (three term test) = 33.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.403
Order of pole (three term test) = 31.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21562.5MB, alloc=44.3MB, time=254.20
memory used=21608.7MB, alloc=44.3MB, time=254.74
memory used=21655.4MB, alloc=44.3MB, time=255.29
x[1] = 0.2839 0.875
h = 0.0001 0.005
y2[1] (numeric) = 11.3934991401 10.4704797192
y2[1] (closed_form) = 13.2333463388 9.70133698355
absolute error = 1.994
relative error = 12.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.35151216048 -0.277582597783
y1[1] (closed_form) = 1.35151216048 -0.277582597783
absolute error = 2.040e-63
relative error = 1.478e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.421
Order of pole (three term test) = 33.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.421
Order of pole (three term test) = 31.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21701.3MB, alloc=44.3MB, time=255.82
memory used=21748.1MB, alloc=44.3MB, time=256.38
x[1] = 0.284 0.88
h = 0.0001 0.003
y2[1] (numeric) = 11.3953035376 10.5161783523
y2[1] (closed_form) = 13.2358748135 9.75807850368
absolute error = 1.991
relative error = 12.11 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.35624617846 -0.279653616731
y1[1] (closed_form) = 1.35624617846 -0.279653616731
absolute error = 2.040e-63
relative error = 1.473e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.436
Order of pole (three term test) = 33.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.436
Order of pole (three term test) = 31.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21794.2MB, alloc=44.3MB, time=256.92
memory used=21841.0MB, alloc=44.3MB, time=257.49
x[1] = 0.2841 0.883
h = 0.001 0.001
y2[1] (numeric) = 11.3971142367 10.5618910791
y2[1] (closed_form) = 13.2378514677 9.79212347061
absolute error = 1.995
relative error = 12.12 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.35908684304 -0.280938715146
y1[1] (closed_form) = 1.35908684304 -0.280938715146
absolute error = 2.040e-63
relative error = 1.470e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.444
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.444
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21886.9MB, alloc=44.3MB, time=258.03
memory used=21933.3MB, alloc=44.3MB, time=258.58
x[1] = 0.2851 0.884
h = 0.001 0.003
y2[1] (numeric) = 11.3989312907 10.6076179468
y2[1] (closed_form) = 13.2494924558 9.80320122134
absolute error = 2.018
relative error = 12.24 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.35965183365 -0.28229904936
y1[1] (closed_form) = 1.35965183365 -0.28229904936
absolute error = 2.040e-63
relative error = 1.469e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.447
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.447
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21979.1MB, alloc=44.3MB, time=259.12
memory used=22025.7MB, alloc=44.3MB, time=259.66
x[1] = 0.2861 0.887
h = 0.0001 0.004
y2[1] (numeric) = 11.4007547531 10.653359002
y2[1] (closed_form) = 13.2617034951 9.83700053797
absolute error = 2.032
relative error = 12.31 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.36214753773 -0.284462941475
y1[1] (closed_form) = 1.36214753773 -0.284462941475
absolute error = 2.040e-63
relative error = 1.466e-61 %
Correct digits = 63
memory used=22072.3MB, alloc=44.3MB, time=260.22
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.457
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22118.2MB, alloc=44.3MB, time=260.75
memory used=22164.6MB, alloc=44.3MB, time=261.30
x[1] = 0.2862 0.891
h = 0.003 0.006
y2[1] (numeric) = 11.4025846778 10.6991142914
y2[1] (closed_form) = 13.2639811561 9.882428267
absolute error = 2.033
relative error = 12.29 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.36598625611 -0.286165279694
y1[1] (closed_form) = 1.36598625611 -0.286165279694
absolute error = 3.027e-63
relative error = 2.169e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.469
Order of pole (three term test) = 33.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.469
Order of pole (three term test) = 31.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22210.6MB, alloc=44.3MB, time=261.83
memory used=22257.2MB, alloc=44.3MB, time=262.38
x[1] = 0.2892 0.897
h = 0.0001 0.005
y2[1] (numeric) = 11.4044211193 10.7448838612
y2[1] (closed_form) = 13.2998191073 9.94977157889
absolute error = 2.055
relative error = 12.37 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.37062816088 -0.291522954273
y1[1] (closed_form) = 1.37062816088 -0.291522954273
absolute error = 3.027e-63
relative error = 2.160e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.487
Order of pole (three term test) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.487
Order of pole (three term test) = 31.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22303.1MB, alloc=44.3MB, time=262.92
memory used=22349.7MB, alloc=44.3MB, time=263.48
x[1] = 0.2893 0.902
h = 0.0001 0.003
y2[1] (numeric) = 11.4062641325 10.7906677576
y2[1] (closed_form) = 13.3024193783 10.0066076339
absolute error = 2.052
relative error = 12.33 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.37550323701 -0.293664364581
y1[1] (closed_form) = 1.37550323701 -0.293664364581
absolute error = 3.027e-63
relative error = 2.152e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.502
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.502
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22395.8MB, alloc=44.3MB, time=264.01
memory used=22442.6MB, alloc=44.3MB, time=264.58
x[1] = 0.2894 0.905
h = 0.001 0.001
y2[1] (numeric) = 11.4081137726 10.8364660265
y2[1] (closed_form) = 13.3044400599 10.0407090952
absolute error = 2.057
relative error = 12.34 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.37842821701 -0.294993018434
y1[1] (closed_form) = 1.37842821701 -0.294993018434
absolute error = 4.031e-63
relative error = 2.860e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.512
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.512
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22488.8MB, alloc=44.3MB, time=265.12
memory used=22535.0MB, alloc=44.3MB, time=265.67
memory used=22581.6MB, alloc=44.3MB, time=266.22
x[1] = 0.2904 0.906
h = 0.001 0.003
y2[1] (numeric) = 11.4099700955 10.8822787135
y2[1] (closed_form) = 13.3161144723 10.0517921194
absolute error = 2.079
relative error = 12.46 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.37900819058 -0.29639554621
y1[1] (closed_form) = 1.37900819058 -0.29639554621
absolute error = 3.041e-63
relative error = 2.156e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.515
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.515
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22627.5MB, alloc=44.3MB, time=266.76
memory used=22673.9MB, alloc=44.3MB, time=267.31
x[1] = 0.2914 0.909
h = 0.0001 0.004
y2[1] (numeric) = 11.4118331574 10.9281058641
y2[1] (closed_form) = 13.3283872978 10.0856354821
absolute error = 2.094
relative error = 12.53 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.38157608051 -0.298629009893
y1[1] (closed_form) = 1.38157608051 -0.298629009893
absolute error = 3.059e-63
relative error = 2.164e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.524
Order of pole (three term test) = 33.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.524
Order of pole (three term test) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22719.8MB, alloc=44.3MB, time=267.84
memory used=22766.2MB, alloc=44.3MB, time=268.39
x[1] = 0.2915 0.913
h = 0.003 0.006
y2[1] (numeric) = 11.413703015 10.9739475235
y2[1] (closed_form) = 13.330723687 10.1311397324
absolute error = 2.094
relative error = 12.51 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.38552812024 -0.300389068015
y1[1] (closed_form) = 1.38552812024 -0.300389068015
absolute error = 3.059e-63
relative error = 2.158e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.537
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.537
Order of pole (three term test) = 31.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22812.0MB, alloc=44.3MB, time=268.92
memory used=22858.6MB, alloc=44.3MB, time=269.47
x[1] = 0.2945 0.919
h = 0.0001 0.005
y2[1] (numeric) = 11.4155797255 11.0198037367
y2[1] (closed_form) = 13.3667063099 10.1985577638
absolute error = 2.117
relative error = 12.59 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.39030107357 -0.305915877496
y1[1] (closed_form) = 1.39030107357 -0.305915877496
absolute error = 3.059e-63
relative error = 2.149e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 33.85 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.556
Order of pole (three term test) = 31.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22904.5MB, alloc=44.3MB, time=270.00
memory used=22951.2MB, alloc=44.3MB, time=270.56
x[1] = 0.2946 0.924
h = 0.0001 0.003
y2[1] (numeric) = 11.4174633465 11.0656745484
y2[1] (closed_form) = 13.369380701 10.2554910972
absolute error = 2.113
relative error = 12.54 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.39531893111 -0.308129792437
y1[1] (closed_form) = 1.39531893111 -0.308129792437
absolute error = 3.059e-63
relative error = 2.141e-61 %
Correct digits = 63
memory used=22997.9MB, alloc=44.3MB, time=271.11
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 33.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.572
Order of pole (three term test) = 31.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23044.1MB, alloc=44.3MB, time=271.66
memory used=23091.0MB, alloc=44.3MB, time=272.22
x[1] = 0.2947 0.927
h = 0.001 0.001
y2[1] (numeric) = 11.419353936 11.1115600033
y2[1] (closed_form) = 13.3714468321 10.2896506848
absolute error = 2.118
relative error = 12.55 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.39832925022 -0.309503289647
y1[1] (closed_form) = 1.39832925022 -0.309503289647
absolute error = 3.059e-63
relative error = 2.136e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.582
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.582
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23137.0MB, alloc=44.3MB, time=272.76
memory used=23183.4MB, alloc=44.3MB, time=273.31
x[1] = 0.2957 0.928
h = 0.001 0.003
y2[1] (numeric) = 11.4212515526 11.1574601455
y2[1] (closed_form) = 13.3831556846 10.3007390857
absolute error = 2.141
relative error = 12.68 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.39892414409 -0.310948785691
y1[1] (closed_form) = 1.39892414409 -0.310948785691
absolute error = 3.081e-63
relative error = 2.150e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.585
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23229.3MB, alloc=44.3MB, time=273.85
memory used=23275.9MB, alloc=44.3MB, time=274.40
x[1] = 0.2967 0.931
h = 0.0001 0.004
y2[1] (numeric) = 11.4231562554 11.2033750192
y2[1] (closed_form) = 13.3954922289 10.3346277167
absolute error = 2.155
relative error = 12.74 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.40156486972 -0.313253438106
y1[1] (closed_form) = 1.40156486972 -0.313253438106
absolute error = 2.119e-63
relative error = 1.475e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.595
Order of pole (three term test) = 33.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.595
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23321.7MB, alloc=44.3MB, time=274.93
memory used=23368.3MB, alloc=44.3MB, time=275.48
x[1] = 0.2968 0.935
h = 0.003 0.006
y2[1] (numeric) = 11.4250681038 11.2493046682
y2[1] (closed_form) = 13.3978892393 10.380210686
absolute error = 2.156
relative error = 12.72 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.40563162216 -0.315072940267
y1[1] (closed_form) = 1.40563162216 -0.315072940267
absolute error = 3.081e-63
relative error = 2.139e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 33.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.608
Order of pole (three term test) = 31.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23414.2MB, alloc=44.3MB, time=276.01
memory used=23460.8MB, alloc=44.3MB, time=276.56
memory used=23507.4MB, alloc=44.3MB, time=277.11
x[1] = 0.2998 0.941
h = 0.0001 0.005
y2[1] (numeric) = 11.4269871577 11.295249136
y2[1] (closed_form) = 13.4340209916 10.4477054238
absolute error = 2.179
relative error = 12.8 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.41053651121 -0.320772517585
y1[1] (closed_form) = 1.41053651121 -0.320772517585
absolute error = 3.105e-63
relative error = 2.146e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 33.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.628
Order of pole (three term test) = 31.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23553.4MB, alloc=44.3MB, time=277.65
memory used=23600.0MB, alloc=44.3MB, time=278.20
x[1] = 0.2999 0.946
h = 0.0001 0.003
y2[1] (numeric) = 11.4289134777 11.3412084661
y2[1] (closed_form) = 13.4367718832 10.5047388062
absolute error = 2.175
relative error = 12.75 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.41569892158 -0.323061116788
y1[1] (closed_form) = 1.41569892158 -0.323061116788
absolute error = 3.105e-63
relative error = 2.138e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.645
Order of pole (three term test) = 33.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.645
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23646.0MB, alloc=44.3MB, time=278.74
memory used=23692.8MB, alloc=44.3MB, time=279.31
x[1] = 0.3 0.949
h = 0.001 0.001
y2[1] (numeric) = 11.4308471247 11.3871827016
y2[1] (closed_form) = 13.4388849197 10.5389581678
absolute error = 2.18
relative error = 12.76 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.41879563195 -0.324480785622
y1[1] (closed_form) = 1.41879563195 -0.324480785622
absolute error = 3.105e-63
relative error = 2.133e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.655
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.655
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23738.8MB, alloc=44.3MB, time=279.86
memory used=23785.3MB, alloc=44.3MB, time=280.41
x[1] = 0.301 0.95
h = 0.001 0.003
y2[1] (numeric) = 11.43278816 11.4331718853
y2[1] (closed_form) = 13.4506292455 10.5500520432
absolute error = 2.203
relative error = 12.89 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.41940538022 -0.325970047709
y1[1] (closed_form) = 1.41940538022 -0.325970047709
absolute error = 3.105e-63
relative error = 2.132e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.658
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.658
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23831.1MB, alloc=44.3MB, time=280.94
memory used=23877.8MB, alloc=44.3MB, time=281.50
x[1] = 0.302 0.953
h = 0.0001 0.004
y2[1] (numeric) = 11.4347366455 11.4791760598
y2[1] (closed_form) = 13.4630314808 10.5839871704
absolute error = 2.217
relative error = 12.95 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.42211960806 -0.328347555463
y1[1] (closed_form) = 1.42211960806 -0.328347555463
absolute error = 3.105e-63
relative error = 2.127e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.669
Order of pole (three term test) = 33.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.669
Order of pole (three term test) = 31.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23924.1MB, alloc=44.3MB, time=282.04
memory used=23970.2MB, alloc=44.3MB, time=282.58
memory used=24016.7MB, alloc=44.3MB, time=283.13
x[1] = 0.3021 0.957
h = 0.003 0.006
y2[1] (numeric) = 11.4366926436 11.5251952675
y2[1] (closed_form) = 13.4654910513 10.6296510784
absolute error = 2.218
relative error = 12.93 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.42630250298 -0.330228279655
y1[1] (closed_form) = 1.42630250298 -0.330228279655
absolute error = 3.105e-63
relative error = 2.121e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.682
Order of pole (three term test) = 33.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.682
Order of pole (three term test) = 31.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24062.5MB, alloc=44.3MB, time=283.66
memory used=24109.2MB, alloc=44.3MB, time=284.22
x[1] = 0.3051 0.963
h = 0.0001 0.005
y2[1] (numeric) = 11.4386562172 11.5712295506
y2[1] (closed_form) = 13.5017764765 10.6972245095
absolute error = 2.241
relative error = 13.01 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.43134023474 -0.336104367285
y1[1] (closed_form) = 1.43134023474 -0.336104367285
absolute error = 3.105e-63
relative error = 2.112e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.703
Order of pole (three term test) = 31.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24155.2MB, alloc=44.3MB, time=284.75
memory used=24201.9MB, alloc=44.3MB, time=285.30
x[1] = 0.3052 0.968
h = 0.0001 0.003
y2[1] (numeric) = 11.4406274296 11.6172789509
y2[1] (closed_form) = 13.5046063072 10.7543607392
absolute error = 2.237
relative error = 12.96 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.43664901787 -0.338469898138
y1[1] (closed_form) = 1.43664901787 -0.338469898138
absolute error = 4.079e-63
relative error = 2.764e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.721
Order of pole (three term test) = 33.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.721
Order of pole (three term test) = 31.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24247.8MB, alloc=44.3MB, time=285.84
memory used=24294.6MB, alloc=44.3MB, time=286.40
x[1] = 0.3053 0.971
h = 0.001 0.001
y2[1] (numeric) = 11.4426063446 11.6633435101
y2[1] (closed_form) = 13.5067677407 10.788641539
absolute error = 2.242
relative error = 12.97 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.43983320027 -0.339937108066
y1[1] (closed_form) = 1.43983320027 -0.339937108066
absolute error = 3.081e-63
relative error = 2.082e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.731
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.731
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24340.7MB, alloc=44.3MB, time=286.95
memory used=24387.2MB, alloc=44.3MB, time=287.50
x[1] = 0.3063 0.972
h = 0.0001 0.004
y2[1] (numeric) = 11.4445930265 11.7094232695
y2[1] (closed_form) = 13.51854859 10.7997409807
absolute error = 2.265
relative error = 13.09 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.44045773362 -0.341470957387
y1[1] (closed_form) = 1.44045773362 -0.341470957387
absolute error = 3.105e-63
relative error = 2.097e-61 %
Correct digits = 63
memory used=24433.7MB, alloc=44.3MB, time=288.04
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.735
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24479.7MB, alloc=44.3MB, time=288.58
memory used=24526.2MB, alloc=44.3MB, time=289.13
x[1] = 0.3064 0.976
h = 0.003 0.006
y2[1] (numeric) = 11.4465875402 11.7555182702
y2[1] (closed_form) = 13.5210625984 10.84547713
absolute error = 2.265
relative error = 13.07 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.4447425337 -0.343404437807
y1[1] (closed_form) = 1.4447425337 -0.343404437807
absolute error = 3.105e-63
relative error = 2.091e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.749
Order of pole (three term test) = 33.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.749
Order of pole (three term test) = 31.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24572.2MB, alloc=44.3MB, time=289.67
memory used=24618.9MB, alloc=44.3MB, time=290.22
x[1] = 0.3094 0.982
h = 0.0001 0.005
y2[1] (numeric) = 11.4485899511 11.8016285532
y2[1] (closed_form) = 13.5574830363 10.9131217946
absolute error = 2.288
relative error = 13.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.44989751851 -0.349433944067
y1[1] (closed_form) = 1.44989751851 -0.349433944067
absolute error = 3.132e-63
relative error = 2.100e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.771
Order of pole (three term test) = 31.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24664.8MB, alloc=44.3MB, time=290.76
memory used=24711.4MB, alloc=44.3MB, time=291.31
x[1] = 0.3095 0.987
h = 0.0001 0.003
y2[1] (numeric) = 11.4506003249 11.8477541591
y2[1] (closed_form) = 13.5603815426 10.9703497954
absolute error = 2.285
relative error = 13.1 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.45533474314 -0.351865773576
y1[1] (closed_form) = 1.45533474314 -0.351865773576
absolute error = 3.132e-63
relative error = 2.092e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.789
Order of pole (three term test) = 34.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.789
Order of pole (three term test) = 31.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24757.4MB, alloc=44.3MB, time=291.86
memory used=24804.4MB, alloc=44.3MB, time=292.42
x[1] = 0.3096 0.99
h = 0.001 0.001
y2[1] (numeric) = 11.4526187279 11.8938951281
y2[1] (closed_form) = 13.5625850977 11.0046854259
absolute error = 2.29
relative error = 13.11 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.45859569527 -0.353373974005
y1[1] (closed_form) = 1.45859569527 -0.353373974005
absolute error = 3.132e-63
relative error = 2.087e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.8
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24850.6MB, alloc=44.3MB, time=292.96
memory used=24897.1MB, alloc=44.3MB, time=293.52
memory used=24943.5MB, alloc=44.3MB, time=294.07
x[1] = 0.3106 0.991
h = 0.001 0.003
y2[1] (numeric) = 11.4546452271 11.9400515003
y2[1] (closed_form) = 13.5743981724 11.0157901804
absolute error = 2.312
relative error = 13.23 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.4592334417 -0.354946703337
y1[1] (closed_form) = 1.4592334417 -0.354946703337
absolute error = 3.105e-63
relative error = 2.067e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.803
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24989.4MB, alloc=44.3MB, time=294.60
memory used=25035.9MB, alloc=44.3MB, time=295.15
x[1] = 0.3116 0.994
h = 0.0001 0.004
y2[1] (numeric) = 11.4566798898 11.9862233156
y2[1] (closed_form) = 13.5869274443 11.0498159548
absolute error = 2.327
relative error = 13.29 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.46208718745 -0.357463491725
y1[1] (closed_form) = 1.46208718745 -0.357463491725
absolute error = 3.105e-63
relative error = 2.063e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.815
Order of pole (three term test) = 34.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.815
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25081.7MB, alloc=44.3MB, time=295.68
memory used=25128.1MB, alloc=44.3MB, time=296.23
x[1] = 0.3117 0.998
h = 0.003 0.006
y2[1] (numeric) = 11.4587227838 12.0324106134
y2[1] (closed_form) = 13.5895077209 11.0956372571
absolute error = 2.328
relative error = 13.27 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.46649091638 -0.35946163176
y1[1] (closed_form) = 1.46649091638 -0.35946163176
absolute error = 3.105e-63
relative error = 2.056e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.829
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.829
Order of pole (three term test) = 31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25174.1MB, alloc=44.3MB, time=296.76
memory used=25220.7MB, alloc=44.3MB, time=297.32
x[1] = 0.3147 1.004
h = 0.0001 0.005
y2[1] (numeric) = 11.4607739776 12.0786134332
y2[1] (closed_form) = 13.6260904997 11.163364369
absolute error = 2.351
relative error = 13.35 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.47178053067 -0.365674899012
y1[1] (closed_form) = 1.47178053067 -0.365674899012
absolute error = 4.079e-63
relative error = 2.690e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.852
Order of pole (three term test) = 34.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.852
Order of pole (three term test) = 30.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25266.6MB, alloc=44.3MB, time=297.86
memory used=25313.3MB, alloc=44.3MB, time=298.41
x[1] = 0.3148 1.009
h = 0.0001 0.003
y2[1] (numeric) = 11.4628335399 12.1248318138
y2[1] (closed_form) = 13.6290726096 11.2207005313
absolute error = 2.347
relative error = 13.3 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.47736767334 -0.368188004331
y1[1] (closed_form) = 1.47736767334 -0.368188004331
absolute error = 3.105e-63
relative error = 2.039e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.871
Order of pole (three term test) = 34.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.871
Order of pole (three term test) = 30.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25359.7MB, alloc=44.3MB, time=298.96
memory used=25406.0MB, alloc=44.3MB, time=299.51
memory used=25452.9MB, alloc=44.3MB, time=300.07
x[1] = 0.3149 1.012
h = 0.001 0.001
y2[1] (numeric) = 11.4649015403 12.171065794
y2[1] (closed_form) = 13.6313274144 11.2551007601
absolute error = 2.352
relative error = 13.31 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.48071820284 -0.369746393097
y1[1] (closed_form) = 1.48071820284 -0.369746393097
absolute error = 3.105e-63
relative error = 2.034e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.882
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.882
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25498.9MB, alloc=44.3MB, time=300.62
memory used=25545.4MB, alloc=44.3MB, time=301.17
x[1] = 0.3159 1.013
h = 0.001 0.003
y2[1] (numeric) = 11.4669780487 12.2173154122
y2[1] (closed_form) = 13.6431790144 11.266211249
absolute error = 2.375
relative error = 13.42 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.4813706059 -0.371365302207
y1[1] (closed_form) = 1.4813706059 -0.371365302207
absolute error = 3.105e-63
relative error = 2.033e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.886
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.886
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25591.2MB, alloc=44.3MB, time=301.70
memory used=25637.7MB, alloc=44.3MB, time=302.25
x[1] = 0.3169 1.016
h = 0.0001 0.004
y2[1] (numeric) = 11.4690631355 12.2635807067
y2[1] (closed_form) = 13.6557798338 11.3002870907
absolute error = 2.389
relative error = 13.48 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.48429987333 -0.373959986455
y1[1] (closed_form) = 1.48429987333 -0.373959986455
absolute error = 3.105e-63
relative error = 2.028e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.898
Order of pole (three term test) = 34.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.898
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25683.7MB, alloc=44.3MB, time=302.78
memory used=25730.2MB, alloc=44.3MB, time=303.34
x[1] = 0.317 1.02
h = 0.003 0.006
y2[1] (numeric) = 11.4711568717 12.3098617153
y2[1] (closed_form) = 13.6584284569 11.3461958316
absolute error = 2.39
relative error = 13.46 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.48882407287 -0.37602472413
y1[1] (closed_form) = 1.48882407287 -0.37602472413
absolute error = 3.105e-63
relative error = 2.022e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.913
Order of pole (three term test) = 34.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.913
Order of pole (three term test) = 30.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25776.1MB, alloc=44.3MB, time=303.86
memory used=25822.7MB, alloc=44.3MB, time=304.42
memory used=25869.3MB, alloc=44.3MB, time=304.97
x[1] = 0.32 1.026
h = 0.0001 0.005
y2[1] (numeric) = 11.4732593289 12.3561584756
y2[1] (closed_form) = 13.6951783799 11.4140073785
absolute error = 2.413
relative error = 13.54 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.49424927924 -0.382425818777
y1[1] (closed_form) = 1.49424927924 -0.382425818777
absolute error = 3.105e-63
relative error = 2.013e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.937
Order of pole (three term test) = 34.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.937
Order of pole (three term test) = 30.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25915.5MB, alloc=44.3MB, time=305.51
memory used=25962.3MB, alloc=44.3MB, time=306.07
x[1] = 0.3201 1.031
h = 0.0001 0.003
y2[1] (numeric) = 11.475370579 12.4024710251
y2[1] (closed_form) = 13.698246708 11.4714545847
absolute error = 2.41
relative error = 13.49 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.49998830116 -0.385022648709
y1[1] (closed_form) = 1.49998830116 -0.385022648709
absolute error = 3.105e-63
relative error = 2.005e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.957
Order of pole (three term test) = 34.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.957
Order of pole (three term test) = 30.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26008.3MB, alloc=44.3MB, time=306.61
memory used=26055.2MB, alloc=44.3MB, time=307.18
x[1] = 0.3202 1.034
h = 0.001 0.001
y2[1] (numeric) = 11.4774906948 12.4487994007
y2[1] (closed_form) = 13.7005543608 11.5059211254
absolute error = 2.415
relative error = 13.5 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.50342957217 -0.386632717719
y1[1] (closed_form) = 1.50342957217 -0.386632717719
absolute error = 3.105e-63
relative error = 2.000e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.968
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.968
Order of pole (three term test) = 30.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26101.2MB, alloc=44.3MB, time=307.72
memory used=26147.6MB, alloc=44.3MB, time=308.27
x[1] = 0.3212 1.035
h = 0.001 0.003
y2[1] (numeric) = 11.4796197492 12.4951436391
y2[1] (closed_form) = 13.7124455893 11.5170374231
absolute error = 2.438
relative error = 13.61 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.50409655175 -0.388298696857
y1[1] (closed_form) = 1.50409655175 -0.388298696857
absolute error = 3.105e-63
relative error = 1.999e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.973
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.973
Order of pole (three term test) = 30.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26193.5MB, alloc=44.3MB, time=308.80
memory used=26240.2MB, alloc=44.3MB, time=309.35
x[1] = 0.3222 1.038
h = 0.0001 0.004
y2[1] (numeric) = 11.481757816 12.541503777
y2[1] (closed_form) = 13.7251200926 11.5511645837
absolute error = 2.452
relative error = 13.67 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.50710207125 -0.390973143098
y1[1] (closed_form) = 1.50710207125 -0.390973143098
absolute error = 4.079e-63
relative error = 2.620e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.985
Order of pole (three term test) = 34.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.985
Order of pole (three term test) = 30.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26286.4MB, alloc=44.3MB, time=309.88
memory used=26332.7MB, alloc=44.3MB, time=310.43
memory used=26379.0MB, alloc=44.3MB, time=310.98
x[1] = 0.3223 1.042
h = 0.003 0.006
y2[1] (numeric) = 11.4839049693 12.5878798504
y2[1] (closed_form) = 13.7278391916 11.5971630726
absolute error = 2.453
relative error = 13.65 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.51174832255 -0.393106474897
y1[1] (closed_form) = 1.51174832255 -0.393106474897
absolute error = 3.105e-63
relative error = 1.988e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.001
Order of pole (three term test) = 34.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.001
Order of pole (three term test) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26424.9MB, alloc=44.3MB, time=311.52
memory used=26471.5MB, alloc=44.3MB, time=312.07
x[1] = 0.3253 1.048
h = 0.0001 0.005
y2[1] (numeric) = 11.4860612839 12.6342718953
y2[1] (closed_form) = 13.7647611582 11.6650610418
absolute error = 2.476
relative error = 13.72 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.51731010164 -0.399699580598
y1[1] (closed_form) = 1.51731010164 -0.399699580598
absolute error = 3.105e-63
relative error = 1.979e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.025
Order of pole (three term test) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.025
Order of pole (three term test) = 30.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26517.5MB, alloc=44.3MB, time=312.61
memory used=26564.0MB, alloc=44.3MB, time=313.16
x[1] = 0.3254 1.053
h = 0.0001 0.003
y2[1] (numeric) = 11.488226835 12.6806799472
y2[1] (closed_form) = 13.7679183843 11.7226222049
absolute error = 2.473
relative error = 13.68 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.52320301373 -0.402382657538
y1[1] (closed_form) = 1.52320301373 -0.402382657538
absolute error = 4.079e-63
relative error = 2.589e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.046
Order of pole (three term test) = 34.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.046
Order of pole (three term test) = 30.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26610.1MB, alloc=44.3MB, time=313.70
memory used=26657.0MB, alloc=44.3MB, time=314.26
x[1] = 0.3255 1.056
h = 0.001 0.001
y2[1] (numeric) = 11.4904016986 12.7271040416
y2[1] (closed_form) = 13.7702805229 11.757156789
absolute error = 2.478
relative error = 13.68 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.52673621971 -0.404045943426
y1[1] (closed_form) = 1.52673621971 -0.404045943426
absolute error = 4.061e-63
relative error = 2.571e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.058
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.058
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26703.1MB, alloc=44.3MB, time=314.81
memory used=26749.6MB, alloc=44.3MB, time=315.36
x[1] = 0.3265 1.057
h = 0.001 0.003
y2[1] (numeric) = 11.4925859509 12.7735442133
y2[1] (closed_form) = 13.7822125026 11.7682789634
absolute error = 2.501
relative error = 13.8 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.52741769136 -0.405759907701
y1[1] (closed_form) = 1.52741769136 -0.405759907701
absolute error = 4.079e-63
relative error = 2.581e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.063
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.063
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26795.8MB, alloc=44.3MB, time=315.90
memory used=26842.0MB, alloc=44.3MB, time=316.45
memory used=26888.6MB, alloc=44.3MB, time=317.00
x[1] = 0.3275 1.06
h = 0.0001 0.004
y2[1] (numeric) = 11.4947796689 12.8200004971
y2[1] (closed_form) = 13.7949628716 11.8024587008
absolute error = 2.515
relative error = 13.85 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.53050020949 -0.408516036216
y1[1] (closed_form) = 1.53050020949 -0.408516036216
absolute error = 4.079e-63
relative error = 2.575e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.075
Order of pole (three term test) = 34.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.075
Order of pole (three term test) = 30.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26934.4MB, alloc=44.3MB, time=317.54
memory used=26980.9MB, alloc=44.3MB, time=318.10
x[1] = 0.3276 1.064
h = 0.003 0.006
y2[1] (numeric) = 11.4969829301 12.8664729274
y2[1] (closed_form) = 13.7977546294 11.8485492717
absolute error = 2.516
relative error = 13.83 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.53527013335 -0.410720018362
y1[1] (closed_form) = 1.53527013335 -0.410720018362
absolute error = 3.105e-63
relative error = 1.954e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.092
Order of pole (three term test) = 34.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.092
Order of pole (three term test) = 30.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27026.8MB, alloc=44.3MB, time=318.63
memory used=27073.5MB, alloc=44.3MB, time=319.19
x[1] = 0.3306 1.07
h = 0.0001 0.005
y2[1] (numeric) = 11.4991958126 12.9129615383
y2[1] (closed_form) = 13.8348536372 11.9165356497
absolute error = 2.539
relative error = 13.91 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.54096948326 -0.417509438169
y1[1] (closed_form) = 1.54096948326 -0.417509438169
absolute error = 3.105e-63
relative error = 1.945e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.118
Order of pole (three term test) = 34.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.118
Order of pole (three term test) = 30.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27119.4MB, alloc=44.3MB, time=319.72
memory used=27166.0MB, alloc=44.3MB, time=320.28
x[1] = 0.3307 1.075
h = 0.0001 0.003
y2[1] (numeric) = 11.5014183949 12.9594663636
y2[1] (closed_form) = 13.8381025083 11.9742137139
absolute error = 2.536
relative error = 13.86 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.5470183465 -0.420281359725
y1[1] (closed_form) = 1.5470183465 -0.420281359725
absolute error = 3.105e-63
relative error = 1.937e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.139
Order of pole (three term test) = 34.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.139
Order of pole (three term test) = 30.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27212.1MB, alloc=44.3MB, time=320.81
memory used=27258.9MB, alloc=44.3MB, time=321.37
memory used=27305.6MB, alloc=44.3MB, time=321.93
x[1] = 0.3308 1.078
h = 0.001 0.001
y2[1] (numeric) = 11.5036507563 13.0059874368
y2[1] (closed_form) = 13.8405208114 12.0088180911
absolute error = 2.541
relative error = 13.87 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.55064471041 -0.421999444826
y1[1] (closed_form) = 1.55064471041 -0.421999444826
absolute error = 3.105e-63
relative error = 1.932e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.152
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.152
Order of pole (three term test) = 30.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27351.7MB, alloc=44.3MB, time=322.47
memory used=27398.3MB, alloc=44.3MB, time=323.02
x[1] = 0.3318 1.079
h = 0.0001 0.004
y2[1] (numeric) = 11.5058929763 13.0525247911
y2[1] (closed_form) = 13.8524946847 12.0199462032
absolute error = 2.564
relative error = 13.98 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.5513405851 -0.423762334605
y1[1] (closed_form) = 1.5513405851 -0.423762334605
absolute error = 3.132e-63
relative error = 1.948e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.157
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.157
Order of pole (three term test) = 30.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27444.2MB, alloc=44.3MB, time=323.56
memory used=27490.6MB, alloc=44.3MB, time=324.10
x[1] = 0.3319 1.083
h = 0.003 0.006
y2[1] (numeric) = 11.5081451355 13.0990784593
y2[1] (closed_form) = 13.8553496391 12.0661188251
absolute error = 2.564
relative error = 13.96 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.55621916659 -0.426027323161
y1[1] (closed_form) = 1.55621916659 -0.426027323161
absolute error = 3.132e-63
relative error = 1.941e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.174
Order of pole (three term test) = 34.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.174
Order of pole (three term test) = 30.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27536.4MB, alloc=44.3MB, time=324.63
memory used=27583.0MB, alloc=44.3MB, time=325.19
x[1] = 0.3349 1.089
h = 0.0001 0.005
y2[1] (numeric) = 11.5104073145 13.1456484741
y2[1] (closed_form) = 13.8926040324 12.1341850843
absolute error = 2.588
relative error = 14.03 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.5620401556 -0.432987606916
y1[1] (closed_form) = 1.5620401556 -0.432987606916
absolute error = 3.132e-63
relative error = 1.932e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.201
Order of pole (three term test) = 34.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.201
Order of pole (three term test) = 30.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27629.0MB, alloc=44.3MB, time=325.72
memory used=27675.7MB, alloc=44.3MB, time=326.28
x[1] = 0.335 1.094
h = 0.0001 0.003
y2[1] (numeric) = 11.5126795949 13.1922348676
y2[1] (closed_form) = 13.8959325999 12.1919672926
absolute error = 2.585
relative error = 13.98 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.56822604706 -0.435836249668
y1[1] (closed_form) = 1.56822604706 -0.435836249668
absolute error = 3.132e-63
relative error = 1.924e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.223
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.223
Order of pole (three term test) = 30.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27722.2MB, alloc=44.3MB, time=326.82
memory used=27768.5MB, alloc=44.3MB, time=327.38
memory used=27815.2MB, alloc=44.3MB, time=327.94
x[1] = 0.3351 1.097
h = 0.001 0.001
y2[1] (numeric) = 11.5149620587 13.2388376717
y2[1] (closed_form) = 13.8983997634 12.2266338578
absolute error = 2.589
relative error = 13.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.57193427948 -0.437601676763
y1[1] (closed_form) = 1.57193427948 -0.437601676763
absolute error = 4.100e-63
relative error = 2.513e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.237
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.237
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27861.1MB, alloc=44.3MB, time=328.48
memory used=27907.6MB, alloc=44.3MB, time=329.04
x[1] = 0.3361 1.098
h = 0.001 0.003
y2[1] (numeric) = 11.5172547885 13.2854569181
y2[1] (closed_form) = 13.9104105564 12.2377676423
absolute error = 2.612
relative error = 14.1 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.57264307537 -0.439407282554
y1[1] (closed_form) = 1.57264307537 -0.439407282554
absolute error = 4.079e-63
relative error = 2.498e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.241
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.241
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27953.5MB, alloc=44.3MB, time=329.57
memory used=28000.2MB, alloc=44.3MB, time=330.14
x[1] = 0.3371 1.101
h = 0.0001 0.004
y2[1] (numeric) = 11.5195578674 13.332092638
y2[1] (closed_form) = 13.9233074004 12.2720495499
absolute error = 2.627
relative error = 14.15 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.57587194149 -0.44231976453
y1[1] (closed_form) = 1.57587194149 -0.44231976453
absolute error = 3.105e-63
relative error = 1.897e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.255
Order of pole (three term test) = 34.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.255
Order of pole (three term test) = 30.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28046.1MB, alloc=44.3MB, time=330.68
memory used=28092.6MB, alloc=44.3MB, time=331.25
x[1] = 0.3372 1.105
h = 0.003 0.006
y2[1] (numeric) = 11.5218713793 13.3787448624
y2[1] (closed_form) = 13.9262391932 12.3183186913
absolute error = 2.628
relative error = 14.13 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.58087734412 -0.444659372678
y1[1] (closed_form) = 1.58087734412 -0.444659372678
absolute error = 4.100e-63
relative error = 2.497e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.273
Order of pole (three term test) = 34.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.273
Order of pole (three term test) = 30.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28138.4MB, alloc=44.3MB, time=331.80
memory used=28185.1MB, alloc=44.3MB, time=332.37
x[1] = 0.3402 1.111
h = 0.0001 0.005
y2[1] (numeric) = 11.5241954084 13.4254136218
y2[1] (closed_form) = 13.9636801757 12.3864771154
absolute error = 2.652
relative error = 14.21 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.58683786057 -0.451824290492
y1[1] (closed_form) = 1.58683786057 -0.451824290492
absolute error = 4.079e-63
relative error = 2.472e-61 %
Correct digits = 63
memory used=28231.8MB, alloc=44.3MB, time=332.94
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.301
Order of pole (three term test) = 34.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.301
Order of pole (three term test) = 30.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28277.9MB, alloc=44.3MB, time=333.50
memory used=28324.8MB, alloc=44.3MB, time=334.07
x[1] = 0.3403 1.116
h = 0.0001 0.003
y2[1] (numeric) = 11.5265300398 13.4720989467
y2[1] (closed_form) = 13.9671056488 12.4443818235
absolute error = 2.648
relative error = 14.16 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.59318370566 -0.454766791343
y1[1] (closed_form) = 1.59318370566 -0.454766791343
absolute error = 3.132e-63
relative error = 1.890e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.324
Order of pole (three term test) = 34.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.324
Order of pole (three term test) = 30.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28370.9MB, alloc=44.3MB, time=334.64
memory used=28417.6MB, alloc=44.3MB, time=335.23
x[1] = 0.3404 1.119
h = 0.001 0.001
y2[1] (numeric) = 11.5288753589 13.5188008668
y2[1] (closed_form) = 13.9696321913 12.4791215089
absolute error = 2.653
relative error = 14.16 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.59698747101 -0.456590071714
y1[1] (closed_form) = 1.59698747101 -0.456590071714
absolute error = 4.100e-63
relative error = 2.468e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.338
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.338
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28463.6MB, alloc=44.3MB, time=335.81
memory used=28510.1MB, alloc=44.3MB, time=336.39
x[1] = 0.3414 1.12
h = 0.001 0.003
y2[1] (numeric) = 11.5312314519 13.5655194119
y2[1] (closed_form) = 13.9816870583 12.49026134
absolute error = 2.676
relative error = 14.27 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.59771050312 -0.458446422643
y1[1] (closed_form) = 1.59771050312 -0.458446422643
absolute error = 3.132e-63
relative error = 1.884e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.343
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.343
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28555.9MB, alloc=44.3MB, time=336.97
memory used=28602.6MB, alloc=44.3MB, time=337.56
x[1] = 0.3424 1.123
h = 0.0001 0.004
y2[1] (numeric) = 11.5335984055 13.6122546113
y2[1] (closed_form) = 13.9946662579 12.5245994859
absolute error = 2.691
relative error = 14.33 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.60101861699 -0.461446379376
y1[1] (closed_form) = 1.60101861699 -0.461446379376
absolute error = 3.132e-63
relative error = 1.880e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.357
Order of pole (three term test) = 34.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.357
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28648.7MB, alloc=44.3MB, time=338.12
memory used=28695.1MB, alloc=44.3MB, time=338.71
memory used=28741.5MB, alloc=44.3MB, time=339.30
x[1] = 0.3425 1.127
h = 0.003 0.006
y2[1] (numeric) = 11.5359763071 13.6590064938
y2[1] (closed_form) = 13.9976772318 12.5709675545
absolute error = 2.691
relative error = 14.31 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.60615257722 -0.463862841145
y1[1] (closed_form) = 1.60615257722 -0.463862841145
absolute error = 3.132e-63
relative error = 1.873e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.376
Order of pole (three term test) = 34.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.376
Order of pole (three term test) = 30.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28787.4MB, alloc=44.3MB, time=339.86
memory used=28834.0MB, alloc=44.3MB, time=340.45
x[1] = 0.3455 1.133
h = 0.0001 0.005
y2[1] (numeric) = 11.5383652444 13.7057750881
y2[1] (closed_form) = 14.0353100989 12.6392201277
absolute error = 2.715
relative error = 14.38 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.61225366766 -0.471237049766
y1[1] (closed_form) = 1.61225366766 -0.471237049766
absolute error = 3.132e-63
relative error = 1.865e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.405
Order of pole (three term test) = 34.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.405
Order of pole (three term test) = 30.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28880.0MB, alloc=44.3MB, time=341.03
memory used=28926.7MB, alloc=44.3MB, time=341.62
x[1] = 0.3456 1.138
h = 0.0001 0.003
y2[1] (numeric) = 11.5407653061 13.7525604225
y2[1] (closed_form) = 14.038835427 12.6972503739
absolute error = 2.712
relative error = 14.33 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.61876167334 -0.474276230234
y1[1] (closed_form) = 1.61876167334 -0.474276230234
absolute error = 3.132e-63
relative error = 1.857e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.43
Order of pole (three term test) = 34.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.43
Order of pole (three term test) = 30.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28972.7MB, alloc=44.3MB, time=342.18
memory used=29019.5MB, alloc=44.3MB, time=342.77
x[1] = 0.3457 1.141
h = 0.001 0.001
y2[1] (numeric) = 11.5431765813 13.7993625249
y2[1] (closed_form) = 14.0414231497 12.7320649845
absolute error = 2.717
relative error = 14.33 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.62266228062 -0.476159082261
y1[1] (closed_form) = 1.62266228062 -0.476159082261
absolute error = 3.132e-63
relative error = 1.852e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.444
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.444
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29065.5MB, alloc=44.3MB, time=343.34
memory used=29111.9MB, alloc=44.3MB, time=343.92
x[1] = 0.3467 1.142
h = 0.001 0.003
y2[1] (numeric) = 11.5455991597 13.8461814228
y2[1] (closed_form) = 14.0535232935 12.7432109026
absolute error = 2.74
relative error = 14.44 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.62339944566 -0.478067193304
y1[1] (closed_form) = 1.62339944566 -0.478067193304
absolute error = 3.132e-63
relative error = 1.851e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.449
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.449
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29158.2MB, alloc=44.3MB, time=344.48
memory used=29204.6MB, alloc=44.3MB, time=345.04
memory used=29251.4MB, alloc=44.3MB, time=345.63
x[1] = 0.3477 1.145
h = 0.0001 0.004
y2[1] (numeric) = 11.5480331317 13.8930171434
y2[1] (closed_form) = 14.0665872187 12.7776065698
absolute error = 2.754
relative error = 14.49 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.6267876159 -0.481156764054
y1[1] (closed_form) = 1.6267876159 -0.481156764054
absolute error = 2.236e-63
relative error = 1.318e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.464
Order of pole (three term test) = 34.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.464
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29297.3MB, alloc=44.3MB, time=346.17
memory used=29343.7MB, alloc=44.3MB, time=346.73
x[1] = 0.3478 1.149
h = 0.003 0.006
y2[1] (numeric) = 11.5504785882 13.9398697138
y2[1] (closed_form) = 14.0696797758 12.8240759999
absolute error = 2.755
relative error = 14.47 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.63205191084 -0.483652378496
y1[1] (closed_form) = 1.63205191084 -0.483652378496
absolute error = 3.162e-63
relative error = 1.858e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.484
Order of pole (three term test) = 34.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.484
Order of pole (three term test) = 30.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29389.7MB, alloc=44.3MB, time=347.27
memory used=29436.5MB, alloc=44.3MB, time=347.83
x[1] = 0.3508 1.155
h = 0.0001 0.005
y2[1] (numeric) = 11.5529356209 13.9867391603
y2[1] (closed_form) = 14.1075099321 12.8924247047
absolute error = 2.779
relative error = 14.54 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.63829463711 -0.491240662874
y1[1] (closed_form) = 1.63829463711 -0.491240662874
absolute error = 3.162e-63
relative error = 1.849e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.515
Order of pole (three term test) = 34.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.515
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29482.5MB, alloc=44.3MB, time=348.38
memory used=29529.2MB, alloc=44.3MB, time=348.94
x[1] = 0.3509 1.16
h = 0.0001 0.003
y2[1] (numeric) = 11.5554043218 14.0336255091
y2[1] (closed_form) = 14.1111381392 12.9505835612
absolute error = 2.776
relative error = 14.49 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.64496706174 -0.494379426373
y1[1] (closed_form) = 1.64496706174 -0.494379426373
absolute error = 2.236e-63
relative error = 1.302e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.54
Order of pole (three term test) = 34.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.54
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29575.3MB, alloc=44.3MB, time=349.48
memory used=29622.1MB, alloc=44.3MB, time=350.05
x[1] = 0.351 1.163
h = 0.001 0.001
y2[1] (numeric) = 11.5578847839 14.0805287861
y2[1] (closed_form) = 14.113788889 12.9854749218
absolute error = 2.781
relative error = 14.5 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.64896585022 -0.496323618183
y1[1] (closed_form) = 1.64896585022 -0.496323618183
absolute error = 2.193e-63
relative error = 1.274e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.555
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.555
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29668.8MB, alloc=44.3MB, time=350.61
memory used=29714.9MB, alloc=44.3MB, time=351.17
memory used=29761.2MB, alloc=44.3MB, time=351.73
x[1] = 0.352 1.164
h = 0.001 0.003
y2[1] (numeric) = 11.5603771005 14.1274490166
y2[1] (closed_form) = 14.1259355343 12.9966269595
absolute error = 2.804
relative error = 14.61 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.64971703927 -0.49828453121
y1[1] (closed_form) = 1.64971703927 -0.49828453121
absolute error = 2.236e-63
relative error = 1.298e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.561
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.561
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29807.1MB, alloc=44.3MB, time=352.28
memory used=29853.8MB, alloc=44.3MB, time=352.84
x[1] = 0.353 1.167
h = 0.0001 0.004
y2[1] (numeric) = 11.5628813658 14.1743862258
y2[1] (closed_form) = 14.1390866072 13.0310814376
absolute error = 2.819
relative error = 14.66 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.65318609007 -0.501465914766
y1[1] (closed_form) = 1.65318609007 -0.501465914766
absolute error = 3.162e-63
relative error = 1.830e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.576
Order of pole (three term test) = 34.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.576
Order of pole (three term test) = 30.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29899.7MB, alloc=44.3MB, time=353.38
memory used=29946.2MB, alloc=44.3MB, time=353.94
x[1] = 0.3531 1.171
h = 0.003 0.006
y2[1] (numeric) = 11.5653976744 14.2213404384
y2[1] (closed_form) = 14.1422632102 13.0776546908
absolute error = 2.819
relative error = 14.64 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.65858253782 -0.504043047413
y1[1] (closed_form) = 1.65858253782 -0.504043047413
absolute error = 2.193e-63
relative error = 1.265e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.597
Order of pole (three term test) = 34.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.597
Order of pole (three term test) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29992.0MB, alloc=44.3MB, time=354.49
memory used=30038.5MB, alloc=44.3MB, time=355.06
x[1] = 0.3561 1.177
h = 0.0001 0.005
y2[1] (numeric) = 11.5679261217 14.2683116788
y2[1] (closed_form) = 14.1802961727 13.1461015074
absolute error = 2.843
relative error = 14.7 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.6649679764 -0.511850323136
y1[1] (closed_form) = 1.6649679764 -0.511850323136
absolute error = 2.236e-63
relative error = 1.284e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.629
Order of pole (three term test) = 34.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.629
Order of pole (three term test) = 30.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30084.7MB, alloc=44.3MB, time=355.60
memory used=30131.0MB, alloc=44.3MB, time=356.16
memory used=30177.6MB, alloc=44.3MB, time=356.73
x[1] = 0.3562 1.182
h = 0.0001 0.003
y2[1] (numeric) = 11.5704668036 14.3152999709
y2[1] (closed_form) = 14.18403036 13.204392081
absolute error = 2.84
relative error = 14.65 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.67180713007 -0.515091656827
y1[1] (closed_form) = 1.67180713007 -0.515091656827
absolute error = 2.236e-63
relative error = 1.278e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.655
Order of pole (three term test) = 34.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.655
Order of pole (three term test) = 30.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30223.7MB, alloc=44.3MB, time=357.28
memory used=30270.6MB, alloc=44.3MB, time=357.86
x[1] = 0.3563 1.185
h = 0.001 0.001
y2[1] (numeric) = 11.5730198167 14.3623053383
y2[1] (closed_form) = 14.1867460301 13.2393620367
absolute error = 2.845
relative error = 14.66 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.67590546946 -0.51709900741
y1[1] (closed_form) = 1.67590546946 -0.51709900741
absolute error = 2.283e-63
relative error = 1.301e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.671
Order of pole (three term test) = 34.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.671
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30316.7MB, alloc=44.3MB, time=358.41
memory used=30363.4MB, alloc=44.3MB, time=358.97
x[1] = 0.3573 1.186
h = 0.0001 0.004
y2[1] (numeric) = 11.5755852582 14.4093278043
y2[1] (closed_form) = 14.1989404243 13.2505202187
absolute error = 2.868
relative error = 14.77 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.67667056769 -0.519113791637
y1[1] (closed_form) = 1.67667056769 -0.519113791637
absolute error = 2.283e-63
relative error = 1.300e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.677
Order of pole (three term test) = 34.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.677
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30409.5MB, alloc=44.3MB, time=359.52
memory used=30456.0MB, alloc=44.3MB, time=360.08
x[1] = 0.3574 1.19
h = 0.003 0.006
y2[1] (numeric) = 11.5781632261 14.4563673918
y2[1] (closed_form) = 14.202190114 13.2971858739
absolute error = 2.869
relative error = 14.74 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.68218326618 -0.521761434123
y1[1] (closed_form) = 1.68218326618 -0.521761434123
absolute error = 2.283e-63
relative error = 1.296e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.698
Order of pole (three term test) = 34.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.698
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30501.8MB, alloc=44.3MB, time=360.62
memory used=30548.4MB, alloc=44.3MB, time=361.19
x[1] = 0.3604 1.196
h = 0.0001 0.005
y2[1] (numeric) = 11.5807538188 14.5034241232
y2[1] (closed_form) = 14.2404009504 13.365721233
absolute error = 2.893
relative error = 14.81 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.68869511025 -0.529759530445
y1[1] (closed_form) = 1.68869511025 -0.529759530445
absolute error = 2.283e-63
relative error = 1.290e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.731
Order of pole (three term test) = 34.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.731
Order of pole (three term test) = 30.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30594.9MB, alloc=44.3MB, time=361.74
memory used=30641.1MB, alloc=44.3MB, time=362.30
memory used=30687.7MB, alloc=44.3MB, time=362.86
x[1] = 0.3605 1.201
h = 0.0001 0.003
y2[1] (numeric) = 11.5833571356 14.5504980206
y2[1] (closed_form) = 14.2442272854 13.4241290134
absolute error = 2.889
relative error = 14.76 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.69568094018 -0.53308958603
y1[1] (closed_form) = 1.69568094018 -0.53308958603
absolute error = 2.332e-63
relative error = 1.312e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.758
Order of pole (three term test) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.758
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30733.8MB, alloc=44.3MB, time=363.40
memory used=30780.6MB, alloc=44.3MB, time=363.98
x[1] = 0.3606 1.204
h = 0.001 0.001
y2[1] (numeric) = 11.5859732762 14.5975891058
y2[1] (closed_form) = 14.246999423 13.4591689194
absolute error = 2.894
relative error = 14.77 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.69986687271 -0.535151589235
y1[1] (closed_form) = 1.69986687271 -0.535151589235
absolute error = 2.332e-63
relative error = 1.309e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.775
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.775
Order of pole (three term test) = 30.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30826.6MB, alloc=44.3MB, time=364.53
memory used=30872.9MB, alloc=44.3MB, time=365.10
x[1] = 0.3616 1.205
h = 0.001 0.003
y2[1] (numeric) = 11.5886023412 14.6446974001
y2[1] (closed_form) = 14.259235861 13.4703329929
absolute error = 2.917
relative error = 14.87 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.70064450637 -0.537213457703
y1[1] (closed_form) = 1.70064450637 -0.537213457703
absolute error = 2.332e-63
relative error = 1.308e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.781
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.781
Order of pole (three term test) = 30.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30918.8MB, alloc=44.3MB, time=365.65
memory used=30965.4MB, alloc=44.3MB, time=366.22
x[1] = 0.3626 1.208
h = 0.0001 0.004
y2[1] (numeric) = 11.5912444316 14.6918229243
y2[1] (closed_form) = 14.2725549888 13.5049014674
absolute error = 2.932
relative error = 14.92 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.7042674619 -0.540570757159
y1[1] (closed_form) = 1.7042674619 -0.540570757159
absolute error = 2.332e-63
relative error = 1.305e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.798
Order of pole (three term test) = 34.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.798
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31011.3MB, alloc=44.3MB, time=366.77
memory used=31057.9MB, alloc=44.3MB, time=367.34
x[1] = 0.3627 1.212
h = 0.003 0.006
y2[1] (numeric) = 11.5938996493 14.7389656992
y2[1] (closed_form) = 14.2758934449 13.5516756313
absolute error = 2.933
relative error = 14.9 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.70991583633 -0.543304478862
y1[1] (closed_form) = 1.70991583633 -0.543304478862
absolute error = 2.283e-63
relative error = 1.272e-61 %
Correct digits = 63
memory used=31104.5MB, alloc=44.3MB, time=367.91
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 34.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.82
Order of pole (three term test) = 30.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31150.4MB, alloc=44.3MB, time=368.46
memory used=31197.0MB, alloc=44.3MB, time=369.03
x[1] = 0.3657 1.218
h = 0.0001 0.005
y2[1] (numeric) = 11.5965680968 14.7861257447
y2[1] (closed_form) = 14.3143176391 13.6203128489
absolute error = 2.957
relative error = 14.97 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.71657249485 -0.551531056354
y1[1] (closed_form) = 1.71657249485 -0.551531056354
absolute error = 2.283e-63
relative error = 1.266e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.855
Order of pole (three term test) = 34.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.855
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31242.9MB, alloc=44.3MB, time=369.59
memory used=31289.6MB, alloc=44.3MB, time=370.16
x[1] = 0.3658 1.223
h = 0.0001 0.003
y2[1] (numeric) = 11.599249877 14.8333030808
y2[1] (closed_form) = 14.3182558986 13.6788582614
absolute error = 2.954
relative error = 14.92 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.72372952933 -0.554969440997
y1[1] (closed_form) = 1.72372952933 -0.554969440997
absolute error = 1.487e-63
relative error = 8.209e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.883
Order of pole (three term test) = 34.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.883
Order of pole (three term test) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31335.6MB, alloc=44.3MB, time=370.73
memory used=31382.5MB, alloc=44.3MB, time=371.31
x[1] = 0.3659 1.226
h = 0.001 0.001
y2[1] (numeric) = 11.601945094 14.8804977266
y2[1] (closed_form) = 14.3210965857 13.713980275
absolute error = 2.959
relative error = 14.92 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.7280176664 -0.557098109841
y1[1] (closed_form) = 1.7280176664 -0.557098109841
absolute error = 2.283e-63
relative error = 1.257e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.901
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.901
Order of pole (three term test) = 30.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31428.6MB, alloc=44.3MB, time=371.88
memory used=31475.1MB, alloc=44.3MB, time=372.46
x[1] = 0.3669 1.227
h = 0.001 0.003
y2[1] (numeric) = 11.604653852 14.9277097013
y2[1] (closed_form) = 14.3333831558 13.7251505317
absolute error = 2.982
relative error = 15.03 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.72880899229 -0.559215914983
y1[1] (closed_form) = 1.72880899229 -0.559215914983
absolute error = 1.414e-63
relative error = 7.783e-62 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.907
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.907
Order of pole (three term test) = 30.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31521.0MB, alloc=44.3MB, time=373.02
memory used=31567.5MB, alloc=44.3MB, time=373.59
memory used=31614.0MB, alloc=44.3MB, time=374.17
x[1] = 0.3679 1.23
h = 0.0001 0.004
y2[1] (numeric) = 11.6073762562 14.9749390233
y2[1] (closed_form) = 14.3467966447 13.759781573
absolute error = 2.997
relative error = 15.08 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.7325152998 -0.56267164658
y1[1] (closed_form) = 1.7325152998 -0.56267164658
absolute error = 2.283e-63
relative error = 1.253e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.924
Order of pole (three term test) = 34.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.924
Order of pole (three term test) = 30.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31659.9MB, alloc=44.3MB, time=374.73
memory used=31706.3MB, alloc=44.3MB, time=375.30
x[1] = 0.368 1.234
h = 0.003 0.006
y2[1] (numeric) = 11.6101124125 15.0221857108
y2[1] (closed_form) = 14.3502265132 13.8066667889
absolute error = 2.998
relative error = 15.05 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.73830128785 -0.565494011167
y1[1] (closed_form) = 1.73830128785 -0.565494011167
absolute error = 2.283e-63
relative error = 1.249e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.948
Order of pole (three term test) = 34.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.948
Order of pole (three term test) = 30.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31752.2MB, alloc=44.3MB, time=375.86
memory used=31798.8MB, alloc=44.3MB, time=376.44
x[1] = 0.371 1.24
h = 0.0001 0.005
y2[1] (numeric) = 11.6128624273 15.0694497815
y2[1] (closed_form) = 14.3888699204 13.8754078381
absolute error = 3.022
relative error = 15.12 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.74510387715 -0.573954372964
y1[1] (closed_form) = 1.74510387715 -0.573954372964
absolute error = 2.283e-63
relative error = 1.242e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.984
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.984
Order of pole (three term test) = 30.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31844.6MB, alloc=44.3MB, time=377.00
memory used=31891.3MB, alloc=44.3MB, time=377.58
x[1] = 0.3711 1.245
h = 0.0001 0.003
y2[1] (numeric) = 11.6156264078 15.1167312528
y2[1] (closed_form) = 14.392923437 13.9340940934
absolute error = 3.019
relative error = 15.07 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.75243457734 -0.577504323451
y1[1] (closed_form) = 1.75243457734 -0.577504323451
absolute error = 2.283e-63
relative error = 1.237e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.014
Order of pole (three term test) = 34.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.014
Order of pole (three term test) = 30.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31937.4MB, alloc=44.3MB, time=378.16
memory used=31984.4MB, alloc=44.3MB, time=378.74
x[1] = 0.3712 1.248
h = 0.001 0.001
y2[1] (numeric) = 11.6184044618 15.1640301415
y2[1] (closed_form) = 14.3958347073 13.9693001208
absolute error = 3.023
relative error = 15.07 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.75682637758 -0.579701628512
y1[1] (closed_form) = 1.75682637758 -0.579701628512
absolute error = 2.283e-63
relative error = 1.234e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.032
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.032
Order of pole (three term test) = 30.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32030.8MB, alloc=44.3MB, time=379.32
memory used=32076.9MB, alloc=44.3MB, time=379.89
memory used=32123.3MB, alloc=44.3MB, time=380.46
x[1] = 0.3722 1.249
h = 0.001 0.003
y2[1] (numeric) = 11.6211966978 15.2113464642
y2[1] (closed_form) = 14.408172725 13.9804765609
absolute error = 3.047
relative error = 15.18 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.75763126256 -0.581876520435
y1[1] (closed_form) = 1.75763126256 -0.581876520435
absolute error = 2.283e-63
relative error = 1.233e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.038
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.038
Order of pole (three term test) = 30.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32169.3MB, alloc=44.3MB, time=381.03
memory used=32216.1MB, alloc=44.3MB, time=381.60
x[1] = 0.3732 1.252
h = 0.0001 0.004
y2[1] (numeric) = 11.6240032251 15.258680237
y2[1] (closed_form) = 14.4216832113 14.0151714843
absolute error = 3.062
relative error = 15.22 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.76142180591 -0.585433124095
y1[1] (closed_form) = 1.76142180591 -0.585433124095
absolute error = 3.195e-63
relative error = 1.721e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.056
Order of pole (three term test) = 34.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.056
Order of pole (three term test) = 30.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32262.0MB, alloc=44.3MB, time=382.16
memory used=32308.4MB, alloc=44.3MB, time=382.74
x[1] = 0.3733 1.256
h = 0.003 0.006
y2[1] (numeric) = 11.6268241537 15.3060314755
y2[1] (closed_form) = 14.4252072057 14.0621703245
absolute error = 3.062
relative error = 15.2 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.76734738731 -0.588346767742
y1[1] (closed_form) = 1.76734738731 -0.588346767742
absolute error = 2.283e-63
relative error = 1.225e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.081
Order of pole (three term test) = 34.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.081
Order of pole (three term test) = 30.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32354.2MB, alloc=44.3MB, time=383.29
memory used=32400.8MB, alloc=44.3MB, time=383.86
x[1] = 0.3763 1.262
h = 0.0001 0.005
y2[1] (numeric) = 11.629659594 15.353400195
y2[1] (closed_form) = 14.4640758052 14.1310171748
absolute error = 3.087
relative error = 15.27 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.77429703575 -0.597046357601
y1[1] (closed_form) = 1.77429703575 -0.597046357601
absolute error = 3.195e-63
relative error = 1.707e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.118
Order of pole (three term test) = 34.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.118
Order of pole (three term test) = 30.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32446.9MB, alloc=44.3MB, time=384.42
memory used=32493.4MB, alloc=44.3MB, time=385.16
memory used=32540.0MB, alloc=44.3MB, time=386.22
x[1] = 0.3764 1.267
h = 0.0001 0.003
y2[1] (numeric) = 11.6325096575 15.4007864102
y2[1] (closed_form) = 14.4682479968 14.1898475212
absolute error = 3.083
relative error = 15.22 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.78180391598 -0.600711202083
y1[1] (closed_form) = 1.78180391598 -0.600711202083
absolute error = 3.195e-63
relative error = 1.699e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.15
Order of pole (three term test) = 34.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.15
Order of pole (three term test) = 30.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32586.1MB, alloc=44.3MB, time=387.24
memory used=32633.0MB, alloc=44.3MB, time=388.32
x[1] = 0.3765 1.27
h = 0.001 0.001
y2[1] (numeric) = 11.635374456 15.4481901355
y2[1] (closed_form) = 14.4712319358 14.22513949
absolute error = 3.088
relative error = 15.22 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.78630086924 -0.602979169409
y1[1] (closed_form) = 1.78630086924 -0.602979169409
absolute error = 3.195e-63
relative error = 1.695e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.169
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.169
Order of pole (three term test) = 30.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32679.0MB, alloc=44.3MB, time=389.35
memory used=32725.3MB, alloc=44.3MB, time=390.41
x[1] = 0.3775 1.271
h = 0.001 0.003
y2[1] (numeric) = 11.6382541023 15.495611385
y2[1] (closed_form) = 14.4836227414 14.2363221047
absolute error = 3.112
relative error = 15.32 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.78711917307 -0.605212327408
y1[1] (closed_form) = 1.78711917307 -0.605212327408
absolute error = 4.148e-63
relative error = 2.199e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.175
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.175
Order of pole (three term test) = 30.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32771.2MB, alloc=44.3MB, time=391.43
memory used=32818.0MB, alloc=44.3MB, time=392.50
x[1] = 0.3785 1.274
h = 0.0001 0.004
y2[1] (numeric) = 11.6411487099 15.5430501721
y2[1] (closed_form) = 14.4972329206 14.271082232
absolute error = 3.127
relative error = 15.37 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.79099485099 -0.608872308692
y1[1] (closed_form) = 1.79099485099 -0.608872308692
absolute error = 4.148e-63
relative error = 2.193e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.194
Order of pole (three term test) = 34.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.194
Order of pole (three term test) = 30.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32863.9MB, alloc=44.3MB, time=393.04
memory used=32910.5MB, alloc=44.3MB, time=393.59
x[1] = 0.3786 1.278
h = 0.003 0.006
y2[1] (numeric) = 11.6440583928 15.5905065099
y2[1] (closed_form) = 14.500853824 14.3181972989
absolute error = 3.127
relative error = 15.35 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.79706204783 -0.611879941745
y1[1] (closed_form) = 1.79706204783 -0.611879941745
absolute error = 4.148e-63
relative error = 2.185e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.22
Order of pole (three term test) = 34.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.22
Order of pole (three term test) = 30.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32956.6MB, alloc=44.3MB, time=394.13
memory used=33002.9MB, alloc=44.3MB, time=394.68
memory used=33049.5MB, alloc=44.3MB, time=395.24
x[1] = 0.3816 1.284
h = 0.0001 0.005
y2[1] (numeric) = 11.6469832658 15.637980411
y2[1] (closed_form) = 14.5399537224 14.3871519154
absolute error = 3.152
relative error = 15.41 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.80415989502 -0.620824346788
y1[1] (closed_form) = 1.80415989502 -0.620824346788
absolute error = 4.123e-63
relative error = 2.161e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.259
Order of pole (three term test) = 34.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.259
Order of pole (three term test) = 30.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33095.5MB, alloc=44.3MB, time=395.78
memory used=33142.2MB, alloc=44.3MB, time=396.33
x[1] = 0.3817 1.289
h = 0.0001 0.003
y2[1] (numeric) = 11.6499234445 15.6854718877
y2[1] (closed_form) = 14.5442480947 14.446129639
absolute error = 3.149
relative error = 15.36 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.81184552312 -0.624607506889
y1[1] (closed_form) = 1.81184552312 -0.624607506889
absolute error = 4.148e-63
relative error = 2.165e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.292
Order of pole (three term test) = 34.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.292
Order of pole (three term test) = 30.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33188.3MB, alloc=44.3MB, time=396.88
memory used=33235.2MB, alloc=44.3MB, time=397.44
x[1] = 0.3818 1.292
h = 0.001 0.001
y2[1] (numeric) = 11.6528790451 15.7329809518
y2[1] (closed_form) = 14.5473068412 14.4815094993
absolute error = 3.153
relative error = 15.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.81644915075 -0.626948219266
y1[1] (closed_form) = 1.81644915075 -0.626948219266
absolute error = 5.099e-63
relative error = 2.654e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.312
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.312
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33281.3MB, alloc=44.3MB, time=397.98
memory used=33328.0MB, alloc=44.3MB, time=398.56
x[1] = 0.3828 1.293
h = 0.0001 0.004
y2[1] (numeric) = 11.6558501847 15.7805076145
y2[1] (closed_form) = 14.5597518005 14.4926982701
absolute error = 3.177
relative error = 15.46 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.8172807257 -0.629240852333
y1[1] (closed_form) = 1.8172807257 -0.629240852333
absolute error = 4.123e-63
relative error = 2.144e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.318
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.318
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33373.9MB, alloc=44.3MB, time=399.10
memory used=33420.4MB, alloc=44.3MB, time=399.64
x[1] = 0.3829 1.297
h = 0.003 0.006
y2[1] (numeric) = 11.6588369809 15.8280518866
y2[1] (closed_form) = 14.5634569756 14.5399166888
absolute error = 3.177
relative error = 15.44 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.82347263713 -0.632329896104
y1[1] (closed_form) = 1.82347263713 -0.632329896104
absolute error = 4.123e-63
relative error = 2.136e-61 %
Correct digits = 63
memory used=33466.9MB, alloc=44.3MB, time=400.18
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.345
Order of pole (three term test) = 35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.345
Order of pole (three term test) = 30.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33513.0MB, alloc=44.3MB, time=400.72
memory used=33559.7MB, alloc=44.3MB, time=401.28
x[1] = 0.3859 1.303
h = 0.0001 0.005
y2[1] (numeric) = 11.661839552 15.8756137787
y2[1] (closed_form) = 14.6027596426 14.6089684936
absolute error = 3.202
relative error = 15.5 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.83070197896 -0.641487831439
y1[1] (closed_form) = 1.83070197896 -0.641487831439
absolute error = 4.123e-63
relative error = 2.125e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.386
Order of pole (three term test) = 35.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.386
Order of pole (three term test) = 30.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33605.6MB, alloc=44.3MB, time=401.81
memory used=33652.1MB, alloc=44.3MB, time=402.36
x[1] = 0.386 1.308
h = 0.0001 0.003
y2[1] (numeric) = 11.6648580174 15.9231933007
y2[1] (closed_form) = 14.6071602504 14.6680772494
absolute error = 3.199
relative error = 15.45 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.83854503131 -0.645373474713
y1[1] (closed_form) = 1.83854503131 -0.645373474713
absolute error = 4.123e-63
relative error = 2.116e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.42
Order of pole (three term test) = 35.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.42
Order of pole (three term test) = 30.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33698.1MB, alloc=44.3MB, time=402.90
memory used=33744.9MB, alloc=44.3MB, time=403.46
x[1] = 0.3861 1.311
h = 0.001 0.001
y2[1] (numeric) = 11.6678924967 15.9707904621
y2[1] (closed_form) = 14.6102840639 14.7035352694
absolute error = 3.204
relative error = 15.46 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.84324262448 -0.647777219775
y1[1] (closed_form) = 1.84324262448 -0.647777219775
absolute error = 4.123e-63
relative error = 2.110e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.44
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.44
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33791.0MB, alloc=44.3MB, time=404.00
memory used=33837.5MB, alloc=44.3MB, time=404.56
x[1] = 0.3871 1.312
h = 0.001 0.003
y2[1] (numeric) = 11.6709431107 16.0184052719
y2[1] (closed_form) = 14.6227766777 14.7147299847
absolute error = 3.227
relative error = 15.56 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.84408622712 -0.650121882632
y1[1] (closed_form) = 1.84408622712 -0.650121882632
absolute error = 5.099e-63
relative error = 2.608e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.447
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.447
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33883.4MB, alloc=44.3MB, time=405.09
memory used=33930.1MB, alloc=44.3MB, time=405.63
memory used=33976.5MB, alloc=44.3MB, time=406.18
x[1] = 0.3881 1.315
h = 0.0001 0.004
y2[1] (numeric) = 11.6740099807 16.0660377386
y2[1] (closed_form) = 14.6365789308 14.7496162478
absolute error = 3.242
relative error = 15.6 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.8481240679 -0.65398008457
y1[1] (closed_form) = 1.8481240679 -0.65398008457
absolute error = 5.099e-63
relative error = 2.601e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 35.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.468
Order of pole (three term test) = 30.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34022.5MB, alloc=44.3MB, time=406.72
memory used=34069.2MB, alloc=44.3MB, time=407.27
x[1] = 0.3882 1.319
h = 0.003 0.006
y2[1] (numeric) = 11.6770932288 16.1136878704
y2[1] (closed_form) = 14.6403863527 14.7969558519
absolute error = 3.243
relative error = 15.58 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.85446150561 -0.657168339072
y1[1] (closed_form) = 1.85446150561 -0.657168339072
absolute error = 5.080e-63
relative error = 2.582e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.496
Order of pole (three term test) = 35.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.496
Order of pole (three term test) = 30.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34115.1MB, alloc=44.3MB, time=407.80
memory used=34161.8MB, alloc=44.3MB, time=408.35
x[1] = 0.3912 1.325
h = 0.0001 0.005
y2[1] (numeric) = 11.6801929779 16.161355675
y2[1] (closed_form) = 14.6799320085 14.8661191429
absolute error = 3.267
relative error = 15.64 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.86184126469 -0.666581863328
y1[1] (closed_form) = 1.86184126469 -0.666581863328
absolute error = 4.123e-63
relative error = 2.085e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.538
Order of pole (three term test) = 35.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.538
Order of pole (three term test) = 30.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34207.8MB, alloc=44.3MB, time=408.89
memory used=34254.4MB, alloc=44.3MB, time=409.45
x[1] = 0.3913 1.33
h = 0.0001 0.003
y2[1] (numeric) = 11.6833093514 16.2090411594
y2[1] (closed_form) = 14.6844615216 14.9253815384
absolute error = 3.264
relative error = 15.59 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.86986803033 -0.670592413166
y1[1] (closed_form) = 1.86986803033 -0.670592413166
absolute error = 4.123e-63
relative error = 2.076e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.574
Order of pole (three term test) = 35.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.574
Order of pole (three term test) = 30.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34300.4MB, alloc=44.3MB, time=409.98
memory used=34347.2MB, alloc=44.3MB, time=410.54
x[1] = 0.3914 1.333
h = 0.001 0.001
y2[1] (numeric) = 11.6864424737 16.2567443305
y2[1] (closed_form) = 14.6876642448 14.960931166
absolute error = 3.269
relative error = 15.59 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.87467523962 -0.673072915352
y1[1] (closed_form) = 1.87467523962 -0.673072915352
absolute error = 4.123e-63
relative error = 2.070e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.596
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.596
Order of pole (three term test) = 30.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34393.6MB, alloc=44.3MB, time=411.09
memory used=34439.9MB, alloc=44.3MB, time=411.64
memory used=34486.4MB, alloc=44.3MB, time=412.19
x[1] = 0.3924 1.334
h = 0.001 0.003
y2[1] (numeric) = 11.6895924699 16.3044651943
y2[1] (closed_form) = 14.7002136243 14.9721319938
absolute error = 3.292
relative error = 15.69 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.87553183267 -0.675479385724
y1[1] (closed_form) = 1.87553183267 -0.675479385724
absolute error = 3.162e-63
relative error = 1.586e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.603
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.603
Order of pole (three term test) = 30.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34532.3MB, alloc=44.3MB, time=412.73
memory used=34578.8MB, alloc=44.3MB, time=413.28
x[1] = 0.3934 1.337
h = 0.0001 0.004
y2[1] (numeric) = 11.6927594658 16.3522037567
y2[1] (closed_form) = 14.7141236057 15.0070873125
absolute error = 3.307
relative error = 15.74 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.87965749225 -0.679448496513
y1[1] (closed_form) = 1.87965749225 -0.679448496513
absolute error = 4.123e-63
relative error = 2.063e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.625
Order of pole (three term test) = 35.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.625
Order of pole (three term test) = 30.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34624.6MB, alloc=44.3MB, time=413.81
memory used=34671.1MB, alloc=44.3MB, time=414.35
x[1] = 0.3935 1.341
h = 0.003 0.006
y2[1] (numeric) = 11.695943588 16.3999600228
y2[1] (closed_form) = 14.7180362661 15.0545507936
absolute error = 3.308
relative error = 15.71 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.88614260204 -0.682738893345
y1[1] (closed_form) = 1.88614260204 -0.682738893345
absolute error = 4.123e-63
relative error = 2.055e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.654
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.654
Order of pole (three term test) = 30.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34717.1MB, alloc=44.3MB, time=414.89
memory used=34763.7MB, alloc=44.3MB, time=415.44
x[1] = 0.3965 1.347
h = 0.0001 0.005
y2[1] (numeric) = 11.6991449638 16.4477339974
y2[1] (closed_form) = 14.7578313998 15.1238275224
absolute error = 3.333
relative error = 15.77 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.89367394757 -0.692414019454
y1[1] (closed_form) = 1.89367394757 -0.692414019454
absolute error = 4.123e-63
relative error = 2.045e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.698
Order of pole (three term test) = 35.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.698
Order of pole (three term test) = 30.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34809.6MB, alloc=44.3MB, time=415.97
memory used=34856.3MB, alloc=44.3MB, time=416.52
x[1] = 0.3966 1.352
h = 0.0001 0.003
y2[1] (numeric) = 11.7023637214 16.4955256849
y2[1] (closed_form) = 14.7624935874 15.1832469575
absolute error = 3.33
relative error = 15.72 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.90188715077 -0.696553176342
y1[1] (closed_form) = 1.90188715077 -0.696553176342
absolute error = 5.099e-63
relative error = 2.518e-61 %
Correct digits = 63
memory used=34903.0MB, alloc=44.3MB, time=417.07
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.735
Order of pole (three term test) = 35.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.735
Order of pole (three term test) = 29.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34949.1MB, alloc=44.3MB, time=417.62
memory used=34995.9MB, alloc=44.3MB, time=418.18
x[1] = 0.3967 1.355
h = 0.001 0.001
y2[1] (numeric) = 11.7055999896 16.5433350889
y2[1] (closed_form) = 14.7657775188 15.2188902092
absolute error = 3.334
relative error = 15.73 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.9068055894 -0.699112687696
y1[1] (closed_form) = 1.9068055894 -0.699112687696
absolute error = 4.123e-63
relative error = 2.030e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.758
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.758
Order of pole (three term test) = 29.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35041.9MB, alloc=44.3MB, time=418.72
memory used=35088.6MB, alloc=44.3MB, time=419.27
x[1] = 0.3977 1.356
h = 0.001 0.003
y2[1] (numeric) = 11.7088538981 16.5911622128
y2[1] (closed_form) = 14.7783851064 15.2300971024
absolute error = 3.358
relative error = 15.82 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.90767500216 -0.701582262519
y1[1] (closed_form) = 1.90767500216 -0.701582262519
absolute error = 4.148e-63
relative error = 2.041e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.765
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.765
Order of pole (three term test) = 29.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35134.6MB, alloc=44.3MB, time=419.81
memory used=35181.3MB, alloc=44.3MB, time=420.36
x[1] = 0.3987 1.359
h = 0.0001 0.004
y2[1] (numeric) = 11.7121255772 16.6390070595
y2[1] (closed_form) = 14.7924057544 15.2651228241
absolute error = 3.373
relative error = 15.87 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.91188943585 -0.705665053945
y1[1] (closed_form) = 1.91188943585 -0.705665053945
absolute error = 4.148e-63
relative error = 2.036e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.788
Order of pole (three term test) = 35.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.788
Order of pole (three term test) = 29.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35227.3MB, alloc=44.3MB, time=420.90
memory used=35273.8MB, alloc=44.3MB, time=421.44
x[1] = 0.3988 1.363
h = 0.003 0.006
y2[1] (numeric) = 11.7154151581 16.686869631
y2[1] (closed_form) = 14.7964267219 15.3127129056
absolute error = 3.374
relative error = 15.84 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.91852440707 -0.709060605717
y1[1] (closed_form) = 1.91852440707 -0.709060605717
absolute error = 4.148e-63
relative error = 2.028e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.818
Order of pole (three term test) = 35.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.818
Order of pole (three term test) = 29.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35319.8MB, alloc=44.3MB, time=421.97
memory used=35366.4MB, alloc=44.3MB, time=422.52
memory used=35413.0MB, alloc=44.3MB, time=423.07
x[1] = 0.4018 1.369
h = 0.0001 0.005
y2[1] (numeric) = 11.7187227729 16.7347499294
y2[1] (closed_form) = 14.8364779628 15.3821050172
absolute error = 3.399
relative error = 15.9 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.92620851635 -0.719003501232
y1[1] (closed_form) = 1.92620851635 -0.719003501232
absolute error = 4.176e-63
relative error = 2.031e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.865
Order of pole (three term test) = 35.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.865
Order of pole (three term test) = 29.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35459.0MB, alloc=44.3MB, time=423.61
memory used=35505.7MB, alloc=44.3MB, time=424.16
x[1] = 0.4019 1.374
h = 0.0001 0.003
y2[1] (numeric) = 11.7220485541 16.7826479557
y2[1] (closed_form) = 14.8412766915 15.4416849323
absolute error = 3.395
relative error = 15.85 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.93461093635 -0.723275067769
y1[1] (closed_form) = 1.93461093635 -0.723275067769
absolute error = 3.195e-63
relative error = 1.547e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.903
Order of pole (three term test) = 35.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.903
Order of pole (three term test) = 29.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35551.8MB, alloc=44.3MB, time=424.70
memory used=35598.5MB, alloc=44.3MB, time=425.26
x[1] = 0.402 1.377
h = 0.001 0.001
y2[1] (numeric) = 11.7253926355 16.830563711
y2[1] (closed_form) = 14.8446441886 15.4774238483
absolute error = 3.4
relative error = 15.85 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.93964224984 -0.725915902298
y1[1] (closed_form) = 1.93964224984 -0.725915902298
absolute error = 4.148e-63
relative error = 2.003e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.927
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.927
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35644.7MB, alloc=44.3MB, time=425.80
memory used=35691.2MB, alloc=44.3MB, time=426.36
x[1] = 0.403 1.378
h = 0.001 0.003
y2[1] (numeric) = 11.7287551511 16.8784971953
y2[1] (closed_form) = 14.8573114545 15.4886367492
absolute error = 3.423
relative error = 15.95 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.94052430274 -0.728449910272
y1[1] (closed_form) = 1.94052430274 -0.728449910272
absolute error = 4.176e-63
relative error = 2.015e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.935
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.935
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35736.9MB, alloc=44.3MB, time=426.89
memory used=35783.5MB, alloc=44.3MB, time=427.44
x[1] = 0.404 1.381
h = 0.0001 0.004
y2[1] (numeric) = 11.7321362362 16.9264484084
y2[1] (closed_form) = 14.8714457743 15.5237342274
absolute error = 3.438
relative error = 15.99 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.94482847982 -0.732649226652
y1[1] (closed_form) = 1.94482847982 -0.732649226652
absolute error = 4.176e-63
relative error = 2.009e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.959
Order of pole (three term test) = 35.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.959
Order of pole (three term test) = 29.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35829.8MB, alloc=44.3MB, time=427.97
memory used=35876.0MB, alloc=44.3MB, time=428.52
memory used=35922.5MB, alloc=44.3MB, time=429.06
x[1] = 0.4041 1.385
h = 0.003 0.006
y2[1] (numeric) = 11.7355360266 16.9744173496
y2[1] (closed_form) = 14.8755781963 15.5714536653
absolute error = 3.439
relative error = 15.97 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.9516155456 -0.736153028866
y1[1] (closed_form) = 1.9516155456 -0.736153028866
absolute error = 4.176e-63
relative error = 2.002e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.99
Order of pole (three term test) = 35.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.99
Order of pole (three term test) = 29.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35968.5MB, alloc=44.3MB, time=429.60
memory used=36015.2MB, alloc=44.3MB, time=430.15
x[1] = 0.4071 1.391
h = 0.0001 0.005
y2[1] (numeric) = 11.7389546591 17.0224040177
y2[1] (closed_form) = 14.9158923175 15.6409630977
absolute error = 3.464
relative error = 16.03 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.95945360313 -0.74637001905
y1[1] (closed_form) = 1.95945360313 -0.74637001905
absolute error = 4.176e-63
relative error = 1.992e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.039
Order of pole (three term test) = 35.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.039
Order of pole (three term test) = 29.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36061.1MB, alloc=44.3MB, time=430.68
memory used=36107.7MB, alloc=44.3MB, time=431.24
x[1] = 0.4072 1.396
h = 0.0001 0.003
y2[1] (numeric) = 11.742392271 17.0704084107
y2[1] (closed_form) = 14.9208315534 15.7007069745
absolute error = 3.461
relative error = 15.98 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.96804807459 -0.750777902335
y1[1] (closed_form) = 1.96804807459 -0.750777902335
absolute error = 4.176e-63
relative error = 1.983e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.079
Order of pole (three term test) = 35.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.079
Order of pole (three term test) = 29.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36153.7MB, alloc=44.3MB, time=431.77
memory used=36200.3MB, alloc=44.3MB, time=432.33
x[1] = 0.4073 1.399
h = 0.001 0.001
y2[1] (numeric) = 11.7458490006 17.1184305264
y2[1] (closed_form) = 14.9242850338 15.7365436193
absolute error = 3.466
relative error = 15.98 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.97319394093 -0.753502437447
y1[1] (closed_form) = 1.97319394093 -0.753502437447
absolute error = 4.176e-63
relative error = 1.977e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.104
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.104
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36246.4MB, alloc=44.3MB, time=432.87
memory used=36292.8MB, alloc=44.3MB, time=433.42
x[1] = 0.4083 1.4
h = 0.003 0.006
y2[1] (numeric) = 11.749324987 17.1664703619
y2[1] (closed_form) = 14.9370134772 15.7477624586
absolute error = 3.489
relative error = 16.08 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.97408844515 -0.756102239592
y1[1] (closed_form) = 1.97408844515 -0.756102239592
absolute error = 4.176e-63
relative error = 1.976e-61 %
Correct digits = 63
memory used=36339.2MB, alloc=44.3MB, time=433.96
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.112
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.112
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36385.4MB, alloc=44.3MB, time=434.50
memory used=36432.1MB, alloc=44.3MB, time=435.05
x[1] = 0.4113 1.406
h = 0.0001 0.005
y2[1] (numeric) = 11.7528203701 17.2145279138
y2[1] (closed_form) = 14.9775154495 15.8173468853
absolute error = 3.514
relative error = 16.13 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.98202599317 -0.766515443146
y1[1] (closed_form) = 1.98202599317 -0.766515443146
absolute error = 4.206e-63
relative error = 1.979e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.162
Order of pole (three term test) = 35.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.162
Order of pole (three term test) = 29.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36478.0MB, alloc=44.3MB, time=435.58
memory used=36524.6MB, alloc=44.3MB, time=436.13
x[1] = 0.4114 1.411
h = 0.0001 0.003
y2[1] (numeric) = 11.7563352906 17.2626031782
y2[1] (closed_form) = 14.9825579285 15.8772019299
absolute error = 3.511
relative error = 16.08 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.99075069374 -0.771024343915
y1[1] (closed_form) = 1.99075069374 -0.771024343915
absolute error = 4.206e-63
relative error = 1.970e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.204
Order of pole (three term test) = 35.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.204
Order of pole (three term test) = 29.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36570.9MB, alloc=44.3MB, time=436.69
memory used=36617.9MB, alloc=44.3MB, time=437.26
x[1] = 0.4115 1.414
h = 0.001 0.001
y2[1] (numeric) = 11.7598698899 17.3106961505
y2[1] (closed_form) = 14.9860745153 15.9131047711
absolute error = 3.516
relative error = 16.08 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.9959741684 -0.773810805567
y1[1] (closed_form) = 1.9959741684 -0.773810805567
absolute error = 4.206e-63
relative error = 1.965e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.229
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.229
Order of pole (three term test) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36664.0MB, alloc=44.3MB, time=437.80
memory used=36710.5MB, alloc=44.3MB, time=438.35
x[1] = 0.4125 1.415
h = 0.001 0.003
y2[1] (numeric) = 11.7634243105 17.3588068259
y2[1] (closed_form) = 14.9988460738 15.9243260625
absolute error = 3.539
relative error = 16.18 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.99687542396 -0.776456981128
y1[1] (closed_form) = 1.99687542396 -0.776456981128
absolute error = 4.206e-63
relative error = 1.963e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.238
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.238
Order of pole (three term test) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36756.5MB, alloc=44.3MB, time=438.88
memory used=36803.2MB, alloc=44.3MB, time=439.44
memory used=36849.9MB, alloc=44.3MB, time=439.98
x[1] = 0.4135 1.418
h = 0.0001 0.004
y2[1] (numeric) = 11.7669986954 17.4069351986
y2[1] (closed_form) = 15.0131811495 15.9595447102
absolute error = 3.554
relative error = 16.22 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.00133021574 -0.780861952185
y1[1] (closed_form) = 2.00133021574 -0.780861952185
absolute error = 3.270e-63
relative error = 1.522e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.263
Order of pole (three term test) = 35.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.263
Order of pole (three term test) = 29.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36895.9MB, alloc=44.3MB, time=440.52
memory used=36942.4MB, alloc=44.3MB, time=441.06
x[1] = 0.4136 1.422
h = 0.003 0.006
y2[1] (numeric) = 11.7705931887 17.4550812626
y2[1] (closed_form) = 15.0175124732 16.0074858417
absolute error = 3.555
relative error = 16.2 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.00837628302 -0.784559685562
y1[1] (closed_form) = 2.00837628302 -0.784559685562
absolute error = 4.206e-63
relative error = 1.951e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.297
Order of pole (three term test) = 35.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.297
Order of pole (three term test) = 29.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36988.4MB, alloc=44.3MB, time=441.60
memory used=37035.0MB, alloc=44.3MB, time=442.15
x[1] = 0.4166 1.428
h = 0.0001 0.005
y2[1] (numeric) = 11.7742079351 17.5032450111
y2[1] (closed_form) = 15.0582891419 16.0771906633
absolute error = 3.58
relative error = 16.25 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.016469624 -0.795258056813
y1[1] (closed_form) = 2.016469624 -0.795258056813
absolute error = 4.238e-63
relative error = 1.955e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.349
Order of pole (three term test) = 35.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.349
Order of pole (three term test) = 29.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37081.0MB, alloc=44.3MB, time=442.68
memory used=37127.7MB, alloc=44.3MB, time=443.24
x[1] = 0.4167 1.433
h = 0.0001 0.003
y2[1] (numeric) = 11.7778430802 17.5514264369
y2[1] (closed_form) = 15.063479146 16.1372155364
absolute error = 3.577
relative error = 16.2 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.02539118289 -0.799910187411
y1[1] (closed_form) = 2.02539118289 -0.799910187411
absolute error = 3.270e-63
relative error = 1.501e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.393
Order of pole (three term test) = 35.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.393
Order of pole (three term test) = 29.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37173.8MB, alloc=44.3MB, time=443.77
memory used=37220.5MB, alloc=44.3MB, time=444.33
x[1] = 0.4168 1.436
h = 0.001 0.001
y2[1] (numeric) = 11.7814987706 17.5996255322
y2[1] (closed_form) = 15.067085992 16.1732195822
absolute error = 3.582
relative error = 16.2 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.03073205346 -0.802784554454
y1[1] (closed_form) = 2.03073205346 -0.802784554454
absolute error = 3.270e-63
relative error = 1.497e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.419
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.419
Order of pole (three term test) = 29.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37267.0MB, alloc=44.3MB, time=444.88
memory used=37313.3MB, alloc=44.3MB, time=445.43
memory used=37359.9MB, alloc=44.3MB, time=445.98
x[1] = 0.4178 1.437
h = 0.001 0.003
y2[1] (numeric) = 11.7851751534 17.6478422886
y2[1] (closed_form) = 15.0799213222 16.1844466296
absolute error = 3.605
relative error = 16.3 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.03164538336 -0.805498891064
y1[1] (closed_form) = 2.03164538336 -0.805498891064
absolute error = 4.238e-63
relative error = 1.939e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.428
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.428
Order of pole (three term test) = 29.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37405.9MB, alloc=44.3MB, time=446.51
memory used=37452.5MB, alloc=44.3MB, time=447.06
x[1] = 0.4188 1.44
h = 0.0001 0.004
y2[1] (numeric) = 11.7888723769 17.6960766971
y2[1] (closed_form) = 15.0943785266 16.2197406215
absolute error = 3.62
relative error = 16.34 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.03619251354 -0.81002842917
y1[1] (closed_form) = 2.03619251354 -0.81002842917
absolute error = 4.206e-63
relative error = 1.919e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.455
Order of pole (three term test) = 35.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.455
Order of pole (three term test) = 29.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37498.4MB, alloc=44.3MB, time=447.60
memory used=37545.0MB, alloc=44.3MB, time=448.14
x[1] = 0.4189 1.444
h = 0.003 0.006
y2[1] (numeric) = 11.7925905901 17.7443287483
y2[1] (closed_form) = 15.0988302442 16.267818596
absolute error = 3.621
relative error = 16.31 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.04339681219 -0.813843219109
y1[1] (closed_form) = 2.04339681219 -0.813843219109
absolute error = 3.270e-63
relative error = 1.486e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.491
Order of pole (three term test) = 35.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.491
Order of pole (three term test) = 29.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37590.9MB, alloc=44.3MB, time=448.68
memory used=37637.7MB, alloc=44.3MB, time=449.23
x[1] = 0.4219 1.45
h = 0.0001 0.005
y2[1] (numeric) = 11.7963299427 17.792598432
y2[1] (closed_form) = 15.139888786 16.3376457238
absolute error = 3.646
relative error = 16.37 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.05164714102 -0.8248335232
y1[1] (closed_form) = 2.05164714102 -0.8248335232
absolute error = 3.311e-63
relative error = 1.497e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.545
Order of pole (three term test) = 35.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.545
Order of pole (three term test) = 29.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37683.7MB, alloc=44.3MB, time=449.76
memory used=37730.5MB, alloc=44.3MB, time=450.32
x[1] = 0.422 1.455
h = 0.0001 0.003
y2[1] (numeric) = 11.8000905854 17.8408857375
y2[1] (closed_form) = 15.1452305634 16.3978440188
absolute error = 3.643
relative error = 16.32 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.06076854081 -0.829633085305
y1[1] (closed_form) = 2.06076854081 -0.829633085305
absolute error = 3.311e-63
relative error = 1.490e-61 %
Correct digits = 63
memory used=37777.2MB, alloc=44.3MB, time=450.87
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.591
Order of pole (three term test) = 35.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.591
Order of pole (three term test) = 29.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37823.3MB, alloc=44.3MB, time=451.42
memory used=37870.2MB, alloc=44.3MB, time=451.98
x[1] = 0.4221 1.458
h = 0.001 0.001
y2[1] (numeric) = 11.8038726698 17.8891906537
y2[1] (closed_form) = 15.1489302574 16.4339513985
absolute error = 3.648
relative error = 16.32 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.06622857195 -0.832597913813
y1[1] (closed_form) = 2.06622857195 -0.832597913813
absolute error = 4.238e-63
relative error = 1.902e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.618
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.618
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37916.1MB, alloc=44.3MB, time=452.51
memory used=37962.6MB, alloc=44.3MB, time=453.07
x[1] = 0.4231 1.459
h = 0.001 0.003
y2[1] (numeric) = 11.8076763481 17.9375131686
y2[1] (closed_form) = 15.1618309383 16.4451841003
absolute error = 3.671
relative error = 16.41 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.06715375957 -0.835381862006
y1[1] (closed_form) = 2.06715375957 -0.835381862006
absolute error = 4.238e-63
relative error = 1.901e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.628
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.628
Order of pole (three term test) = 29.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38008.5MB, alloc=44.3MB, time=453.60
memory used=38055.3MB, alloc=44.3MB, time=454.15
x[1] = 0.4241 1.462
h = 0.0001 0.004
y2[1] (numeric) = 11.8115017737 17.9858532699
y2[1] (closed_form) = 15.176413538 16.4805548105
absolute error = 3.686
relative error = 16.45 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.07179424493 -0.840039092751
y1[1] (closed_form) = 2.07179424493 -0.840039092751
absolute error = 4.238e-63
relative error = 1.896e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.656
Order of pole (three term test) = 35.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.656
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38101.3MB, alloc=44.3MB, time=454.68
memory used=38147.8MB, alloc=44.3MB, time=455.24
x[1] = 0.4242 1.466
h = 0.003 0.006
y2[1] (numeric) = 11.8153491007 18.0342109444
y2[1] (closed_form) = 15.1809891072 16.528772506
absolute error = 3.687
relative error = 16.43 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.07915916988 -0.843974358672
y1[1] (closed_form) = 2.07915916988 -0.843974358672
absolute error = 4.272e-63
relative error = 1.904e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.693
Order of pole (three term test) = 35.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.693
Order of pole (three term test) = 29.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38193.8MB, alloc=44.3MB, time=455.76
memory used=38240.5MB, alloc=44.3MB, time=456.31
memory used=38287.1MB, alloc=44.3MB, time=456.86
x[1] = 0.4272 1.472
h = 0.0001 0.005
y2[1] (numeric) = 11.8192184839 18.0825861787
y2[1] (closed_form) = 15.2223368558 16.5987238414
absolute error = 3.713
relative error = 16.48 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.08756768493 -0.855263530456
y1[1] (closed_form) = 2.08756768493 -0.855263530456
absolute error = 4.238e-63
relative error = 1.879e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.75
Order of pole (three term test) = 35.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.75
Order of pole (three term test) = 29.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38333.1MB, alloc=44.3MB, time=457.40
memory used=38379.9MB, alloc=44.3MB, time=457.95
x[1] = 0.4273 1.477
h = 0.0001 0.003
y2[1] (numeric) = 11.8231100793 18.1309789584
y2[1] (closed_form) = 15.2278347645 16.6590991953
absolute error = 3.709
relative error = 16.43 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.09689196493 -0.860214839571
y1[1] (closed_form) = 2.09689196493 -0.860214839571
absolute error = 3.311e-63
relative error = 1.461e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.797
Order of pole (three term test) = 35.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.797
Order of pole (three term test) = 29.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38426.1MB, alloc=44.3MB, time=458.49
memory used=38473.0MB, alloc=44.3MB, time=459.06
x[1] = 0.4274 1.48
h = 0.001 0.001
y2[1] (numeric) = 11.8270240434 18.1793892689
y2[1] (closed_form) = 15.2316299617 16.6953120638
absolute error = 3.714
relative error = 16.43 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.10247295456 -0.863272754653
y1[1] (closed_form) = 2.10247295456 -0.863272754653
absolute error = 4.238e-63
relative error = 1.865e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.826
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.826
Order of pole (three term test) = 29.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38519.1MB, alloc=44.3MB, time=459.60
memory used=38565.8MB, alloc=44.3MB, time=460.15
x[1] = 0.4284 1.481
h = 0.0001 0.004
y2[1] (numeric) = 11.8309605339 18.2278170946
y2[1] (closed_form) = 15.2445976031 16.7065503054
absolute error = 3.737
relative error = 16.52 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.10340977243 -0.866127799464
y1[1] (closed_form) = 2.10340977243 -0.866127799464
absolute error = 4.238e-63
relative error = 1.863e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.836
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.836
Order of pole (three term test) = 29.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38611.8MB, alloc=44.3MB, time=460.69
memory used=38658.1MB, alloc=44.3MB, time=461.24
x[1] = 0.4285 1.485
h = 0.003 0.006
y2[1] (numeric) = 11.8349197092 18.2762624195
y2[1] (closed_form) = 15.2492809048 16.7548921321
absolute error = 3.738
relative error = 16.5 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.11091640365 -0.870167622718
y1[1] (closed_form) = 2.11091640365 -0.870167622718
absolute error = 4.238e-63
relative error = 1.856e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.875
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.875
Order of pole (three term test) = 29.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38704.2MB, alloc=44.3MB, time=461.77
memory used=38750.5MB, alloc=44.3MB, time=462.33
memory used=38797.1MB, alloc=44.3MB, time=462.88
x[1] = 0.4315 1.491
h = 0.0001 0.005
y2[1] (numeric) = 11.8389017286 18.324725227
y2[1] (closed_form) = 15.2908820781 16.8249554625
absolute error = 3.764
relative error = 16.55 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.11946571737 -0.881717831422
y1[1] (closed_form) = 2.11946571737 -0.881717831422
absolute error = 3.311e-63
relative error = 1.442e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.934
Order of pole (three term test) = 35.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.934
Order of pole (three term test) = 29.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38843.0MB, alloc=44.3MB, time=463.42
memory used=38889.7MB, alloc=44.3MB, time=463.97
x[1] = 0.4316 1.496
h = 0.0001 0.003
y2[1] (numeric) = 11.8429067523 18.3732054999
y2[1] (closed_form) = 15.2965157859 16.8854881017
absolute error = 3.76
relative error = 16.5 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.12896898703 -0.886800836883
y1[1] (closed_form) = 2.12896898703 -0.886800836883
absolute error = 3.311e-63
relative error = 1.435e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.983
Order of pole (three term test) = 35.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.983
Order of pole (three term test) = 29.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38935.8MB, alloc=44.3MB, time=464.51
memory used=38982.6MB, alloc=44.3MB, time=465.07
x[1] = 0.4317 1.499
h = 0.001 0.001
y2[1] (numeric) = 11.8469349414 18.4217032203
y2[1] (closed_form) = 15.3003940754 16.9217946987
absolute error = 3.765
relative error = 16.5 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.13465671163 -0.88993956318
y1[1] (closed_form) = 2.13465671163 -0.88993956318
absolute error = 3.311e-63
relative error = 1.431e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.013
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.013
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39028.8MB, alloc=44.3MB, time=465.61
memory used=39075.3MB, alloc=44.3MB, time=466.16
x[1] = 0.4327 1.5
h = 0.001 0.003
y2[1] (numeric) = 11.8509864578 18.4702183696
y2[1] (closed_form) = 15.3134206038 16.9330384314
absolute error = 3.788
relative error = 16.59 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.13560422134 -0.892856886926
y1[1] (closed_form) = 2.13560422134 -0.892856886926
absolute error = 3.311e-63
relative error = 1.430e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.023
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.023
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39121.0MB, alloc=44.3MB, time=466.69
memory used=39167.7MB, alloc=44.3MB, time=467.25
x[1] = 0.4337 1.503
h = 0.0001 0.004
y2[1] (numeric) = 11.8550614645 18.5187509288
y2[1] (closed_form) = 15.3282445355 16.9685571626
absolute error = 3.803
relative error = 16.63 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.1404227814 -0.897759176755
y1[1] (closed_form) = 2.1404227814 -0.897759176755
absolute error = 3.311e-63
relative error = 1.426e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.054
Order of pole (three term test) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.054
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39214.2MB, alloc=44.3MB, time=467.82
memory used=39260.2MB, alloc=44.3MB, time=468.36
memory used=39306.8MB, alloc=44.3MB, time=468.90
x[1] = 0.4338 1.507
h = 0.003 0.006
y2[1] (numeric) = 11.8591601253 18.5673008781
y2[1] (closed_form) = 15.3330583262 17.0170442022
absolute error = 3.804
relative error = 16.61 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.14809465904 -0.901926056482
y1[1] (closed_form) = 2.14809465904 -0.901926056482
absolute error = 3.270e-63
relative error = 1.403e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.094
Order of pole (three term test) = 36.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.094
Order of pole (three term test) = 29.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39352.7MB, alloc=44.3MB, time=469.44
memory used=39399.3MB, alloc=44.3MB, time=469.99
x[1] = 0.4368 1.513
h = 0.0001 0.005
y2[1] (numeric) = 11.8632826046 18.6158681971
y2[1] (closed_form) = 15.3749627611 17.0872353406
absolute error = 3.83
relative error = 16.66 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.15680448203 -0.913788486239
y1[1] (closed_form) = 2.15680448203 -0.913788486239
absolute error = 3.270e-63
relative error = 1.396e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.156
Order of pole (three term test) = 36.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.156
Order of pole (three term test) = 29.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39445.3MB, alloc=44.3MB, time=470.53
memory used=39491.9MB, alloc=44.3MB, time=471.08
x[1] = 0.4369 1.518
h = 0.0001 0.003
y2[1] (numeric) = 11.8674290683 18.6644528649
y2[1] (closed_form) = 15.3807609664 17.1479519801
absolute error = 3.827
relative error = 16.61 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.16651649436 -0.919031543195
y1[1] (closed_form) = 2.16651649436 -0.919031543195
absolute error = 3.311e-63
relative error = 1.407e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.208
Order of pole (three term test) = 36.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.208
Order of pole (three term test) = 29.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39537.9MB, alloc=44.3MB, time=471.64
memory used=39584.8MB, alloc=44.3MB, time=472.20
x[1] = 0.437 1.521
h = 0.001 0.001
y2[1] (numeric) = 11.8715996826 18.7130548596
y2[1] (closed_form) = 15.384739856 17.1843681782
absolute error = 3.831
relative error = 16.61 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.17232864536 -0.922268407721
y1[1] (closed_form) = 2.17232864536 -0.922268407721
absolute error = 4.238e-63
relative error = 1.796e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.239
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.239
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39631.0MB, alloc=44.3MB, time=472.74
memory used=39677.5MB, alloc=44.3MB, time=473.29
memory used=39723.9MB, alloc=44.3MB, time=473.84
x[1] = 0.438 1.522
h = 0.001 0.003
y2[1] (numeric) = 11.875794615 18.7616741591
y2[1] (closed_form) = 15.3978364278 17.1956172226
absolute error = 3.855
relative error = 16.7 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.17328735042 -0.925259688404
y1[1] (closed_form) = 2.17328735042 -0.925259688404
absolute error = 4.238e-63
relative error = 1.794e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.249
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.249
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39770.0MB, alloc=44.3MB, time=474.38
memory used=39816.8MB, alloc=44.3MB, time=474.93
x[1] = 0.439 1.525
h = 0.0001 0.004
y2[1] (numeric) = 11.8800140338 18.8103107403
y2[1] (closed_form) = 15.4127955047 17.2312166765
absolute error = 3.87
relative error = 16.74 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.17820228454 -0.930299047435
y1[1] (closed_form) = 2.17820228454 -0.930299047435
absolute error = 4.238e-63
relative error = 1.789e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.281
Order of pole (three term test) = 36.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.281
Order of pole (three term test) = 29.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39862.7MB, alloc=44.3MB, time=475.46
memory used=39909.3MB, alloc=44.3MB, time=476.01
x[1] = 0.4391 1.529
h = 0.003 0.006
y2[1] (numeric) = 11.8842581082 18.8589645797
y2[1] (closed_form) = 15.4177435025 17.2798519089
absolute error = 3.87
relative error = 16.71 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.1860419346 -0.934596672629
y1[1] (closed_form) = 2.1860419346 -0.934596672629
absolute error = 4.238e-63
relative error = 1.783e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.323
Order of pole (three term test) = 36.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.323
Order of pole (three term test) = 29.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39955.3MB, alloc=44.3MB, time=476.54
memory used=40001.9MB, alloc=44.3MB, time=477.09
x[1] = 0.4421 1.535
h = 0.0001 0.005
y2[1] (numeric) = 11.8885270083 18.9076356531
y2[1] (closed_form) = 15.4599590034 17.3501727254
absolute error = 3.896
relative error = 16.77 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.19491347133 -0.946778763074
y1[1] (closed_form) = 2.19491347133 -0.946778763074
absolute error = 4.238e-63
relative error = 1.773e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.388
Order of pole (three term test) = 36.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.388
Order of pole (three term test) = 29.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40047.9MB, alloc=44.3MB, time=477.62
memory used=40094.6MB, alloc=44.3MB, time=478.18
x[1] = 0.4422 1.54
h = 0.0001 0.003
y2[1] (numeric) = 11.8928209052 18.9563239354
y2[1] (closed_form) = 15.465926393 17.4110771321
absolute error = 3.893
relative error = 16.72 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.20483743149 -0.952186526969
y1[1] (closed_form) = 2.20483743149 -0.952186526969
absolute error = 4.238e-63
relative error = 1.765e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.442
Order of pole (three term test) = 36.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.442
Order of pole (three term test) = 29.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40141.0MB, alloc=44.3MB, time=478.72
memory used=40187.5MB, alloc=44.3MB, time=479.28
memory used=40234.5MB, alloc=44.3MB, time=479.84
x[1] = 0.4423 1.543
h = 0.001 0.001
y2[1] (numeric) = 11.8971399708 19.0050294012
y2[1] (closed_form) = 15.4700087373 17.4476051618
absolute error = 3.898
relative error = 16.71 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.21077590389 -0.955524360982
y1[1] (closed_form) = 2.21077590389 -0.955524360982
absolute error = 4.238e-63
relative error = 1.760e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.475
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.475
Order of pole (three term test) = 29.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40280.4MB, alloc=44.3MB, time=480.38
memory used=40326.8MB, alloc=44.3MB, time=480.93
x[1] = 0.4433 1.544
h = 0.001 0.003
y2[1] (numeric) = 11.901484378 19.0537520242
y2[1] (closed_form) = 15.4831770556 17.4588593653
absolute error = 3.921
relative error = 16.8 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.21174554377 -0.95859118598
y1[1] (closed_form) = 2.21174554377 -0.95859118598
absolute error = 4.272e-63
relative error = 1.772e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.486
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.486
Order of pole (three term test) = 29.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40372.7MB, alloc=44.3MB, time=481.46
memory used=40419.4MB, alloc=44.3MB, time=482.02
x[1] = 0.4443 1.547
h = 0.0001 0.004
y2[1] (numeric) = 11.9058543007 19.1024917775
y2[1] (closed_form) = 15.4982748445 17.4945409381
absolute error = 3.936
relative error = 16.84 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.21675791752 -0.963771058023
y1[1] (closed_form) = 2.21675791752 -0.963771058023
absolute error = 4.272e-63
relative error = 1.767e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.519
Order of pole (three term test) = 36.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.519
Order of pole (three term test) = 29.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40465.5MB, alloc=44.3MB, time=482.56
memory used=40512.1MB, alloc=44.3MB, time=483.10
x[1] = 0.4444 1.551
h = 0.003 0.006
y2[1] (numeric) = 11.9102499136 19.1512486335
y2[1] (closed_form) = 15.5033608633 17.5433273796
absolute error = 3.936
relative error = 16.81 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.224767912 -0.968203216414
y1[1] (closed_form) = 2.224767912 -0.968203216414
absolute error = 4.272e-63
relative error = 1.761e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.563
Order of pole (three term test) = 36.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.563
Order of pole (three term test) = 29.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40557.9MB, alloc=44.3MB, time=483.63
memory used=40604.5MB, alloc=44.3MB, time=484.18
x[1] = 0.4474 1.557
h = 0.0001 0.005
y2[1] (numeric) = 11.9146713924 19.2000225639
y2[1] (closed_form) = 15.5458954066 17.6137797308
absolute error = 3.963
relative error = 16.87 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.23380236612 -0.98071259064
y1[1] (closed_form) = 2.23380236612 -0.98071259064
absolute error = 3.354e-63
relative error = 1.375e-61 %
Correct digits = 63
memory used=40651.1MB, alloc=44.3MB, time=484.73
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.63
Order of pole (three term test) = 36.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.63
Order of pole (three term test) = 29.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40697.2MB, alloc=44.3MB, time=485.27
memory used=40743.9MB, alloc=44.3MB, time=485.82
x[1] = 0.4475 1.562
h = 0.0001 0.003
y2[1] (numeric) = 11.9191189137 19.2488135399
y2[1] (closed_form) = 15.5520367882 17.6748757178
absolute error = 3.959
relative error = 16.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.24394153748 -0.98628984144
y1[1] (closed_form) = 2.24394153748 -0.98628984144
absolute error = 4.272e-63
relative error = 1.743e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.687
Order of pole (three term test) = 36.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.687
Order of pole (three term test) = 29.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40790.0MB, alloc=44.3MB, time=486.36
memory used=40836.8MB, alloc=44.3MB, time=486.92
x[1] = 0.4476 1.565
h = 0.001 0.001
y2[1] (numeric) = 11.9235926552 19.2976215319
y2[1] (closed_form) = 15.5562255151 17.7115178366
absolute error = 3.964
relative error = 16.81 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.25000826033 -0.98973155169
y1[1] (closed_form) = 2.25000826033 -0.98973155169
absolute error = 4.308e-63
relative error = 1.753e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.721
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.721
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40882.8MB, alloc=44.3MB, time=487.46
memory used=40929.1MB, alloc=44.3MB, time=488.01
x[1] = 0.4486 1.566
h = 0.001 0.003
y2[1] (numeric) = 11.9280927953 19.3464465095
y2[1] (closed_form) = 15.5694673168 17.722777032
absolute error = 3.987
relative error = 16.9 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.25098856187 -0.992875545377
y1[1] (closed_form) = 2.25098856187 -0.992875545377
absolute error = 4.272e-63
relative error = 1.736e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.732
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.732
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40975.0MB, alloc=44.3MB, time=488.54
memory used=41021.6MB, alloc=44.3MB, time=489.10
x[1] = 0.4496 1.569
h = 0.0001 0.004
y2[1] (numeric) = 11.9326195136 19.3952884417
y2[1] (closed_form) = 15.5847074669 17.7585421253
absolute error = 4.002
relative error = 16.94 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.25609945247 -0.998199461027
y1[1] (closed_form) = 2.25609945247 -0.998199461027
absolute error = 4.308e-63
relative error = 1.746e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.767
Order of pole (three term test) = 36.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.767
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41067.6MB, alloc=44.3MB, time=489.63
memory used=41114.0MB, alloc=44.3MB, time=490.18
memory used=41160.6MB, alloc=44.3MB, time=490.73
x[1] = 0.4497 1.573
h = 0.003 0.006
y2[1] (numeric) = 11.9371729904 19.444147297
y2[1] (closed_form) = 15.5899354188 17.8074828289
absolute error = 4.003
relative error = 16.91 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.26428240963 -1.00277004141
y1[1] (closed_form) = 2.26428240963 -1.00277004141
absolute error = 4.472e-63
relative error = 1.806e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.813
Order of pole (three term test) = 36.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.813
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41206.5MB, alloc=44.3MB, time=491.26
memory used=41253.3MB, alloc=44.3MB, time=491.82
x[1] = 0.4527 1.579
h = 0.0001 0.005
y2[1] (numeric) = 11.9417534072 19.4930230428
y2[1] (closed_form) = 15.6327971569 17.878068557
absolute error = 4.029
relative error = 16.96 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.27348098276 -1.01561450972
y1[1] (closed_form) = 2.27348098276 -1.01561450972
absolute error = 4.472e-63
relative error = 1.796e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.883
Order of pole (three term test) = 36.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.883
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41299.2MB, alloc=44.3MB, time=492.35
memory used=41345.8MB, alloc=44.3MB, time=492.90
x[1] = 0.4528 1.584
h = 0.0001 0.003
y2[1] (numeric) = 11.9463609463 19.5419156463
y2[1] (closed_form) = 15.6391174625 17.9393599841
absolute error = 4.025
relative error = 16.91 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.2838386873 -1.02136615485
y1[1] (closed_form) = 2.2838386873 -1.02136615485
absolute error = 4.472e-63
relative error = 1.788e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.942
Order of pole (three term test) = 36.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.942
Order of pole (three term test) = 29.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41392.0MB, alloc=44.3MB, time=493.44
memory used=41438.9MB, alloc=44.3MB, time=494.00
x[1] = 0.4529 1.587
h = 0.001 0.001
y2[1] (numeric) = 11.950995791 19.5908250735
y2[1] (closed_form) = 15.6434155747 17.9761184766
absolute error = 4.03
relative error = 16.91 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.29003562387 -1.02491472537
y1[1] (closed_form) = 2.29003562387 -1.02491472537
absolute error = 4.472e-63
relative error = 1.782e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.978
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.978
Order of pole (three term test) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41485.1MB, alloc=44.3MB, time=494.54
memory used=41531.8MB, alloc=44.3MB, time=495.10
x[1] = 0.4539 1.588
h = 0.0001 0.004
y2[1] (numeric) = 11.9556581256 19.63975129
y2[1] (closed_form) = 15.6567326316 17.987382482
absolute error = 4.053
relative error = 17 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.29102630078 -1.02813754978
y1[1] (closed_form) = 2.29102630078 -1.02813754978
absolute error = 4.123e-63
relative error = 1.642e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.99
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.99
Order of pole (three term test) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41578.1MB, alloc=44.3MB, time=495.63
memory used=41624.5MB, alloc=44.3MB, time=496.18
memory used=41671.2MB, alloc=44.3MB, time=496.73
x[1] = 0.454 1.592
h = 0.003 0.006
y2[1] (numeric) = 11.9603481353 19.6886942606
y2[1] (closed_form) = 15.6620840764 18.0364601984
absolute error = 4.054
relative error = 16.97 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.29936198451 -1.03282836853
y1[1] (closed_form) = 2.29936198451 -1.03282836853
absolute error = 4.472e-63
relative error = 1.774e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.038
Order of pole (three term test) = 36.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.038
Order of pole (three term test) = 29.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41717.2MB, alloc=44.3MB, time=497.26
memory used=41764.0MB, alloc=44.3MB, time=497.82
x[1] = 0.457 1.598
h = 0.0001 0.005
y2[1] (numeric) = 11.9650660064 19.7376539494
y2[1] (closed_form) = 15.7052325003 18.1071662294
absolute error = 4.08
relative error = 17.02 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.30870690732 -1.0459657003
y1[1] (closed_form) = 2.30870690732 -1.0459657003
absolute error = 4.472e-63
relative error = 1.764e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.111
Order of pole (three term test) = 36.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.111
Order of pole (three term test) = 29.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41809.8MB, alloc=44.3MB, time=498.36
memory used=41856.4MB, alloc=44.3MB, time=498.91
x[1] = 0.4571 1.603
h = 0.0001 0.003
y2[1] (numeric) = 11.9698119259 19.7866303198
y2[1] (closed_form) = 15.7117084725 18.1686312255
absolute error = 4.077
relative error = 16.97 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.31925758243 -1.05186882944
y1[1] (closed_form) = 2.31925758243 -1.05186882944
absolute error = 4.472e-63
relative error = 1.756e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.173
Order of pole (three term test) = 36.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.173
Order of pole (three term test) = 29.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41902.4MB, alloc=44.3MB, time=499.44
memory used=41949.4MB, alloc=44.3MB, time=500.01
x[1] = 0.4572 1.606
h = 0.001 0.001
y2[1] (numeric) = 11.9745860822 19.8356233344
y2[1] (closed_form) = 15.7161017796 18.2054930922
absolute error = 4.081
relative error = 16.97 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.32556952384 -1.05551024799
y1[1] (closed_form) = 2.32556952384 -1.05551024799
absolute error = 4.472e-63
relative error = 1.751e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.21
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.21
Order of pole (three term test) = 29.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41995.6MB, alloc=44.3MB, time=500.55
memory used=42042.1MB, alloc=44.3MB, time=501.11
x[1] = 0.4582 1.607
h = 0.001 0.003
y2[1] (numeric) = 11.9793886644 19.8846329551
y2[1] (closed_form) = 15.7294850053 18.2167620062
absolute error = 4.104
relative error = 17.05 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.32656985855 -1.05880216876
y1[1] (closed_form) = 2.32656985855 -1.05880216876
absolute error = 4.472e-63
relative error = 1.750e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.222
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.222
Order of pole (three term test) = 29.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42088.4MB, alloc=44.3MB, time=501.64
memory used=42134.7MB, alloc=44.3MB, time=502.19
memory used=42181.5MB, alloc=44.3MB, time=502.74
x[1] = 0.4592 1.61
h = 0.0001 0.004
y2[1] (numeric) = 11.9842198627 19.9336591432
y2[1] (closed_form) = 15.7449990251 18.2526880606
absolute error = 4.119
relative error = 17.09 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.3318687909 -1.06440261346
y1[1] (closed_form) = 2.3318687909 -1.06440261346
absolute error = 4.123e-63
relative error = 1.609e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.26
Order of pole (three term test) = 36.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.26
Order of pole (three term test) = 29.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42227.4MB, alloc=44.3MB, time=503.28
memory used=42273.9MB, alloc=44.3MB, time=503.82
x[1] = 0.4593 1.614
h = 0.003 0.006
y2[1] (numeric) = 11.9890798681 19.982701859
y2[1] (closed_form) = 15.750499915 18.3019258691
absolute error = 4.12
relative error = 17.06 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.34038248279 -1.06923933502
y1[1] (closed_form) = 2.34038248279 -1.06923933502
absolute error = 4.123e-63
relative error = 1.602e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 36.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.31
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42319.9MB, alloc=44.3MB, time=504.36
memory used=42366.5MB, alloc=44.3MB, time=504.91
x[1] = 0.4623 1.62
h = 0.0001 0.005
y2[1] (numeric) = 11.9939688728 20.0317610622
y2[1] (closed_form) = 15.793991165 18.372768765
absolute error = 4.146
relative error = 17.11 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.34989384914 -1.08272679133
y1[1] (closed_form) = 2.34989384914 -1.08272679133
absolute error = 4.472e-63
relative error = 1.728e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.386
Order of pole (three term test) = 36.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.386
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42412.5MB, alloc=44.3MB, time=505.44
memory used=42459.3MB, alloc=44.3MB, time=506.00
x[1] = 0.4624 1.625
h = 0.0001 0.003
y2[1] (numeric) = 11.99888707 20.080836712
y2[1] (closed_form) = 15.8006555317 18.4344365724
absolute error = 4.143
relative error = 17.06 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.36066945821 -1.08881375477
y1[1] (closed_form) = 2.36066945821 -1.08881375477
absolute error = 4.472e-63
relative error = 1.720e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.45
Order of pole (three term test) = 36.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.45
Order of pole (three term test) = 29.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42505.4MB, alloc=44.3MB, time=506.54
memory used=42552.2MB, alloc=44.3MB, time=507.10
x[1] = 0.4625 1.628
h = 0.001 0.001
y2[1] (numeric) = 12.0038346538 20.1299287663
y2[1] (closed_form) = 15.8051639903 18.4714191755
absolute error = 4.147
relative error = 17.06 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.36711539622 -1.0925677737
y1[1] (closed_form) = 2.36711539622 -1.0925677737
absolute error = 4.472e-63
relative error = 1.715e-61 %
Correct digits = 63
memory used=42599.2MB, alloc=44.3MB, time=507.66
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.489
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.489
Order of pole (three term test) = 29.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42645.3MB, alloc=44.3MB, time=508.20
memory used=42691.8MB, alloc=44.3MB, time=508.75
x[1] = 0.4635 1.629
h = 0.001 0.003
y2[1] (numeric) = 12.0088118193 20.1790371828
y2[1] (closed_form) = 15.8186258653 18.4826925418
absolute error = 4.17
relative error = 17.14 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.36812555771 -1.09594172432
y1[1] (closed_form) = 2.36812555771 -1.09594172432
absolute error = 5.385e-63
relative error = 2.064e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.502
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.502
Order of pole (three term test) = 29.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42737.6MB, alloc=44.3MB, time=509.28
memory used=42784.3MB, alloc=44.3MB, time=509.84
x[1] = 0.4645 1.632
h = 0.0001 0.004
y2[1] (numeric) = 12.0138187627 20.228161918
y2[1] (closed_form) = 15.8342931422 18.518706199
absolute error = 4.185
relative error = 17.18 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.37352619559 -1.10169679566
y1[1] (closed_form) = 2.37352619559 -1.10169679566
absolute error = 5.099e-63
relative error = 1.949e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.541
Order of pole (three term test) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.541
Order of pole (three term test) = 29.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42830.2MB, alloc=44.3MB, time=510.37
memory used=42876.7MB, alloc=44.3MB, time=510.92
x[1] = 0.4646 1.636
h = 0.003 0.006
y2[1] (numeric) = 12.0188556811 20.2773029281
y2[1] (closed_form) = 15.8399476835 18.5681072615
absolute error = 4.186
relative error = 17.15 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.38222064922 -1.10668361076
y1[1] (closed_form) = 2.38222064922 -1.10668361076
absolute error = 5.099e-63
relative error = 1.941e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.594
Order of pole (three term test) = 36.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.594
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42922.6MB, alloc=44.3MB, time=511.45
memory used=42969.2MB, alloc=44.3MB, time=512.00
x[1] = 0.4676 1.642
h = 0.0001 0.005
y2[1] (numeric) = 12.0239227728 20.326460168
y2[1] (closed_form) = 15.8837904394 18.6390888194
absolute error = 4.213
relative error = 17.2 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.39189965004 -1.12052955906
y1[1] (closed_form) = 2.39189965004 -1.12052955906
absolute error = 5.099e-63
relative error = 1.930e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.673
Order of pole (three term test) = 36.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.673
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43015.5MB, alloc=44.3MB, time=512.53
memory used=43062.1MB, alloc=44.3MB, time=513.08
memory used=43108.8MB, alloc=44.3MB, time=513.64
x[1] = 0.4677 1.647
h = 0.0001 0.003
y2[1] (numeric) = 12.029020237 20.3756335924
y2[1] (closed_form) = 15.8906485043 18.7009634368
absolute error = 4.209
relative error = 17.15 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.40290368634 -1.12680564505
y1[1] (closed_form) = 2.40290368634 -1.12680564505
absolute error = 5.385e-63
relative error = 2.029e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.74
Order of pole (three term test) = 36.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.74
Order of pole (three term test) = 29.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43154.9MB, alloc=44.3MB, time=514.19
memory used=43201.8MB, alloc=44.3MB, time=514.75
x[1] = 0.4678 1.65
h = 0.001 0.001
y2[1] (numeric) = 12.0341482737 20.4248231548
y2[1] (closed_form) = 15.8952753424 18.7380691416
absolute error = 4.213
relative error = 17.15 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.40948568428 -1.13067547922
y1[1] (closed_form) = 2.40948568428 -1.13067547922
absolute error = 5.099e-63
relative error = 1.916e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.781
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.781
Order of pole (three term test) = 28.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43247.9MB, alloc=44.3MB, time=515.29
memory used=43294.6MB, alloc=44.3MB, time=515.85
x[1] = 0.4688 1.651
h = 0.001 0.003
y2[1] (numeric) = 12.0393070844 20.474028808
y2[1] (closed_form) = 15.9088177421 18.7493467334
absolute error = 4.236
relative error = 17.23 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.41050534625 -1.13413323353
y1[1] (closed_form) = 2.41050534625 -1.13413323353
absolute error = 5.099e-63
relative error = 1.914e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.794
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.794
Order of pole (three term test) = 29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43340.4MB, alloc=44.3MB, time=516.38
memory used=43387.1MB, alloc=44.3MB, time=516.93
x[1] = 0.4698 1.654
h = 0.0001 0.004
y2[1] (numeric) = 12.0444968712 20.5232505042
y2[1] (closed_form) = 15.9246422623 18.7854494134
absolute error = 4.252
relative error = 17.26 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.41600880976 -1.14004681492
y1[1] (closed_form) = 2.41600880976 -1.14004681492
absolute error = 5.385e-63
relative error = 2.016e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.835
Order of pole (three term test) = 36.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.835
Order of pole (three term test) = 28.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43433.1MB, alloc=44.3MB, time=517.46
memory used=43479.7MB, alloc=44.3MB, time=518.01
x[1] = 0.4699 1.658
h = 0.003 0.006
y2[1] (numeric) = 12.0497178374 20.5724881947
y2[1] (closed_form) = 15.9304547697 18.8350169305
absolute error = 4.252
relative error = 17.24 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.4248868261 -1.14518802485
y1[1] (closed_form) = 2.4248868261 -1.14518802485
absolute error = 5.385e-63
relative error = 2.008e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.89
Order of pole (three term test) = 36.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.89
Order of pole (three term test) = 28.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43526.0MB, alloc=44.3MB, time=518.55
memory used=43572.2MB, alloc=44.3MB, time=519.10
memory used=43619.0MB, alloc=44.3MB, time=519.64
x[1] = 0.4729 1.664
h = 0.0001 0.005
y2[1] (numeric) = 12.0549701875 20.62174183
y2[1] (closed_form) = 15.9746579038 18.9061389289
absolute error = 4.279
relative error = 17.29 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.43473464515 -1.15940103514
y1[1] (closed_form) = 2.43473464515 -1.15940103514
absolute error = 5.385e-63
relative error = 1.997e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.973
Order of pole (three term test) = 37.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.973
Order of pole (three term test) = 28.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43664.9MB, alloc=44.3MB, time=520.18
memory used=43711.5MB, alloc=44.3MB, time=520.74
x[1] = 0.473 1.669
h = 0.0001 0.003
y2[1] (numeric) = 12.0602541267 20.6710113599
y2[1] (closed_form) = 15.9817151072 18.9682244039
absolute error = 4.275
relative error = 17.24 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.44597066198 -1.16587167142
y1[1] (closed_form) = 2.44597066198 -1.16587167142
absolute error = 5.831e-63
relative error = 2.152e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.043
Order of pole (three term test) = 37.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.043
Order of pole (three term test) = 28.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43757.7MB, alloc=44.3MB, time=521.28
memory used=43804.6MB, alloc=44.3MB, time=521.85
x[1] = 0.4731 1.672
h = 0.001 0.001
y2[1] (numeric) = 12.0655698615 20.7202967332
y2[1] (closed_form) = 15.9864636355 19.0054556043
absolute error = 4.279
relative error = 17.23 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.45269081822 -1.16986062021
y1[1] (closed_form) = 2.45269081822 -1.16986062021
absolute error = 5.831e-63
relative error = 2.146e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.086
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.086
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43850.7MB, alloc=44.3MB, time=522.39
memory used=43897.2MB, alloc=44.3MB, time=522.94
x[1] = 0.4741 1.673
h = 0.001 0.003
y2[1] (numeric) = 12.0709175994 20.7695978982
y2[1] (closed_form) = 16.0000884728 19.0167371778
absolute error = 4.302
relative error = 17.31 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.45371963914 -1.17340399249
y1[1] (closed_form) = 2.45371963914 -1.17340399249
absolute error = 5.831e-63
relative error = 2.144e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.1
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.1
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43943.1MB, alloc=44.3MB, time=523.47
memory used=43989.8MB, alloc=44.3MB, time=524.02
x[1] = 0.4751 1.676
h = 0.0001 0.004
y2[1] (numeric) = 12.0762975488 20.8189148021
y2[1] (closed_form) = 16.0160743152 19.0529303047
absolute error = 4.317
relative error = 17.35 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.45932705827 -1.17948006356
y1[1] (closed_form) = 2.45932705827 -1.17948006356
absolute error = 5.831e-63
relative error = 2.138e-61 %
Correct digits = 63
memory used=44036.4MB, alloc=44.3MB, time=524.57
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.143
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.143
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44082.4MB, alloc=44.3MB, time=525.10
memory used=44128.9MB, alloc=44.3MB, time=525.65
x[1] = 0.4752 1.68
h = 0.003 0.006
y2[1] (numeric) = 12.0817099194 20.8682473915
y2[1] (closed_form) = 16.0220492141 19.1026675161
absolute error = 4.318
relative error = 17.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.46839148601 -1.18478008284
y1[1] (closed_form) = 2.46839148601 -1.18478008284
absolute error = 5.831e-63
relative error = 2.130e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.2
Order of pole (three term test) = 37.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.2
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44175.0MB, alloc=44.3MB, time=526.19
memory used=44221.7MB, alloc=44.3MB, time=526.75
x[1] = 0.4782 1.686
h = 0.0001 0.005
y2[1] (numeric) = 12.0871549217 20.917595612
y2[1] (closed_form) = 16.0666217958 19.1739317133
absolute error = 4.345
relative error = 17.37 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.47840929841 -1.19936893184
y1[1] (closed_form) = 2.47840929841 -1.19936893184
absolute error = 5.831e-63
relative error = 2.118e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.287
Order of pole (three term test) = 37.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.287
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44267.8MB, alloc=44.3MB, time=527.30
memory used=44314.5MB, alloc=44.3MB, time=527.85
x[1] = 0.4783 1.691
h = 0.0001 0.003
y2[1] (numeric) = 12.0926327674 20.9669594087
y2[1] (closed_form) = 16.0738837178 19.2362321433
absolute error = 4.341
relative error = 17.32 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.48988090945 -1.20603968896
y1[1] (closed_form) = 2.48988090945 -1.20603968896
absolute error = 5.831e-63
relative error = 2.108e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.36
Order of pole (three term test) = 37.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.36
Order of pole (three term test) = 28.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44360.5MB, alloc=44.3MB, time=528.38
memory used=44407.4MB, alloc=44.3MB, time=528.95
x[1] = 0.4784 1.694
h = 0.001 0.001
y2[1] (numeric) = 12.0981436693 21.0163387255
y2[1] (closed_form) = 16.0787573319 19.2735912619
absolute error = 4.345
relative error = 17.31 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.49674135757 -1.21015113829
y1[1] (closed_form) = 2.49674135757 -1.21015113829
absolute error = 5.831e-63
relative error = 2.102e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.405
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.405
Order of pole (three term test) = 28.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44453.9MB, alloc=44.3MB, time=529.50
memory used=44500.6MB, alloc=44.3MB, time=530.05
memory used=44547.2MB, alloc=44.3MB, time=530.60
x[1] = 0.4794 1.695
h = 0.0001 0.004
y2[1] (numeric) = 12.1036878412 21.0657335058
y2[1] (closed_form) = 16.0924665584 19.2848765561
absolute error = 4.368
relative error = 17.39 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.49777898014 -1.21378198397
y1[1] (closed_form) = 2.49777898014 -1.21378198397
absolute error = 5.385e-63
relative error = 1.939e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.419
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.419
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44593.0MB, alloc=44.3MB, time=531.13
memory used=44639.4MB, alloc=44.3MB, time=531.68
x[1] = 0.4795 1.699
h = 0.003 0.006
y2[1] (numeric) = 12.109265498 21.1151436919
y2[1] (closed_form) = 16.0985827943 19.3347644674
absolute error = 4.369
relative error = 17.36 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.50700814778 -1.21922005686
y1[1] (closed_form) = 2.50700814778 -1.21922005686
absolute error = 5.831e-63
relative error = 2.092e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.479
Order of pole (three term test) = 37.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.479
Order of pole (three term test) = 28.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44685.4MB, alloc=44.3MB, time=532.21
memory used=44732.0MB, alloc=44.3MB, time=532.76
x[1] = 0.4825 1.705
h = 0.0001 0.005
y2[1] (numeric) = 12.1148768555 21.1645692254
y2[1] (closed_form) = 16.1434790785 19.406157008
absolute error = 4.396
relative error = 17.41 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.51717784127 -1.23413756062
y1[1] (closed_form) = 2.51717784127 -1.23413756062
absolute error = 5.000e-63
relative error = 1.784e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.569
Order of pole (three term test) = 37.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.569
Order of pole (three term test) = 28.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44778.0MB, alloc=44.3MB, time=533.29
memory used=44824.6MB, alloc=44.3MB, time=533.84
x[1] = 0.4826 1.71
h = 0.0001 0.003
y2[1] (numeric) = 12.1205221309 21.2140100472
y2[1] (closed_form) = 16.1509191654 19.4686483153
absolute error = 4.392
relative error = 17.36 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.52885766091 -1.24098228127
y1[1] (closed_form) = 2.52885766091 -1.24098228127
absolute error = 5.000e-63
relative error = 1.775e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.645
Order of pole (three term test) = 37.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.645
Order of pole (three term test) = 28.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44870.6MB, alloc=44.3MB, time=534.38
memory used=44917.4MB, alloc=44.3MB, time=534.94
x[1] = 0.4827 1.713
h = 0.001 0.001
y2[1] (numeric) = 12.1262015423 21.2634660971
y2[1] (closed_form) = 16.1559016708 19.5061210504
absolute error = 4.396
relative error = 17.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.5358421189 -1.24520024748
y1[1] (closed_form) = 2.5358421189 -1.24520024748
absolute error = 6.403e-63
relative error = 2.267e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.691
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.691
Order of pole (three term test) = 28.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44964.0MB, alloc=44.3MB, time=535.49
memory used=45010.5MB, alloc=44.3MB, time=536.04
memory used=45056.9MB, alloc=44.3MB, time=536.62
x[1] = 0.4837 1.714
h = 0.001 0.003
y2[1] (numeric) = 12.1319153088 21.3129373141
y2[1] (closed_form) = 16.1696850897 19.5174103622
absolute error = 4.419
relative error = 17.44 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.53688809184 -1.24890780639
y1[1] (closed_form) = 2.53688809184 -1.24890780639
absolute error = 5.000e-63
relative error = 1.768e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.707
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.707
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45103.0MB, alloc=44.3MB, time=537.16
memory used=45149.7MB, alloc=44.3MB, time=537.71
x[1] = 0.4847 1.717
h = 0.0001 0.004
y2[1] (numeric) = 12.1376636508 21.3624236365
y2[1] (closed_form) = 16.185981179 19.5537776324
absolute error = 4.434
relative error = 17.47 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.54269404002 -1.25529589263
y1[1] (closed_form) = 2.54269404002 -1.25529589263
absolute error = 5.657e-63
relative error = 1.995e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.753
Order of pole (three term test) = 37.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.753
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45195.6MB, alloc=44.3MB, time=538.24
memory used=45242.1MB, alloc=44.3MB, time=538.79
x[1] = 0.4848 1.721
h = 0.003 0.006
y2[1] (numeric) = 12.1434467896 21.4119250016
y2[1] (closed_form) = 16.192268306 19.6038414278
absolute error = 4.434
relative error = 17.44 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.55211510349 -1.26090126446
y1[1] (closed_form) = 2.55211510349 -1.26090126446
absolute error = 5.000e-63
relative error = 1.756e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.815
Order of pole (three term test) = 37.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.815
Order of pole (three term test) = 28.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45288.1MB, alloc=44.3MB, time=539.32
memory used=45334.8MB, alloc=44.3MB, time=539.88
x[1] = 0.4878 1.727
h = 0.0001 0.005
y2[1] (numeric) = 12.1492649477 21.4614413459
y2[1] (closed_form) = 16.2375514335 19.675379495
absolute error = 4.461
relative error = 17.49 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.56245705931 -1.27621148959
y1[1] (closed_form) = 2.56245705931 -1.27621148959
absolute error = 5.657e-63
relative error = 1.976e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.91
Order of pole (three term test) = 37.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.91
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45381.0MB, alloc=44.3MB, time=540.41
memory used=45427.7MB, alloc=44.3MB, time=540.96
x[1] = 0.4879 1.732
h = 0.0001 0.003
y2[1] (numeric) = 12.1551183488 21.510972605
y2[1] (closed_form) = 16.2452069568 19.7380935864
absolute error = 4.458
relative error = 17.44 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.57437942985 -1.28326704353
y1[1] (closed_form) = 2.57437942985 -1.28326704353
absolute error = 5.657e-63
relative error = 1.967e-61 %
Correct digits = 63
memory used=45474.4MB, alloc=44.3MB, time=541.51
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.989
Order of pole (three term test) = 37.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.989
Order of pole (three term test) = 28.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45520.7MB, alloc=44.3MB, time=542.08
memory used=45567.7MB, alloc=44.3MB, time=542.64
x[1] = 0.488 1.735
h = 0.001 0.001
y2[1] (numeric) = 12.1610072175 21.5605187136
y2[1] (closed_form) = 16.2503210693 19.7756988684
absolute error = 4.462
relative error = 17.43 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.58150828701 -1.28761402158
y1[1] (closed_form) = 2.58150828701 -1.28761402158
absolute error = 6.403e-63
relative error = 2.220e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.037
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.037
Order of pole (three term test) = 28.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45613.6MB, alloc=44.3MB, time=543.18
memory used=45660.2MB, alloc=44.3MB, time=543.73
x[1] = 0.489 1.736
h = 0.001 0.003
y2[1] (numeric) = 12.1669317795 21.6100796057
y2[1] (closed_form) = 16.2641926177 19.7869913911
absolute error = 4.485
relative error = 17.51 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.58256237593 -1.29141262338
y1[1] (closed_form) = 2.58256237593 -1.29141262338
absolute error = 5.657e-63
relative error = 1.959e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.053
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.053
Order of pole (three term test) = 28.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45706.0MB, alloc=44.3MB, time=544.26
memory used=45752.8MB, alloc=44.3MB, time=544.82
x[1] = 0.49 1.739
h = 0.0001 0.004
y2[1] (numeric) = 12.1728922618 21.6596552142
y2[1] (closed_form) = 16.2806622108 19.8234532531
absolute error = 4.499
relative error = 17.54 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.58847561482 -1.29797512061
y1[1] (closed_form) = 2.58847561482 -1.29797512061
absolute error = 5.657e-63
relative error = 1.954e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.102
Order of pole (three term test) = 37.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.102
Order of pole (three term test) = 28.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45798.8MB, alloc=44.3MB, time=545.35
memory used=45845.3MB, alloc=44.3MB, time=545.90
x[1] = 0.4901 1.743
h = 0.003 0.006
y2[1] (numeric) = 12.1788888925 21.7092454713
y2[1] (closed_form) = 16.2871249865 19.8736962878
absolute error = 4.5
relative error = 17.51 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.59809156211 -1.30375254414
y1[1] (closed_form) = 2.59809156211 -1.30375254414
absolute error = 5.657e-63
relative error = 1.946e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.167
Order of pole (three term test) = 37.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.167
Order of pole (three term test) = 28.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45891.3MB, alloc=44.3MB, time=546.42
memory used=45937.8MB, alloc=44.3MB, time=546.98
memory used=45984.4MB, alloc=44.3MB, time=547.53
x[1] = 0.4931 1.749
h = 0.0001 0.005
y2[1] (numeric) = 12.1849219007 21.758850308
y2[1] (closed_form) = 16.3328046162 19.9453815779
absolute error = 4.527
relative error = 17.56 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.60860692478 -1.31946488285
y1[1] (closed_form) = 2.60860692478 -1.31946488285
absolute error = 5.657e-63
relative error = 1.935e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.265
Order of pole (three term test) = 37.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.265
Order of pole (three term test) = 28.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46030.6MB, alloc=44.3MB, time=548.06
memory used=46077.3MB, alloc=44.3MB, time=548.62
x[1] = 0.4932 1.754
h = 0.0001 0.003
y2[1] (numeric) = 12.1909915165 21.8084696549
y2[1] (closed_form) = 16.3406815753 20.0083226978
absolute error = 4.523
relative error = 17.51 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.62077563643 -1.32673726738
y1[1] (closed_form) = 2.62077563643 -1.32673726738
absolute error = 5.000e-63
relative error = 1.702e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.348
Order of pole (three term test) = 37.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.348
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46123.6MB, alloc=44.3MB, time=549.16
memory used=46170.5MB, alloc=44.3MB, time=549.72
x[1] = 0.4933 1.757
h = 0.001 0.001
y2[1] (numeric) = 12.1970979715 21.8581034413
y2[1] (closed_form) = 16.3459309443 20.0460630346
absolute error = 4.527
relative error = 17.5 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.62805112917 -1.33121690173
y1[1] (closed_form) = 2.62805112917 -1.33121690173
absolute error = 5.000e-63
relative error = 1.697e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.399
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.399
Order of pole (three term test) = 28.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46216.7MB, alloc=44.3MB, time=550.27
memory used=46263.2MB, alloc=44.3MB, time=550.84
x[1] = 0.4943 1.758
h = 0.001 0.003
y2[1] (numeric) = 12.2032414981 21.9077515957
y2[1] (closed_form) = 16.3598926889 20.0573584546
absolute error = 4.55
relative error = 17.58 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.62911292875 -1.33510852412
y1[1] (closed_form) = 2.62911292875 -1.33510852412
absolute error = 5.000e-63
relative error = 1.696e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.415
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.415
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46309.2MB, alloc=44.3MB, time=551.38
memory used=46355.9MB, alloc=44.3MB, time=551.93
x[1] = 0.4953 1.761
h = 0.0001 0.004
y2[1] (numeric) = 12.20942233 21.9574140459
y2[1] (closed_form) = 16.3765402424 20.0939163457
absolute error = 4.565
relative error = 17.61 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.63513462384 -1.34184980341
y1[1] (closed_form) = 2.63513462384 -1.34184980341
absolute error = 5.385e-63
relative error = 1.821e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.466
Order of pole (three term test) = 37.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.466
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46402.1MB, alloc=44.3MB, time=552.46
memory used=46448.6MB, alloc=44.3MB, time=553.01
memory used=46495.2MB, alloc=44.3MB, time=553.56
x[1] = 0.4954 1.765
h = 0.003 0.006
y2[1] (numeric) = 12.2156407019 22.0070907184
y2[1] (closed_form) = 16.3831835463 20.1443420158
absolute error = 4.565
relative error = 17.58 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.64494849169 -1.34780415531
y1[1] (closed_form) = 2.64494849169 -1.34780415531
absolute error = 5.831e-63
relative error = 1.964e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.534
Order of pole (three term test) = 37.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.534
Order of pole (three term test) = 28.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46541.3MB, alloc=44.3MB, time=554.10
memory used=46587.9MB, alloc=44.3MB, time=554.65
x[1] = 0.4984 1.771
h = 0.0001 0.005
y2[1] (numeric) = 12.2218968498 22.056781539
y2[1] (closed_form) = 16.429269552 20.2161761995
absolute error = 4.592
relative error = 17.63 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.65563839101 -1.36392822358
y1[1] (closed_form) = 2.65563839101 -1.36392822358
absolute error = 5.831e-63
relative error = 1.953e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.637
Order of pole (three term test) = 37.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.637
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46633.9MB, alloc=44.3MB, time=555.18
memory used=46680.6MB, alloc=44.3MB, time=555.73
x[1] = 0.4985 1.776
h = 0.0001 0.003
y2[1] (numeric) = 12.2281910108 22.1064864328
y2[1] (closed_form) = 16.4373741005 20.2793486443
absolute error = 4.589
relative error = 17.58 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.6680572957 -1.37142359231
y1[1] (closed_form) = 2.6680572957 -1.37142359231
absolute error = 5.385e-63
relative error = 1.795e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.724
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.724
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46726.7MB, alloc=44.3MB, time=556.28
memory used=46773.6MB, alloc=44.3MB, time=556.85
x[1] = 0.4986 1.779
h = 0.001 0.001
y2[1] (numeric) = 12.2345234231 22.1562053236
y2[1] (closed_form) = 16.4427624686 20.3172265739
absolute error = 4.593
relative error = 17.57 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.67548169637 -1.3760396221
y1[1] (closed_form) = 2.67548169637 -1.3760396221
absolute error = 5.385e-63
relative error = 1.790e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.776
Order of pole (three term test) = 37.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.776
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46819.7MB, alloc=44.3MB, time=557.40
memory used=46866.2MB, alloc=44.3MB, time=557.94
x[1] = 0.4996 1.78
h = 0.001 0.003
y2[1] (numeric) = 12.240894326 22.2059381345
y2[1] (closed_form) = 16.4568165175 20.3285245579
absolute error = 4.615
relative error = 17.65 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.67655078311 -1.38002628698
y1[1] (closed_form) = 2.67655078311 -1.38002628698
absolute error = 5.385e-63
relative error = 1.788e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.794
Order of pole (three term test) = 37.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.794
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46912.5MB, alloc=44.3MB, time=558.49
memory used=46958.9MB, alloc=44.3MB, time=559.04
memory used=47005.6MB, alloc=44.3MB, time=559.59
x[1] = 0.5006 1.783
h = 0.0001 0.004
y2[1] (numeric) = 12.24730396 22.2556847875
y2[1] (closed_form) = 16.4736465918 20.3651799176
absolute error = 4.63
relative error = 17.68 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.68268210764 -1.3869508262
y1[1] (closed_form) = 2.68268210764 -1.3869508262
absolute error = 5.385e-63
relative error = 1.783e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.847
Order of pole (three term test) = 38.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.847
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47051.4MB, alloc=44.3MB, time=560.12
memory used=47097.9MB, alloc=44.3MB, time=560.67
x[1] = 0.5007 1.787
h = 0.003 0.006
y2[1] (numeric) = 12.2537525669 22.3054452038
y2[1] (closed_form) = 16.4804754281 20.4157916601
absolute error = 4.63
relative error = 17.65 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.69269698176 -1.39308710997
y1[1] (closed_form) = 2.69269698176 -1.39308710997
absolute error = 4.472e-63
relative error = 1.475e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.918
Order of pole (three term test) = 38.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.918
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47143.7MB, alloc=44.3MB, time=561.20
memory used=47190.5MB, alloc=44.3MB, time=561.76
x[1] = 0.5037 1.793
h = 0.0001 0.005
y2[1] (numeric) = 12.2602403895 22.3552193036
y2[1] (closed_form) = 16.5269779039 20.4877763814
absolute error = 4.658
relative error = 17.69 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.70356253107 -1.40963275221
y1[1] (closed_form) = 2.70356253107 -1.40963275221
absolute error = 4.472e-63
relative error = 1.467e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.025
Order of pole (three term test) = 38.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.025
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47236.5MB, alloc=44.3MB, time=562.29
memory used=47283.2MB, alloc=44.3MB, time=562.84
x[1] = 0.5038 1.798
h = 0.0001 0.003
y2[1] (numeric) = 12.2667676718 22.4050070063
y2[1] (closed_form) = 16.5353163528 20.5511844998
absolute error = 4.654
relative error = 17.64 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.71623554282 -1.41735741875
y1[1] (closed_form) = 2.71623554282 -1.41735741875
absolute error = 5.099e-63
relative error = 1.664e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.116
Order of pole (three term test) = 38.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.116
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47329.3MB, alloc=44.3MB, time=563.38
memory used=47376.3MB, alloc=44.3MB, time=563.94
x[1] = 0.5039 1.801
h = 0.001 0.001
y2[1] (numeric) = 12.273334659 22.45480823
y2[1] (closed_form) = 16.540847558 20.5892025905
absolute error = 4.657
relative error = 17.63 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.72381115982 -1.42211368003
y1[1] (closed_form) = 2.72381115982 -1.42211368003
absolute error = 5.385e-63
relative error = 1.753e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.171
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.171
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47423.0MB, alloc=44.3MB, time=564.50
memory used=47469.2MB, alloc=44.3MB, time=565.04
memory used=47516.0MB, alloc=44.3MB, time=565.60
x[1] = 0.5049 1.802
h = 0.0001 0.004
y2[1] (numeric) = 12.2799415973 22.5046228923
y2[1] (closed_form) = 16.5549960625 20.6005027848
absolute error = 4.68
relative error = 17.71 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.72488709138 -1.42619745435
y1[1] (closed_form) = 2.72488709138 -1.42619745435
absolute error = 5.385e-63
relative error = 1.751e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.189
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.189
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47561.9MB, alloc=44.3MB, time=566.13
memory used=47608.5MB, alloc=44.3MB, time=566.68
x[1] = 0.505 1.806
h = 0.003 0.006
y2[1] (numeric) = 12.2865887344 22.5544509093
y2[1] (closed_form) = 16.561986431 20.65127977
absolute error = 4.68
relative error = 17.68 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.7350797442 -1.4324919994
y1[1] (closed_form) = 2.7350797442 -1.4324919994
absolute error = 5.385e-63
relative error = 1.744e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.263
Order of pole (three term test) = 38.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.263
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47654.4MB, alloc=44.3MB, time=567.20
memory used=47701.1MB, alloc=44.3MB, time=567.76
x[1] = 0.508 1.812
h = 0.0001 0.005
y2[1] (numeric) = 12.293276319 22.6042921967
y2[1] (closed_form) = 16.6088538256 20.7234004925
absolute error = 4.708
relative error = 17.73 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.74610255054 -1.44940646943
y1[1] (closed_form) = 2.74610255054 -1.44940646943
absolute error = 5.385e-63
relative error = 1.734e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.375
Order of pole (three term test) = 38.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.375
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47747.0MB, alloc=44.3MB, time=568.29
memory used=47793.7MB, alloc=44.3MB, time=568.84
x[1] = 0.5081 1.817
h = 0.0001 0.003
y2[1] (numeric) = 12.300004601 22.6541466688
y2[1] (closed_form) = 16.6173959065 20.7870178851
absolute error = 4.704
relative error = 17.68 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.7590003078 -1.45733059711
y1[1] (closed_form) = 2.7590003078 -1.45733059711
absolute error = 5.385e-63
relative error = 1.726e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.469
Order of pole (three term test) = 38.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.469
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47840.0MB, alloc=44.3MB, time=569.39
memory used=47886.7MB, alloc=44.3MB, time=569.95
x[1] = 0.5082 1.82
h = 0.001 0.001
y2[1] (numeric) = 12.3067738313 22.7040142392
y2[1] (closed_form) = 16.6230514974 20.8251604672
absolute error = 4.707
relative error = 17.67 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.76670969743 -1.46220887309
y1[1] (closed_form) = 2.76670969743 -1.46220887309
absolute error = 6.083e-63
relative error = 1.944e-61 %
Correct digits = 63
memory used=47933.7MB, alloc=44.3MB, time=570.51
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.526
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.526
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47979.6MB, alloc=44.3MB, time=571.05
memory used=48026.0MB, alloc=44.3MB, time=571.60
x[1] = 0.5092 1.821
h = 0.001 0.003
y2[1] (numeric) = 12.3135842624 22.7538948202
y2[1] (closed_form) = 16.6372830415 20.8364634256
absolute error = 4.73
relative error = 17.74 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.7677923428 -1.46637785212
y1[1] (closed_form) = 2.7677923428 -1.46637785212
absolute error = 6.325e-63
relative error = 2.019e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.545
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.545
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48071.9MB, alloc=44.3MB, time=572.14
memory used=48118.6MB, alloc=44.3MB, time=572.69
x[1] = 0.5102 1.824
h = 0.0001 0.004
y2[1] (numeric) = 12.3204361478 22.8037883235
y2[1] (closed_form) = 16.6544640443 20.8733062967
absolute error = 4.745
relative error = 17.77 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.77413312325 -1.47365434959
y1[1] (closed_form) = 2.77413312325 -1.47365434959
absolute error = 5.385e-63
relative error = 1.714e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.602
Order of pole (three term test) = 38.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.602
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48164.6MB, alloc=44.3MB, time=573.22
memory used=48211.2MB, alloc=44.3MB, time=573.78
x[1] = 0.5103 1.828
h = 0.003 0.006
y2[1] (numeric) = 12.327329742 22.8536946594
y2[1] (closed_form) = 16.6616495583 20.9242759245
absolute error = 4.744
relative error = 17.74 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.78453271859 -1.48014044657
y1[1] (closed_form) = 2.78453271859 -1.48014044657
absolute error = 6.083e-63
relative error = 1.929e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.679
Order of pole (three term test) = 38.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.679
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48257.0MB, alloc=44.3MB, time=574.30
memory used=48303.9MB, alloc=44.3MB, time=574.86
x[1] = 0.5133 1.834
h = 0.0001 0.005
y2[1] (numeric) = 12.334265301 22.9036137374
y2[1] (closed_form) = 16.7089527892 20.9965502931
absolute error = 4.772
relative error = 17.78 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.79573332059 -1.49749542029
y1[1] (closed_form) = 2.79573332059 -1.49749542029
absolute error = 6.083e-63
relative error = 1.918e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.796
Order of pole (three term test) = 38.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.796
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48350.3MB, alloc=44.3MB, time=575.40
memory used=48396.7MB, alloc=44.3MB, time=575.94
memory used=48443.4MB, alloc=44.3MB, time=576.50
x[1] = 0.5134 1.839
h = 0.0001 0.003
y2[1] (numeric) = 12.3412430819 22.9535454662
y2[1] (closed_form) = 16.7177408941 21.0604116721
absolute error = 4.768
relative error = 17.73 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.80889271409 -1.5056609845
y1[1] (closed_form) = 2.80889271409 -1.5056609845
absolute error = 6.325e-63
relative error = 1.984e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.895
Order of pole (three term test) = 38.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.895
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48489.5MB, alloc=44.3MB, time=577.04
memory used=48536.4MB, alloc=44.3MB, time=577.60
x[1] = 0.5135 1.842
h = 0.001 0.001
y2[1] (numeric) = 12.348263343 23.0034897531
y2[1] (closed_form) = 16.7235466944 21.0986993245
absolute error = 4.772
relative error = 17.72 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.81675776056 -1.51068686727
y1[1] (closed_form) = 2.81675776056 -1.51068686727
absolute error = 6.325e-63
relative error = 1.979e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.954
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.954
Order of pole (three term test) = 28.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48582.4MB, alloc=44.3MB, time=578.15
memory used=48629.0MB, alloc=44.3MB, time=578.70
x[1] = 0.5145 1.843
h = 0.001 0.003
y2[1] (numeric) = 12.3553263439 23.0534465047
y2[1] (closed_form) = 16.7378768181 21.1100038054
absolute error = 4.794
relative error = 17.8 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.81784640109 -1.51495693041
y1[1] (closed_form) = 2.81784640109 -1.51495693041
absolute error = 6.083e-63
relative error = 1.901e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.974
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.974
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48674.8MB, alloc=44.3MB, time=579.24
memory used=48721.5MB, alloc=44.3MB, time=579.79
x[1] = 0.5155 1.846
h = 0.0001 0.004
y2[1] (numeric) = 12.3624323452 23.1034156264
y2[1] (closed_form) = 16.7552539636 21.1469483309
absolute error = 4.809
relative error = 17.82 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.82430026333 -1.52243009444
y1[1] (closed_form) = 2.82430026333 -1.52243009444
absolute error = 6.083e-63
relative error = 1.896e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.03
Order of pole (three term test) = 38.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.03
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48767.6MB, alloc=44.3MB, time=580.32
memory used=48814.2MB, alloc=44.3MB, time=580.88
x[1] = 0.5156 1.85
h = 0.003 0.006
y2[1] (numeric) = 12.369581609 23.1533970225
y2[1] (closed_form) = 16.7626400013 21.1981141599
absolute error = 4.809
relative error = 17.79 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.83491002992 -1.52911312588
y1[1] (closed_form) = 2.83491002992 -1.52911312588
absolute error = 6.083e-63
relative error = 1.888e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.11
Order of pole (three term test) = 38.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.11
Order of pole (three term test) = 28.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48860.6MB, alloc=44.3MB, time=581.42
memory used=48906.7MB, alloc=44.3MB, time=581.96
memory used=48953.2MB, alloc=44.3MB, time=582.51
x[1] = 0.5186 1.856
h = 0.0001 0.005
y2[1] (numeric) = 12.3767743985 23.2033905966
y2[1] (closed_form) = 16.8103898201 21.2705437354
absolute error = 4.837
relative error = 17.84 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.84628948669 -1.54691912799
y1[1] (closed_form) = 2.84628948669 -1.54691912799
absolute error = 6.083e-63
relative error = 1.878e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.24
Order of pole (three term test) = 38.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.24
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48999.3MB, alloc=44.3MB, time=583.04
memory used=49045.9MB, alloc=44.3MB, time=583.59
x[1] = 0.5187 1.861
h = 0.0001 0.003
y2[1] (numeric) = 12.3840109781 23.253396251
y2[1] (closed_form) = 16.8194307325 21.3346536043
absolute error = 4.833
relative error = 17.79 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.85971461176 -1.5553329206
y1[1] (closed_form) = 2.85971461176 -1.5553329206
absolute error = 6.083e-63
relative error = 1.869e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.34
Order of pole (three term test) = 38.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.34
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49092.1MB, alloc=44.3MB, time=584.13
memory used=49138.9MB, alloc=44.3MB, time=584.70
x[1] = 0.5188 1.864
h = 0.001 0.001
y2[1] (numeric) = 12.3912916134 23.3034138869
y2[1] (closed_form) = 16.8253908662 21.3730889846
absolute error = 4.836
relative error = 17.78 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.86773772881 -1.56051053584
y1[1] (closed_form) = 2.86773772881 -1.56051053584
absolute error = 6e-63
relative error = 1.838e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.4
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.4
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49185.1MB, alloc=44.3MB, time=585.25
memory used=49231.8MB, alloc=44.3MB, time=585.80
x[1] = 0.5198 1.865
h = 0.001 0.003
y2[1] (numeric) = 12.3986165715 23.3534434048
y2[1] (closed_form) = 16.839821848 21.3843945729
absolute error = 4.858
relative error = 17.85 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.86883186496 -1.5648838838
y1[1] (closed_form) = 2.86883186496 -1.5648838838
absolute error = 6.083e-63
relative error = 1.861e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.42
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.42
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49277.7MB, alloc=44.3MB, time=586.34
memory used=49324.5MB, alloc=44.3MB, time=586.89
x[1] = 0.5208 1.868
h = 0.0001 0.004
y2[1] (numeric) = 12.4059861204 23.4034847037
y2[1] (closed_form) = 16.8574001191 21.4214421985
absolute error = 4.873
relative error = 17.88 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.87540000859 -1.57255862673
y1[1] (closed_form) = 2.87540000859 -1.57255862673
absolute error = 6e-63
relative error = 1.831e-61 %
Correct digits = 63
memory used=49371.2MB, alloc=44.3MB, time=587.44
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.49
Order of pole (three term test) = 38.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.49
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49417.3MB, alloc=44.3MB, time=587.97
memory used=49463.9MB, alloc=44.3MB, time=588.52
x[1] = 0.5209 1.872
h = 0.003 0.006
y2[1] (numeric) = 12.4134005297 23.453537682
y2[1] (closed_form) = 16.8649921962 21.4728078302
absolute error = 4.872
relative error = 17.84 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.88622322507 -1.57944411397
y1[1] (closed_form) = 2.88622322507 -1.57944411397
absolute error = 6e-63
relative error = 1.824e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.57
Order of pole (three term test) = 38.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.57
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49509.8MB, alloc=44.3MB, time=589.05
memory used=49556.4MB, alloc=44.3MB, time=589.60
x[1] = 0.5239 1.878
h = 0.0001 0.005
y2[1] (numeric) = 12.4208600698 23.5036022366
y2[1] (closed_form) = 16.9131995943 21.5453941398
absolute error = 4.901
relative error = 17.89 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.89778257209 -1.59771191652
y1[1] (closed_form) = 2.89778257209 -1.59771191652
absolute error = 6e-63
relative error = 1.813e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.7
Order of pole (three term test) = 38.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.7
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49602.4MB, alloc=44.3MB, time=590.14
memory used=49649.0MB, alloc=44.3MB, time=590.69
x[1] = 0.524 1.883
h = 0.0001 0.003
y2[1] (numeric) = 12.4283650128 23.5536782637
y2[1] (closed_form) = 16.9225002709 21.6097570563
absolute error = 4.897
relative error = 17.84 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.91147758729 -1.60638090454
y1[1] (closed_form) = 2.91147758729 -1.60638090454
absolute error = 6e-63
relative error = 1.804e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 39.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.8
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49695.1MB, alloc=44.3MB, time=591.22
memory used=49742.0MB, alloc=44.3MB, time=591.79
x[1] = 0.5241 1.886
h = 0.001 0.001
y2[1] (numeric) = 12.4359156318 23.6037656583
y2[1] (closed_form) = 16.9286189666 21.6483428536
absolute error = 4.9
relative error = 17.83 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.91966122533 -1.61171448399
y1[1] (closed_form) = 2.91966122533 -1.61171448399
absolute error = 6e-63
relative error = 1.799e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.87
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.87
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49788.3MB, alloc=44.3MB, time=592.33
memory used=49834.7MB, alloc=44.3MB, time=592.88
memory used=49881.2MB, alloc=44.3MB, time=593.44
x[1] = 0.5251 1.887
h = 0.001 0.003
y2[1] (numeric) = 12.4435122013 23.6538643141
y2[1] (closed_form) = 16.9431531311 21.6596491112
absolute error = 4.922
relative error = 17.9 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.92076033601 -1.61619336584
y1[1] (closed_form) = 2.92076033601 -1.61619336584
absolute error = 7e-63
relative error = 2.097e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.89
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.89
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49927.2MB, alloc=44.3MB, time=593.97
memory used=49973.9MB, alloc=44.3MB, time=594.52
x[1] = 0.5261 1.89
h = 0.0001 0.004
y2[1] (numeric) = 12.4511549969 23.7039741242
y2[1] (closed_form) = 16.9609376266 21.6968012828
absolute error = 4.936
relative error = 17.92 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.9274439657 -1.62407471858
y1[1] (closed_form) = 2.9274439657 -1.62407471858
absolute error = 6.083e-63
relative error = 1.817e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.96
Order of pole (three term test) = 39.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.96
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50019.9MB, alloc=44.3MB, time=595.06
memory used=50066.5MB, alloc=44.3MB, time=595.60
x[1] = 0.5262 1.894
h = 0.003 0.006
y2[1] (numeric) = 12.4588442957 23.7540949801
y2[1] (closed_form) = 16.9687413993 21.7483703615
absolute error = 4.936
relative error = 17.89 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.9384839608 -1.63116832502
y1[1] (closed_form) = 2.9384839608 -1.63116832502
absolute error = 7.071e-63
relative error = 2.104e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.04
Order of pole (three term test) = 39.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.04
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50112.5MB, alloc=44.3MB, time=596.14
memory used=50159.3MB, alloc=44.3MB, time=596.69
x[1] = 0.5292 1.9
h = 0.0001 0.005
y2[1] (numeric) = 12.4665803759 23.8042267726
y2[1] (closed_form) = 17.0174176131 21.8211148974
absolute error = 4.964
relative error = 17.94 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.95022420787 -1.64990895256
y1[1] (closed_form) = 2.95022420787 -1.64990895256
absolute error = 6e-63
relative error = 1.775e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.18
Order of pole (three term test) = 39.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.18
Order of pole (three term test) = 28.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50205.3MB, alloc=44.3MB, time=597.23
memory used=50252.1MB, alloc=44.3MB, time=597.78
x[1] = 0.5293 1.905
h = 0.0001 0.003
y2[1] (numeric) = 12.474363517 23.8543693911
y2[1] (closed_form) = 17.026985188 21.8857354741
absolute error = 4.96
relative error = 17.89 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.96419333531 -1.65884028232
y1[1] (closed_form) = 2.96419333531 -1.65884028232
absolute error = 7e-63
relative error = 2.061e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.29
Order of pole (three term test) = 39.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.29
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50298.5MB, alloc=44.3MB, time=598.32
memory used=50344.9MB, alloc=44.3MB, time=598.88
memory used=50391.8MB, alloc=44.3MB, time=599.45
x[1] = 0.5294 1.908
h = 0.001 0.001
y2[1] (numeric) = 12.4821939998 23.9045227243
y2[1] (closed_form) = 17.0332667819 21.9244744091
absolute error = 4.963
relative error = 17.88 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.97253998156 -1.66433416623
y1[1] (closed_form) = 2.97253998156 -1.66433416623
absolute error = 6e-63
relative error = 1.761e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.36
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.36
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50437.9MB, alloc=44.3MB, time=599.99
memory used=50484.6MB, alloc=44.3MB, time=600.54
x[1] = 0.5304 1.909
h = 0.0001 0.004
y2[1] (numeric) = 12.4900721065 23.9546866593
y2[1] (closed_form) = 17.047906501 21.9357808741
absolute error = 4.985
relative error = 17.94 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.97364352332 -1.66892088033
y1[1] (closed_form) = 2.97364352332 -1.66892088033
absolute error = 6e-63
relative error = 1.760e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.38
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.38
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50530.5MB, alloc=44.3MB, time=601.08
memory used=50577.0MB, alloc=44.3MB, time=601.63
x[1] = 0.5305 1.913
h = 0.003 0.006
y2[1] (numeric) = 12.4979981205 24.0048610824
y2[1] (closed_form) = 17.0558946499 21.9875306409
absolute error = 4.984
relative error = 17.91 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.98487539181 -1.67619563777
y1[1] (closed_form) = 2.98487539181 -1.67619563777
absolute error = 6.083e-63
relative error = 1.777e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.47
Order of pole (three term test) = 39.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.47
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50623.0MB, alloc=44.3MB, time=602.16
memory used=50669.7MB, alloc=44.3MB, time=602.71
x[1] = 0.5335 1.919
h = 0.0001 0.005
y2[1] (numeric) = 12.5059723263 24.0550458788
y2[1] (closed_form) = 17.1049816856 22.0604183106
absolute error = 5.013
relative error = 17.96 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.99677795485 -1.6953501114
y1[1] (closed_form) = 2.99677795485 -1.6953501114
absolute error = 6e-63
relative error = 1.743e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.61
Order of pole (three term test) = 39.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.61
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50715.7MB, alloc=44.3MB, time=603.24
memory used=50762.3MB, alloc=44.3MB, time=603.80
x[1] = 0.5336 1.924
h = 0.0001 0.003
y2[1] (numeric) = 12.5139950101 24.1052409323
y2[1] (closed_form) = 17.1147817041 22.1252677065
absolute error = 5.009
relative error = 17.91 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.01098970289 -1.70450978391
y1[1] (closed_form) = 3.01098970289 -1.70450978391
absolute error = 6e-63
relative error = 1.734e-61 %
Correct digits = 63
memory used=50808.9MB, alloc=44.3MB, time=604.35
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.73
Order of pole (three term test) = 39.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.73
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50855.1MB, alloc=44.3MB, time=604.90
memory used=50902.1MB, alloc=44.3MB, time=605.46
x[1] = 0.5337 1.927
h = 0.001 0.001
y2[1] (numeric) = 12.5220664592 24.1554461259
y2[1] (closed_form) = 17.1212052026 22.164142673
absolute error = 5.012
relative error = 17.89 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.01948066303 -1.71014323015
y1[1] (closed_form) = 3.01948066303 -1.71014323015
absolute error = 6e-63
relative error = 1.729e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.8
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.8
Order of pole (three term test) = 28.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50948.2MB, alloc=44.3MB, time=606.00
memory used=50994.8MB, alloc=44.3MB, time=606.56
x[1] = 0.5347 1.928
h = 0.001 0.003
y2[1] (numeric) = 12.530186962 24.2056613412
y2[1] (closed_form) = 17.1359377211 22.1754502247
absolute error = 5.033
relative error = 17.96 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.0205888888 -1.71482459787
y1[1] (closed_form) = 3.0205888888 -1.71482459787
absolute error = 5e-63
relative error = 1.440e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.82
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.82
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51040.8MB, alloc=44.3MB, time=607.09
memory used=51087.6MB, alloc=44.3MB, time=607.64
x[1] = 0.5357 1.931
h = 0.0001 0.004
y2[1] (numeric) = 12.5383568086 24.2558864588
y2[1] (closed_form) = 17.1541186441 22.2128033834
absolute error = 5.048
relative error = 17.99 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.02749324057 -1.72310280025
y1[1] (closed_form) = 3.02749324057 -1.72310280025
absolute error = 5e-63
relative error = 1.435e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.89
Order of pole (three term test) = 39.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.89
Order of pole (three term test) = 28.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51133.6MB, alloc=44.3MB, time=608.18
memory used=51180.2MB, alloc=44.3MB, time=608.72
x[1] = 0.5358 1.935
h = 0.003 0.006
y2[1] (numeric) = 12.5465762903 24.306121358
y2[1] (closed_form) = 17.1623293545 22.264763566
absolute error = 5.047
relative error = 17.95 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.0389482873 -1.73059656385
y1[1] (closed_form) = 3.0389482873 -1.73059656385
absolute error = 5.099e-63
relative error = 1.458e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.99
Order of pole (three term test) = 39.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.99
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51226.0MB, alloc=44.3MB, time=609.25
memory used=51272.7MB, alloc=44.3MB, time=609.80
memory used=51319.4MB, alloc=44.3MB, time=610.36
x[1] = 0.5388 1.941
h = 0.0001 0.005
y2[1] (numeric) = 12.5548456995 24.3563659172
y2[1] (closed_form) = 17.2119067692 22.3378122789
absolute error = 5.076
relative error = 18 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.0510336924 -1.75024505552
y1[1] (closed_form) = 3.0510336924 -1.75024505552
absolute error = 5e-63
relative error = 1.422e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.13
Order of pole (three term test) = 39.71 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.13
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51365.5MB, alloc=44.3MB, time=610.89
memory used=51412.2MB, alloc=44.3MB, time=611.45
x[1] = 0.5389 1.946
h = 0.0001 0.003
y2[1] (numeric) = 12.5631653302 24.4066200135
y2[1] (closed_form) = 17.2219873917 22.4029281553
absolute error = 5.071
relative error = 17.95 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.06552766938 -1.75968080709
y1[1] (closed_form) = 3.06552766938 -1.75968080709
absolute error = 5e-63
relative error = 1.415e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.26
Order of pole (three term test) = 39.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.26
Order of pole (three term test) = 28.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51458.3MB, alloc=44.3MB, time=611.99
memory used=51505.1MB, alloc=44.3MB, time=612.55
x[1] = 0.539 1.949
h = 0.001 0.001
y2[1] (numeric) = 12.5715354776 24.4568835227
y2[1] (closed_form) = 17.2285821184 22.4419614617
absolute error = 5.074
relative error = 17.93 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.07418641914 -1.76548290105
y1[1] (closed_form) = 3.07418641914 -1.76548290105
absolute error = 5.099e-63
relative error = 1.438e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.33
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.33
Order of pole (three term test) = 28.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51551.3MB, alloc=44.3MB, time=613.09
memory used=51597.8MB, alloc=44.3MB, time=613.64
x[1] = 0.54 1.95
h = 0.001 0.003
y2[1] (numeric) = 12.5799564382 24.5071563195
y2[1] (closed_form) = 17.2434247401 22.4532683251
absolute error = 5.096
relative error = 18 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.0752980314 -1.77027651919
y1[1] (closed_form) = 3.0752980314 -1.77027651919
absolute error = 6.083e-63
relative error = 1.714e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.35
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.35
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51643.7MB, alloc=44.3MB, time=614.18
memory used=51690.4MB, alloc=44.3MB, time=614.73
x[1] = 0.541 1.953
h = 0.0001 0.004
y2[1] (numeric) = 12.58842851 24.5574382777
y2[1] (closed_form) = 17.2618271198 22.490730227
absolute error = 5.11
relative error = 18.02 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.08232140286 -1.77877638708
y1[1] (closed_form) = 3.08232140286 -1.77877638708
absolute error = 6e-63
relative error = 1.686e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.43
Order of pole (three term test) = 39.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.43
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51736.5MB, alloc=44.3MB, time=615.26
memory used=51783.0MB, alloc=44.3MB, time=615.81
memory used=51829.6MB, alloc=44.3MB, time=616.36
x[1] = 0.5411 1.957
h = 0.003 0.006
y2[1] (numeric) = 12.5969519921 24.6077292694
y2[1] (closed_form) = 17.2702664686 22.5429045967
absolute error = 5.109
relative error = 17.99 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.09400310278 -1.78649524493
y1[1] (closed_form) = 3.09400310278 -1.78649524493
absolute error = 6e-63
relative error = 1.679e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.53
Order of pole (three term test) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.53
Order of pole (three term test) = 28.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51875.7MB, alloc=44.3MB, time=616.89
memory used=51922.4MB, alloc=44.3MB, time=617.44
x[1] = 0.5441 1.963
h = 0.0001 0.005
y2[1] (numeric) = 12.6055271853 24.6580291661
y2[1] (closed_form) = 17.3203462312 22.6161157362
absolute error = 5.138
relative error = 18.04 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.10627227759 -1.80664953138
y1[1] (closed_form) = 3.10627227759 -1.80664953138
absolute error = 7e-63
relative error = 1.948e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.68
Order of pole (three term test) = 39.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.68
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51968.6MB, alloc=44.3MB, time=617.98
memory used=52015.3MB, alloc=44.3MB, time=618.53
x[1] = 0.5442 1.968
h = 0.0001 0.003
y2[1] (numeric) = 12.6141543913 24.7083378375
y2[1] (closed_form) = 17.3307151231 22.6815028669
absolute error = 5.134
relative error = 17.98 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.12105289106 -1.81636904422
y1[1] (closed_form) = 3.12105289106 -1.81636904422
absolute error = 7e-63
relative error = 1.938e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.81
Order of pole (three term test) = 40.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.81
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52061.4MB, alloc=44.3MB, time=619.07
memory used=52108.2MB, alloc=44.3MB, time=619.63
x[1] = 0.5443 1.971
h = 0.001 0.001
y2[1] (numeric) = 12.6228339135 24.7586551526
y2[1] (closed_form) = 17.3374857353 22.720697327
absolute error = 5.136
relative error = 17.97 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.12988202499 -1.8223444506
y1[1] (closed_form) = 3.12988202499 -1.8223444506
absolute error = 7.071e-63
relative error = 1.952e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.88
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.88
Order of pole (three term test) = 28.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52154.4MB, alloc=44.3MB, time=620.18
memory used=52200.9MB, alloc=44.3MB, time=620.73
x[1] = 0.5453 1.972
h = 0.001 0.003
y2[1] (numeric) = 12.6315660566 24.808980979
y2[1] (closed_form) = 17.3524409729 22.7320029685
absolute error = 5.158
relative error = 18.03 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.1309964126 -1.82725276392
y1[1] (closed_form) = 3.1309964126 -1.82725276392
absolute error = 7.071e-63
relative error = 1.951e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.91
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.91
Order of pole (three term test) = 28.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52247.1MB, alloc=44.3MB, time=621.28
memory used=52293.4MB, alloc=44.3MB, time=621.82
memory used=52340.2MB, alloc=44.3MB, time=622.37
x[1] = 0.5463 1.975
h = 0.0001 0.004
y2[1] (numeric) = 12.6403511265 24.859315183
y2[1] (closed_form) = 17.3710703804 22.7695750561
absolute error = 5.172
relative error = 18.06 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.13814002356 -1.83597981057
y1[1] (closed_form) = 3.13814002356 -1.83597981057
absolute error = 7.071e-63
relative error = 1.945e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.99
Order of pole (three term test) = 40.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.99
Order of pole (three term test) = 28.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52386.0MB, alloc=44.3MB, time=622.90
memory used=52432.5MB, alloc=44.3MB, time=623.45
x[1] = 0.5464 1.979
h = 0.003 0.006
y2[1] (numeric) = 12.6491894307 24.9096576297
y2[1] (closed_form) = 17.3797445986 22.8219674284
absolute error = 5.171
relative error = 18.03 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.15005190244 -1.84393000626
y1[1] (closed_form) = 3.15005190244 -1.84393000626
absolute error = 6e-63
relative error = 1.644e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.09
Order of pole (three term test) = 40.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.09
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52478.5MB, alloc=44.3MB, time=623.99
memory used=52525.2MB, alloc=44.3MB, time=624.54
x[1] = 0.5494 1.985
h = 0.0001 0.005
y2[1] (numeric) = 12.6580812778 24.9600081831
y2[1] (closed_form) = 17.430338945 22.8953423348
absolute error = 5.2
relative error = 18.07 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.16250574041 -1.86460213767
y1[1] (closed_form) = 3.16250574041 -1.86460213767
absolute error = 7e-63
relative error = 1.907e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.25
Order of pole (three term test) = 40.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.25
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52571.3MB, alloc=44.3MB, time=625.07
memory used=52617.9MB, alloc=44.3MB, time=625.62
x[1] = 0.5495 1.99
h = 0.0001 0.003
y2[1] (numeric) = 12.6670269781 25.010366706
y2[1] (closed_form) = 17.4410039663 22.9610055503
absolute error = 5.195
relative error = 18.02 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.17757746242 -1.87461329023
y1[1] (closed_form) = 3.17757746242 -1.87461329023
absolute error = 7e-63
relative error = 1.897e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.38
Order of pole (three term test) = 40.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.38
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52664.0MB, alloc=44.3MB, time=626.16
memory used=52710.8MB, alloc=44.3MB, time=626.74
x[1] = 0.5496 1.993
h = 0.001 0.001
y2[1] (numeric) = 12.6760268429 25.0607330597
y2[1] (closed_form) = 17.4479552394 23.0003640102
absolute error = 5.198
relative error = 18 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.18657961237 -1.88076679246
y1[1] (closed_form) = 3.18657961237 -1.88076679246
absolute error = 7e-63
relative error = 1.892e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.46
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.46
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52757.6MB, alloc=44.3MB, time=627.29
memory used=52803.7MB, alloc=44.3MB, time=627.85
memory used=52850.3MB, alloc=44.3MB, time=628.40
x[1] = 0.5506 1.994
h = 0.001 0.003
y2[1] (numeric) = 12.6850811853 25.1111071046
y2[1] (closed_form) = 17.4630256566 23.0116678693
absolute error = 5.219
relative error = 18.07 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.1876961387 -1.88579229866
y1[1] (closed_form) = 3.1876961387 -1.88579229866
absolute error = 7e-63
relative error = 1.890e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.49
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.49
Order of pole (three term test) = 29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52896.3MB, alloc=44.3MB, time=628.94
memory used=52942.9MB, alloc=44.3MB, time=629.48
x[1] = 0.5516 1.997
h = 0.0001 0.004
y2[1] (numeric) = 12.6941903194 25.1614886996
y2[1] (closed_form) = 17.4818877922 23.0493515824
absolute error = 5.233
relative error = 18.09 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.19496121079 -1.89475216896
y1[1] (closed_form) = 3.19496121079 -1.89475216896
absolute error = 7e-63
relative error = 1.884e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.57
Order of pole (three term test) = 40.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.57
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52988.8MB, alloc=44.3MB, time=630.02
memory used=53035.3MB, alloc=44.3MB, time=630.56
x[1] = 0.5517 2.001
h = 0.003 0.006
y2[1] (numeric) = 12.703354561 25.2118777024
y2[1] (closed_form) = 17.4908032688 23.1019658177
absolute error = 5.232
relative error = 18.06 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.2071068454 -1.90294010523
y1[1] (closed_form) = 3.2071068454 -1.90294010523
absolute error = 7e-63
relative error = 1.877e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.68
Order of pole (three term test) = 40.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.68
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53081.0MB, alloc=44.3MB, time=631.10
memory used=53127.7MB, alloc=44.3MB, time=631.65
x[1] = 0.5547 2.007
h = 0.0001 0.005
y2[1] (numeric) = 12.7125742271 25.2622739695
y2[1] (closed_form) = 17.5419247078 23.1755057859
absolute error = 5.261
relative error = 18.1 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.21974620341 -1.92414241094
y1[1] (closed_form) = 3.21974620341 -1.92414241094
absolute error = 7e-63
relative error = 1.866e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.84
Order of pole (three term test) = 40.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.84
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53173.8MB, alloc=44.3MB, time=632.18
memory used=53220.3MB, alloc=44.3MB, time=632.76
memory used=53267.0MB, alloc=44.3MB, time=633.31
x[1] = 0.5548 2.012
h = 0.0001 0.003
y2[1] (numeric) = 12.7218496362 25.3126773561
y2[1] (closed_form) = 17.5528939179 23.2414499732
absolute error = 5.256
relative error = 18.05 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.23511357073 -1.93445328254
y1[1] (closed_form) = 3.23511357073 -1.93445328254
absolute error = 8e-63
relative error = 2.122e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.98
Order of pole (three term test) = 40.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.98
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53313.0MB, alloc=44.3MB, time=633.85
memory used=53359.7MB, alloc=44.3MB, time=634.41
x[1] = 0.5549 2.015
h = 0.001 0.001
y2[1] (numeric) = 12.7311811081 25.3630877161
y2[1] (closed_form) = 17.5600307477 23.2809753117
absolute error = 5.259
relative error = 18.03 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.24429140587 -1.94078978559
y1[1] (closed_form) = 3.24429140587 -1.94078978559
absolute error = 8e-63
relative error = 2.116e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.07
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.07
Order of pole (three term test) = 29.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53406.0MB, alloc=44.3MB, time=634.96
memory used=53452.6MB, alloc=44.3MB, time=635.50
x[1] = 0.5559 2.016
h = 0.0001 0.004
y2[1] (numeric) = 12.7405689642 25.4135049022
y2[1] (closed_form) = 17.5752189603 23.2922768005
absolute error = 5.28
relative error = 18.09 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.24540940793 -1.94593503632
y1[1] (closed_form) = 3.24540940793 -1.94593503632
absolute error = 8e-63
relative error = 2.114e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.1
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.1
Order of pole (three term test) = 29.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53498.6MB, alloc=44.3MB, time=636.04
memory used=53545.0MB, alloc=44.3MB, time=636.59
x[1] = 0.556 2.02
h = 0.003 0.006
y2[1] (numeric) = 12.7500135271 25.4639287658
y2[1] (closed_form) = 17.5843446373 23.3450881138
absolute error = 5.278
relative error = 18.06 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.25776209368 -1.95433001975
y1[1] (closed_form) = 3.25776209368 -1.95433001975
absolute error = 8e-63
relative error = 2.106e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.21
Order of pole (three term test) = 40.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.21
Order of pole (three term test) = 29.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53590.8MB, alloc=44.3MB, time=637.13
memory used=53637.4MB, alloc=44.3MB, time=637.69
x[1] = 0.559 2.026
h = 0.0001 0.005
y2[1] (numeric) = 12.7595151209 25.5143591568
y2[1] (closed_form) = 17.635928023 23.4187776491
absolute error = 5.308
relative error = 18.1 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.27056831816 -1.97599654921
y1[1] (closed_form) = 3.27056831816 -1.97599654921
absolute error = 8e-63
relative error = 2.094e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.38
Order of pole (three term test) = 40.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.38
Order of pole (three term test) = 29.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53683.9MB, alloc=44.3MB, time=638.24
memory used=53730.2MB, alloc=44.3MB, time=638.80
memory used=53776.8MB, alloc=44.3MB, time=639.36
x[1] = 0.5591 2.031
h = 0.0001 0.003
y2[1] (numeric) = 12.7690740711 25.5647959242
y2[1] (closed_form) = 17.6471622511 23.4849714027
absolute error = 5.303
relative error = 18.05 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.28619755461 -1.98656843903
y1[1] (closed_form) = 3.28619755461 -1.98656843903
absolute error = 8e-63
relative error = 2.083e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.53
Order of pole (three term test) = 40.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.53
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53823.0MB, alloc=44.3MB, time=639.92
memory used=53869.7MB, alloc=44.3MB, time=640.50
x[1] = 0.5592 2.034
h = 0.001 0.001
y2[1] (numeric) = 12.7786907048 25.6152389153
y2[1] (closed_form) = 17.6544607815 23.524645007
absolute error = 5.305
relative error = 18.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.2955310414 -1.99306434906
y1[1] (closed_form) = 3.2955310414 -1.99306434906
absolute error = 9e-63
relative error = 2.337e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.61
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.61
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53915.8MB, alloc=44.3MB, time=641.05
memory used=53962.1MB, alloc=44.3MB, time=641.60
x[1] = 0.5602 2.035
h = 0.001 0.003
y2[1] (numeric) = 12.7883653503 25.6656879763
y2[1] (closed_form) = 17.669752562 23.5359454095
absolute error = 5.326
relative error = 18.1 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.29665123082 -1.99831475075
y1[1] (closed_form) = 3.29665123082 -1.99831475075
absolute error = 8e-63
relative error = 2.075e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.64
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.64
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54008.1MB, alloc=44.3MB, time=642.15
memory used=54054.7MB, alloc=44.3MB, time=643.08
x[1] = 0.5612 2.038
h = 0.0001 0.004
y2[1] (numeric) = 12.7980983375 25.716142952
y2[1] (closed_form) = 17.6890620066 23.5738435901
absolute error = 5.34
relative error = 18.12 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.30414850674 -2.00772185709
y1[1] (closed_form) = 3.30414850674 -2.00772185709
absolute error = 8.062e-63
relative error = 2.085e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.73
Order of pole (three term test) = 41.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.73
Order of pole (three term test) = 29.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54100.6MB, alloc=44.3MB, time=643.79
memory used=54147.2MB, alloc=44.3MB, time=644.35
x[1] = 0.5613 2.042
h = 0.003 0.006
y2[1] (numeric) = 12.8078899977 25.7666036859
y2[1] (closed_form) = 17.6984412165 23.6268841495
absolute error = 5.338
relative error = 18.08 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.31674182085 -2.01636688756
y1[1] (closed_form) = 3.31674182085 -2.01636688756
absolute error = 8e-63
relative error = 2.061e-61 %
Correct digits = 63
memory used=54193.7MB, alloc=44.3MB, time=644.91
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.85
Order of pole (three term test) = 41.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.85
Order of pole (three term test) = 29.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54239.7MB, alloc=44.3MB, time=645.45
memory used=54286.3MB, alloc=44.3MB, time=646.01
x[1] = 0.5643 2.048
h = 0.0001 0.005
y2[1] (numeric) = 12.8177406635 25.8170700201
y2[1] (closed_form) = 17.7505757032 23.7007411846
absolute error = 5.368
relative error = 18.13 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.3297352089 -2.03858728735
y1[1] (closed_form) = 3.3297352089 -2.03858728735
absolute error = 8e-63
relative error = 2.049e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.03
Order of pole (three term test) = 41.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.03
Order of pole (three term test) = 29.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54332.3MB, alloc=44.3MB, time=646.56
memory used=54379.2MB, alloc=44.3MB, time=647.12
x[1] = 0.5644 2.053
h = 0.0001 0.003
y2[1] (numeric) = 12.8276506692 25.8675417955
y2[1] (closed_form) = 17.7621296044 23.7672252581
absolute error = 5.363
relative error = 18.07 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.34566880747 -2.04947442494
y1[1] (closed_form) = 3.34566880747 -2.04947442494
absolute error = 9e-63
relative error = 2.294e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.18
Order of pole (three term test) = 41.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.18
Order of pole (three term test) = 29.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54425.3MB, alloc=44.3MB, time=647.68
memory used=54472.1MB, alloc=44.3MB, time=648.25
x[1] = 0.5645 2.056
h = 0.001 0.001
y2[1] (numeric) = 12.8376203504 25.9180188517
y2[1] (closed_form) = 17.7696230974 23.8070712471
absolute error = 5.365
relative error = 18.06 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.3551831078 -2.05616276333
y1[1] (closed_form) = 3.3551831078 -2.05616276333
absolute error = 9.055e-63
relative error = 2.301e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.27
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.27
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54518.2MB, alloc=44.3MB, time=648.80
memory used=54564.7MB, alloc=44.3MB, time=649.36
x[1] = 0.5655 2.057
h = 0.001 0.003
y2[1] (numeric) = 12.8476500442 25.9685010266
y2[1] (closed_form) = 17.7850376908 23.818368141
absolute error = 5.385
relative error = 18.12 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.35630349799 -2.06153781323
y1[1] (closed_form) = 3.35630349799 -2.06153781323
absolute error = 8.062e-63
relative error = 2.047e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.3
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.3
Order of pole (three term test) = 29.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54610.6MB, alloc=44.3MB, time=649.91
memory used=54657.3MB, alloc=44.3MB, time=650.47
memory used=54704.0MB, alloc=44.3MB, time=651.03
x[1] = 0.5665 2.06
h = 0.0001 0.004
y2[1] (numeric) = 12.857740089 26.018988157
y2[1] (closed_form) = 17.8045968937 23.8563821182
absolute error = 5.399
relative error = 18.14 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.36392580584 -2.07119462999
y1[1] (closed_form) = 3.36392580584 -2.07119462999
absolute error = 8.062e-63
relative error = 2.041e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.39
Order of pole (three term test) = 41.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.39
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54749.9MB, alloc=44.3MB, time=651.57
memory used=54796.3MB, alloc=44.3MB, time=652.13
x[1] = 0.5666 2.064
h = 0.003 0.006
y2[1] (numeric) = 12.8678908251 26.0694800785
y2[1] (closed_form) = 17.8142364982 23.909655915
absolute error = 5.397
relative error = 18.1 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.37676347372 -2.08009658595
y1[1] (closed_form) = 3.37676347372 -2.08009658595
absolute error = 9.055e-63
relative error = 2.283e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.52
Order of pole (three term test) = 41.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.52
Order of pole (three term test) = 29.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54842.2MB, alloc=44.3MB, time=652.67
memory used=54888.7MB, alloc=44.3MB, time=653.23
x[1] = 0.5696 2.07
h = 0.0001 0.005
y2[1] (numeric) = 12.8781025938 26.1199766249
y2[1] (closed_form) = 17.8669354092 23.9836816054
absolute error = 5.427
relative error = 18.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.38994476712 -2.10288401714
y1[1] (closed_form) = 3.38994476712 -2.10288401714
absolute error = 8.246e-63
relative error = 2.067e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.7
Order of pole (three term test) = 41.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.7
Order of pole (three term test) = 29.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54934.7MB, alloc=44.3MB, time=653.77
memory used=54981.3MB, alloc=44.3MB, time=654.34
x[1] = 0.5697 2.075
h = 0.0001 0.003
y2[1] (numeric) = 12.8883757381 26.170477629
y2[1] (closed_form) = 17.8788176395 24.050461053
absolute error = 5.422
relative error = 18.09 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.40618745323 -2.1140950822
y1[1] (closed_form) = 3.40618745323 -2.1140950822
absolute error = 8.246e-63
relative error = 2.057e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.86
Order of pole (three term test) = 41.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.86
Order of pole (three term test) = 29.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55027.4MB, alloc=44.3MB, time=654.88
memory used=55074.1MB, alloc=44.3MB, time=655.45
x[1] = 0.5698 2.078
h = 0.001 0.001
y2[1] (numeric) = 12.8987106025 26.220982922
y2[1] (closed_form) = 17.8865113519 24.0904824012
absolute error = 5.424
relative error = 18.08 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.41588534504 -2.12098111721
y1[1] (closed_form) = 3.41588534504 -2.12098111721
absolute error = 8.246e-63
relative error = 2.051e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.96
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.96
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55120.6MB, alloc=44.3MB, time=656.01
memory used=55166.8MB, alloc=44.3MB, time=656.58
memory used=55213.3MB, alloc=44.3MB, time=657.15
x[1] = 0.5708 2.079
h = 0.001 0.003
y2[1] (numeric) = 12.9091075329 26.2714923338
y2[1] (closed_form) = 17.9020515293 24.101775115
absolute error = 5.444
relative error = 18.13 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.41700519327 -2.12648352722
y1[1] (closed_form) = 3.41700519327 -2.12648352722
absolute error = 8.246e-63
relative error = 2.049e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.99
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.99
Order of pole (three term test) = 29.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55259.4MB, alloc=44.3MB, time=658.20
memory used=55306.1MB, alloc=44.3MB, time=658.85
x[1] = 0.5718 2.082
h = 0.0001 0.004
y2[1] (numeric) = 12.9195668767 26.3220056929
y2[1] (closed_form) = 17.9218667178 24.1399063131
absolute error = 5.458
relative error = 18.15 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.42475375608 -2.13639623483
y1[1] (closed_form) = 3.42475375608 -2.13639623483
absolute error = 8.062e-63
relative error = 1.997e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.08
Order of pole (three term test) = 41.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.08
Order of pole (three term test) = 29.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55352.0MB, alloc=44.3MB, time=659.40
memory used=55398.3MB, alloc=44.3MB, time=659.97
x[1] = 0.5719 2.086
h = 0.003 0.006
y2[1] (numeric) = 12.9300889829 26.3725228264
y2[1] (closed_form) = 17.9317737515 24.1934173844
absolute error = 5.456
relative error = 18.12 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.43783955463 -2.14556216886
y1[1] (closed_form) = 3.43783955463 -2.14556216886
absolute error = 8.062e-63
relative error = 1.989e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.21
Order of pole (three term test) = 41.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.21
Order of pole (three term test) = 29.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55444.2MB, alloc=44.3MB, time=660.52
memory used=55490.9MB, alloc=44.3MB, time=661.09
x[1] = 0.5749 2.092
h = 0.0001 0.005
y2[1] (numeric) = 12.9406742018 26.4230435598
y2[1] (closed_form) = 17.9850507069 24.2676128309
absolute error = 5.486
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.45120944861 -2.16893009487
y1[1] (closed_form) = 3.45120944861 -2.16893009487
absolute error = 9.055e-63
relative error = 2.222e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.41
Order of pole (three term test) = 41.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.41
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55537.0MB, alloc=44.3MB, time=661.64
memory used=55583.8MB, alloc=44.3MB, time=662.22
memory used=55630.6MB, alloc=44.3MB, time=662.79
x[1] = 0.575 2.097
h = 0.0001 0.003
y2[1] (numeric) = 12.9513228855 26.4735677176
y2[1] (closed_form) = 17.9972701411 24.3346927647
absolute error = 5.481
relative error = 18.11 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.46776601303 -2.18047398685
y1[1] (closed_form) = 3.46776601303 -2.18047398685
absolute error = 9.055e-63
relative error = 2.211e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.57
Order of pole (three term test) = 42.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.57
Order of pole (three term test) = 29.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55676.7MB, alloc=44.3MB, time=663.34
memory used=55723.7MB, alloc=44.3MB, time=663.93
x[1] = 0.5751 2.1
h = 0.001 0.001
y2[1] (numeric) = 12.9620353872 26.5240951225
y2[1] (closed_form) = 18.0051694619 24.37489248
absolute error = 5.482
relative error = 18.09 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.47765031187 -2.18756311972
y1[1] (closed_form) = 3.47765031187 -2.18756311972
absolute error = 9.055e-63
relative error = 2.204e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.67
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.67
Order of pole (three term test) = 29.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55769.7MB, alloc=44.3MB, time=664.48
memory used=55816.3MB, alloc=44.3MB, time=665.06
x[1] = 0.5761 2.101
h = 0.001 0.003
y2[1] (numeric) = 12.9728120621 26.5746255959
y2[1] (closed_form) = 18.0208380506 24.3861803112
absolute error = 5.502
relative error = 18.15 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.47876884545 -2.19319565968
y1[1] (closed_form) = 3.47876884545 -2.19319565968
absolute error = 9.055e-63
relative error = 2.202e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.71
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.71
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55862.2MB, alloc=44.3MB, time=665.62
memory used=55908.9MB, alloc=44.3MB, time=666.19
x[1] = 0.5771 2.104
h = 0.0001 0.004
y2[1] (numeric) = 12.9836532664 26.6251589578
y2[1] (closed_form) = 18.040915596 24.4244301482
absolute error = 5.515
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.48664488415 -2.20337058466
y1[1] (closed_form) = 3.48664488415 -2.20337058466
absolute error = 9.220e-63
relative error = 2.235e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.81
Order of pole (three term test) = 42.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.81
Order of pole (three term test) = 29.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55955.0MB, alloc=44.3MB, time=666.74
memory used=56001.3MB, alloc=44.3MB, time=667.32
x[1] = 0.5772 2.108
h = 0.003 0.006
y2[1] (numeric) = 12.9945593582 26.6756950266
y2[1] (closed_form) = 18.0510972709 24.4781825766
absolute error = 5.513
relative error = 18.13 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.49998264181 -2.21280772757
y1[1] (closed_form) = 3.49998264181 -2.21280772757
absolute error = 9.055e-63
relative error = 2.187e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.94
Order of pole (three term test) = 42.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.94
Order of pole (three term test) = 29.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56047.4MB, alloc=44.3MB, time=667.87
memory used=56094.0MB, alloc=44.3MB, time=668.45
memory used=56140.5MB, alloc=44.3MB, time=669.02
x[1] = 0.5802 2.114
h = 0.0001 0.005
y2[1] (numeric) = 13.005530697 26.7262336195
y2[1] (closed_form) = 18.1049661936 24.5525488227
absolute error = 5.543
relative error = 18.17 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.51354178219 -2.23676992047
y1[1] (closed_form) = 3.51354178219 -2.23676992047
absolute error = 9.055e-63
relative error = 2.174e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.15
Order of pole (three term test) = 42.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.15
Order of pole (three term test) = 30.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56186.6MB, alloc=44.3MB, time=669.59
memory used=56233.3MB, alloc=44.3MB, time=670.18
x[1] = 0.5803 2.119
h = 0.0001 0.003
y2[1] (numeric) = 13.0165676439 26.7767745521
y2[1] (closed_form) = 18.1175319302 24.6199344133
absolute error = 5.538
relative error = 18.12 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.53041708123 -2.24865576378
y1[1] (closed_form) = 3.53041708123 -2.24865576378
absolute error = 9e-63
relative error = 2.150e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.32
Order of pole (three term test) = 42.49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.32
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56279.4MB, alloc=44.3MB, time=670.75
memory used=56326.2MB, alloc=44.3MB, time=671.35
x[1] = 0.5804 2.122
h = 0.001 0.001
y2[1] (numeric) = 13.0276705613 26.8273176384
y2[1] (closed_form) = 18.1256423837 24.660315537
absolute error = 5.539
relative error = 18.1 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.54049064025 -2.25595353178
y1[1] (closed_form) = 3.54049064025 -2.25595353178
absolute error = 8e-63
relative error = 1.906e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.42
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.42
Order of pole (three term test) = 30.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56372.4MB, alloc=44.3MB, time=671.92
memory used=56419.1MB, alloc=44.3MB, time=672.51
x[1] = 0.5814 2.123
h = 0.0001 0.004
y2[1] (numeric) = 13.0388398135 26.8778626913
y2[1] (closed_form) = 18.1414422686 24.6715977505
absolute error = 5.559
relative error = 18.15 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.54160705553 -2.26171903056
y1[1] (closed_form) = 3.54160705553 -2.26171903056
absolute error = 8e-63
relative error = 1.904e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.46
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.46
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56465.1MB, alloc=44.3MB, time=673.07
memory used=56511.5MB, alloc=44.3MB, time=673.65
x[1] = 0.5815 2.127
h = 0.003 0.006
y2[1] (numeric) = 13.0500757659 26.9284095218
y2[1] (closed_form) = 18.151863317 24.7255646274
absolute error = 5.557
relative error = 18.12 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.55516814758 -2.27139248606
y1[1] (closed_form) = 3.55516814758 -2.27139248606
absolute error = 8.062e-63
relative error = 1.911e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.6
Order of pole (three term test) = 42.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.6
Order of pole (three term test) = 30.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56557.7MB, alloc=44.3MB, time=674.22
memory used=56604.2MB, alloc=44.3MB, time=674.79
memory used=56650.9MB, alloc=44.3MB, time=675.38
x[1] = 0.5845 2.133
h = 0.0001 0.005
y2[1] (numeric) = 13.0613787859 26.9789579397
y2[1] (closed_form) = 18.2062511208 24.8000859647
absolute error = 5.587
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.56889797026 -2.29587520898
y1[1] (closed_form) = 3.56889797026 -2.29587520898
absolute error = 8.062e-63
relative error = 1.900e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.81
Order of pole (three term test) = 42.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.81
Order of pole (three term test) = 30.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56697.0MB, alloc=44.3MB, time=675.95
memory used=56743.7MB, alloc=44.3MB, time=676.54
x[1] = 0.5846 2.138
h = 0.0001 0.003
y2[1] (numeric) = 13.0727492422 27.0295077531
y2[1] (closed_form) = 18.2191186778 24.8677431166
absolute error = 5.582
relative error = 18.11 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.58605578976 -2.30805899813
y1[1] (closed_form) = 3.58605578976 -2.30805899813
absolute error = 8.062e-63
relative error = 1.891e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.99
Order of pole (three term test) = 42.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.99
Order of pole (three term test) = 30.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56789.8MB, alloc=44.3MB, time=677.11
memory used=56836.6MB, alloc=44.3MB, time=677.71
x[1] = 0.5847 2.141
h = 0.001 0.001
y2[1] (numeric) = 13.0841875051 27.0800587688
y2[1] (closed_form) = 18.2274131858 24.9082854586
absolute error = 5.583
relative error = 18.09 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.59629714873 -2.31553859124
y1[1] (closed_form) = 3.59629714873 -2.31553859124
absolute error = 8.062e-63
relative error = 1.885e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.1
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.1
Order of pole (three term test) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56882.7MB, alloc=44.3MB, time=678.28
memory used=56929.3MB, alloc=44.3MB, time=678.85
x[1] = 0.5857 2.142
h = 0.001 0.003
y2[1] (numeric) = 13.0956939465 27.130610792
y2[1] (closed_form) = 18.2433285203 24.9195638348
absolute error = 5.602
relative error = 18.14 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.5974127035 -2.32142088655
y1[1] (closed_form) = 3.5974127035 -2.32142088655
absolute error = 8.062e-63
relative error = 1.883e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.13
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.13
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56975.1MB, alloc=44.3MB, time=679.40
memory used=57021.8MB, alloc=44.3MB, time=679.96
x[1] = 0.5867 2.145
h = 0.0001 0.004
y2[1] (numeric) = 13.1072689398 27.1811636263
y2[1] (closed_form) = 18.2639102622 24.958041492
absolute error = 5.615
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.60553249203 -2.33209953621
y1[1] (closed_form) = 3.60553249203 -2.33209953621
absolute error = 8.062e-63
relative error = 1.878e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.24
Order of pole (three term test) = 42.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.24
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57068.2MB, alloc=44.3MB, time=680.50
memory used=57114.4MB, alloc=44.3MB, time=681.06
memory used=57161.1MB, alloc=44.3MB, time=681.64
x[1] = 0.5868 2.149
h = 0.003 0.006
y2[1] (numeric) = 13.1189128601 27.2317170738
y2[1] (closed_form) = 18.2746198079 25.0122575366
absolute error = 5.613
relative error = 18.12 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.61935289583 -2.34205809711
y1[1] (closed_form) = 3.61935289583 -2.34205809711
absolute error = 9.055e-63
relative error = 2.101e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.39
Order of pole (three term test) = 43.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.39
Order of pole (three term test) = 30.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57207.0MB, alloc=44.3MB, time=682.19
memory used=57253.6MB, alloc=44.3MB, time=682.76
x[1] = 0.5898 2.155
h = 0.0001 0.005
y2[1] (numeric) = 13.1306260839 27.2822709352
y2[1] (closed_form) = 18.3296263056 25.0869516273
absolute error = 5.643
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.63327319814 -2.36716155095
y1[1] (closed_form) = 3.63327319814 -2.36716155095
absolute error = 8.062e-63
relative error = 1.859e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.61
Order of pole (three term test) = 43.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.61
Order of pole (three term test) = 30.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57299.6MB, alloc=44.3MB, time=683.36
memory used=57346.4MB, alloc=44.3MB, time=683.93
x[1] = 0.5899 2.16
h = 0.0001 0.003
y2[1] (numeric) = 13.1424089895 27.3328250094
y2[1] (closed_form) = 18.3428576462 25.1549243283
absolute error = 5.638
relative error = 18.11 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.65075907846 -2.37970482705
y1[1] (closed_form) = 3.65075907846 -2.37970482705
absolute error = 8e-63
relative error = 1.836e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.8
Order of pole (three term test) = 43.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.8
Order of pole (three term test) = 30.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57392.4MB, alloc=44.3MB, time=684.49
memory used=57439.3MB, alloc=44.3MB, time=685.08
x[1] = 0.59 2.163
h = 0.001 0.001
y2[1] (numeric) = 13.1542619565 27.3833790942
y2[1] (closed_form) = 18.3513739005 25.1956538966
absolute error = 5.639
relative error = 18.09 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.66119517679 -2.38740369699
y1[1] (closed_form) = 3.66119517679 -2.38740369699
absolute error = 8e-63
relative error = 1.830e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.91
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.91
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57485.5MB, alloc=44.3MB, time=685.66
memory used=57532.0MB, alloc=44.3MB, time=686.24
x[1] = 0.591 2.164
h = 0.001 0.003
y2[1] (numeric) = 13.1661853664 27.4339329853
y2[1] (closed_form) = 18.3674260655 25.2069252347
absolute error = 5.658
relative error = 18.14 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.66230706737 -2.39342438636
y1[1] (closed_form) = 3.66230706737 -2.39342438636
absolute error = 8.062e-63
relative error = 1.843e-61 %
Correct digits = 63
memory used=57578.6MB, alloc=44.3MB, time=686.82
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.95
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.95
Order of pole (three term test) = 30.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57624.6MB, alloc=44.3MB, time=687.38
memory used=57671.4MB, alloc=44.3MB, time=687.97
x[1] = 0.592 2.167
h = 0.0001 0.004
y2[1] (numeric) = 13.1781796021 27.4844864772
y2[1] (closed_form) = 18.3882891993 25.2455256275
absolute error = 5.671
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.67055788601 -2.40438417325
y1[1] (closed_form) = 3.67055788601 -2.40438417325
absolute error = 9e-63
relative error = 2.051e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.06
Order of pole (three term test) = 43.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.06
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57717.5MB, alloc=44.3MB, time=688.53
memory used=57764.1MB, alloc=44.3MB, time=689.10
x[1] = 0.5921 2.171
h = 0.003 0.006
y2[1] (numeric) = 13.1902450483 27.5350393627
y2[1] (closed_form) = 18.3992949845 25.2999950569
absolute error = 5.668
relative error = 18.12 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.68464158009 -2.41463560306
y1[1] (closed_form) = 3.68464158009 -2.41463560306
absolute error = 9e-63
relative error = 2.043e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.22
Order of pole (three term test) = 43.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.22
Order of pole (three term test) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57810.0MB, alloc=44.3MB, time=689.67
memory used=57856.8MB, alloc=44.3MB, time=690.25
x[1] = 0.5951 2.177
h = 0.0001 0.005
y2[1] (numeric) = 13.2023820909 27.5855914331
y2[1] (closed_form) = 18.4549350041 25.3748627685
absolute error = 5.699
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.69875285405 -2.44037447951
y1[1] (closed_form) = 3.69875285405 -2.44037447951
absolute error = 9e-63
relative error = 2.031e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.45
Order of pole (three term test) = 43.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.45
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57902.8MB, alloc=44.3MB, time=690.81
memory used=57949.4MB, alloc=44.3MB, time=691.38
x[1] = 0.5952 2.182
h = 0.0001 0.003
y2[1] (numeric) = 13.2145911179 27.636142478
y2[1] (closed_form) = 18.4685398964 25.4431563601
absolute error = 5.693
relative error = 18.11 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.7165718421 -2.45328703935
y1[1] (closed_form) = 3.7165718421 -2.45328703935
absolute error = 1.0e-62
relative error = 2.246e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.65
Order of pole (three term test) = 43.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.65
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57995.8MB, alloc=44.3MB, time=691.95
memory used=58042.5MB, alloc=44.3MB, time=692.54
memory used=58089.5MB, alloc=44.3MB, time=693.13
x[1] = 0.5953 2.185
h = 0.001 0.001
y2[1] (numeric) = 13.2268725186 27.6866922855
y2[1] (closed_form) = 18.4772838261 25.4840762937
absolute error = 5.694
relative error = 18.09 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.72720564232 -2.46121113009
y1[1] (closed_form) = 3.72720564232 -2.46121113009
absolute error = 1.005e-62
relative error = 2.250e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.76
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.76
Order of pole (three term test) = 31.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58135.4MB, alloc=44.3MB, time=693.70
memory used=58181.8MB, alloc=44.3MB, time=694.28
x[1] = 0.5963 2.186
h = 0.001 0.003
y2[1] (numeric) = 13.239226684 27.7372406422
y2[1] (closed_form) = 18.4934758774 25.4953397618
absolute error = 5.713
relative error = 18.14 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.72831297152 -2.46737321779
y1[1] (closed_form) = 3.72831297152 -2.46737321779
absolute error = 1.005e-62
relative error = 2.248e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.8
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.8
Order of pole (three term test) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58227.8MB, alloc=44.3MB, time=694.83
memory used=58274.4MB, alloc=44.3MB, time=695.40
x[1] = 0.5973 2.189
h = 0.0001 0.004
y2[1] (numeric) = 13.2516540067 27.7877873328
y2[1] (closed_form) = 18.5146273615 25.5340642779
absolute error = 5.725
relative error = 18.15 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.736696026 -2.47862106298
y1[1] (closed_form) = 3.736696026 -2.47862106298
absolute error = 1.005e-62
relative error = 2.241e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.92
Order of pole (three term test) = 43.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.92
Order of pole (three term test) = 31.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58320.4MB, alloc=44.3MB, time=695.95
memory used=58367.1MB, alloc=44.3MB, time=696.52
x[1] = 0.5974 2.193
h = 0.003 0.006
y2[1] (numeric) = 13.2641548811 27.8383321406
y2[1] (closed_form) = 18.5259373227 25.5887913554
absolute error = 5.722
relative error = 18.11 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.75104704061 -2.48917332011
y1[1] (closed_form) = 3.75104704061 -2.48917332011
absolute error = 1.005e-62
relative error = 2.232e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.08
Order of pole (three term test) = 44.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.08
Order of pole (three term test) = 31.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58413.2MB, alloc=44.3MB, time=697.07
memory used=58459.7MB, alloc=44.3MB, time=697.64
x[1] = 0.6004 2.199
h = 0.0001 0.005
y2[1] (numeric) = 13.276729703 27.8888748473
y2[1] (closed_form) = 18.5822260215 25.6638334868
absolute error = 5.753
relative error = 18.16 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.76534971711 -2.51556264512
y1[1] (closed_form) = 3.76534971711 -2.51556264512
absolute error = 1.005e-62
relative error = 2.219e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.32
Order of pole (three term test) = 44.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.32
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58506.2MB, alloc=44.3MB, time=698.20
memory used=58552.5MB, alloc=44.3MB, time=698.79
memory used=58599.3MB, alloc=44.3MB, time=699.37
x[1] = 0.6005 2.204
h = 0.0001 0.003
y2[1] (numeric) = 13.2893788699 27.9394152328
y2[1] (closed_form) = 18.5962144787 25.7324533698
absolute error = 5.747
relative error = 18.1 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.78350692552 -2.52885453152
y1[1] (closed_form) = 3.78350692552 -2.52885453152
absolute error = 1.005e-62
relative error = 2.208e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.53
Order of pole (three term test) = 44.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.53
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58645.5MB, alloc=44.3MB, time=699.93
memory used=58692.3MB, alloc=44.3MB, time=700.50
x[1] = 0.6006 2.207
h = 0.001 0.001
y2[1] (numeric) = 13.3021027811 27.9899530757
y2[1] (closed_form) = 18.6051921612 25.7735668412
absolute error = 5.748
relative error = 18.08 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.7943414278 -2.53700993584
y1[1] (closed_form) = 3.7943414278 -2.53700993584
absolute error = 1.005e-62
relative error = 2.202e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.65
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.65
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58738.3MB, alloc=44.3MB, time=701.05
memory used=58784.7MB, alloc=44.3MB, time=701.62
x[1] = 0.6016 2.208
h = 0.001 0.003
y2[1] (numeric) = 13.3149018373 28.0404881525
y2[1] (closed_form) = 18.6215272166 25.7848215714
absolute error = 5.766
relative error = 18.13 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.79544326336 -2.54331648955
y1[1] (closed_form) = 3.79544326336 -2.54331648955
absolute error = 1.005e-62
relative error = 2.200e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.69
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.69
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58830.4MB, alloc=44.3MB, time=702.16
memory used=58877.0MB, alloc=44.3MB, time=702.72
x[1] = 0.6026 2.211
h = 0.0001 0.004
y2[1] (numeric) = 13.327776441 28.0910202383
y2[1] (closed_form) = 18.64297417 25.8236715877
absolute error = 5.779
relative error = 18.14 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.8039597525 -2.55485947626
y1[1] (closed_form) = 3.8039597525 -2.55485947626
absolute error = 1.005e-62
relative error = 2.193e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.82
Order of pole (three term test) = 44.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.82
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58923.2MB, alloc=44.3MB, time=703.26
memory used=58969.9MB, alloc=44.3MB, time=703.82
x[1] = 0.6027 2.215
h = 0.003 0.006
y2[1] (numeric) = 13.3407269964 28.1415491066
y2[1] (closed_form) = 18.6545964423 25.8786606233
absolute error = 5.776
relative error = 18.1 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.81858216963 -2.56572071865
y1[1] (closed_form) = 3.81858216963 -2.56572071865
absolute error = 9.055e-63
relative error = 1.968e-61 %
Correct digits = 63
memory used=59016.4MB, alloc=44.3MB, time=704.38
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.99
Order of pole (three term test) = 44.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.99
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59062.3MB, alloc=44.3MB, time=704.92
memory used=59109.0MB, alloc=44.3MB, time=705.48
x[1] = 0.6057 2.221
h = 0.0001 0.005
y2[1] (numeric) = 13.3537539093 28.1920745291
y2[1] (closed_form) = 18.7115493139 25.9538779014
absolute error = 5.807
relative error = 18.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.83307661513 -2.59277585934
y1[1] (closed_form) = 3.83307661513 -2.59277585934
absolute error = 1.0e-62
relative error = 2.161e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.24
Order of pole (three term test) = 44.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.24
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59155.0MB, alloc=44.3MB, time=706.03
memory used=59201.8MB, alloc=44.3MB, time=706.59
x[1] = 0.6058 2.226
h = 0.0001 0.003
y2[1] (numeric) = 13.3668575871 28.2425962759
y2[1] (closed_form) = 18.7259316003 26.022829536
absolute error = 5.801
relative error = 18.09 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.85157722229 -2.60645736697
y1[1] (closed_form) = 3.85157722229 -2.60645736697
absolute error = 1.005e-62
relative error = 2.161e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.45
Order of pole (three term test) = 44.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.45
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59247.8MB, alloc=44.3MB, time=707.14
memory used=59294.7MB, alloc=44.3MB, time=707.72
x[1] = 0.6059 2.229
h = 0.001 0.001
y2[1] (numeric) = 13.380038439 28.2931141155
y2[1] (closed_form) = 18.7351492647 26.0641397516
absolute error = 5.8
relative error = 18.07 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.86261546433 -2.61485032989
y1[1] (closed_form) = 3.86261546433 -2.61485032989
absolute error = 1.005e-62
relative error = 2.155e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.58
Order of pole (three term test) = 44.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.58
Order of pole (three term test) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59340.9MB, alloc=44.3MB, time=708.27
memory used=59387.5MB, alloc=44.3MB, time=708.82
x[1] = 0.6069 2.23
h = 0.0001 0.004
y2[1] (numeric) = 13.3932968757 28.3436278144
y2[1] (closed_form) = 18.7516305051 26.0753848384
absolute error = 5.819
relative error = 18.12 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.86371083781 -2.62130448189
y1[1] (closed_form) = 3.86371083781 -2.62130448189
absolute error = 1.005e-62
relative error = 2.152e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.62
Order of pole (three term test) = 44.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.62
Order of pole (three term test) = 32.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59433.7MB, alloc=44.3MB, time=709.36
memory used=59480.2MB, alloc=44.3MB, time=709.92
memory used=59526.7MB, alloc=44.3MB, time=710.48
x[1] = 0.607 2.234
h = 0.003 0.006
y2[1] (numeric) = 13.4066333099 28.3941371378
y2[1] (closed_form) = 18.7635250829 26.1306067015
absolute error = 5.815
relative error = 18.08 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.87857399405 -2.63243507682
y1[1] (closed_form) = 3.87857399405 -2.63243507682
absolute error = 1.005e-62
relative error = 2.144e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.8
Order of pole (three term test) = 45.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.8
Order of pole (three term test) = 32.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59572.7MB, alloc=44.3MB, time=711.02
memory used=59619.5MB, alloc=44.3MB, time=711.58
x[1] = 0.61 2.24
h = 0.0001 0.005
y2[1] (numeric) = 13.4200481555 28.4446418489
y2[1] (closed_form) = 18.8210602248 26.2059834343
absolute error = 5.847
relative error = 18.12 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.89324193641 -2.66007361175
y1[1] (closed_form) = 3.89324193641 -2.66007361175
absolute error = 1.005e-62
relative error = 2.131e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.06
Order of pole (three term test) = 45.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.06
Order of pole (three term test) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59665.5MB, alloc=44.3MB, time=712.12
memory used=59712.2MB, alloc=44.3MB, time=712.68
x[1] = 0.6101 2.245
h = 0.0001 0.003
y2[1] (numeric) = 13.4335418287 28.4951417092
y2[1] (closed_form) = 18.83578588 26.2752299096
absolute error = 5.841
relative error = 18.07 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.91204713947 -2.67409475692
y1[1] (closed_form) = 3.91204713947 -2.67409475692
absolute error = 1.005e-62
relative error = 2.121e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.28
Order of pole (three term test) = 45.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.28
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59758.2MB, alloc=44.3MB, time=713.23
memory used=59805.1MB, alloc=44.3MB, time=713.80
x[1] = 0.6102 2.248
h = 0.001 0.001
y2[1] (numeric) = 13.4471147468 28.5456364787
y2[1] (closed_form) = 18.8452128231 26.3167150319
absolute error = 5.84
relative error = 18.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.92326614897 -2.68269484522
y1[1] (closed_form) = 3.92326614897 -2.68269484522
absolute error = 1.005e-62
relative error = 2.115e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.42
Order of pole (three term test) = 45.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.42
Order of pole (three term test) = 32.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59851.5MB, alloc=44.3MB, time=714.37
memory used=59898.1MB, alloc=44.3MB, time=714.93
x[1] = 0.6112 2.249
h = 0.001 0.003
y2[1] (numeric) = 13.4607673292 28.5961259155
y2[1] (closed_form) = 18.8618226213 26.3279528578
absolute error = 5.858
relative error = 18.09 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.92435696629 -2.6892786967
y1[1] (closed_form) = 3.92435696629 -2.6892786967
absolute error = 1.005e-62
relative error = 2.112e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.46
Order of pole (three term test) = 45.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.46
Order of pole (three term test) = 32.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59944.2MB, alloc=44.3MB, time=715.48
memory used=59990.8MB, alloc=44.3MB, time=716.03
memory used=60037.4MB, alloc=44.3MB, time=716.58
x[1] = 0.6122 2.252
h = 0.0001 0.004
y2[1] (numeric) = 13.4744999969 28.6466097758
y2[1] (closed_form) = 18.8838373526 26.3670437525
absolute error = 5.87
relative error = 18.1 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.93312863143 -2.70138867251
y1[1] (closed_form) = 3.93312863143 -2.70138867251
absolute error = 1.005e-62
relative error = 2.106e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.6
Order of pole (three term test) = 45.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.6
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60083.3MB, alloc=44.3MB, time=717.12
memory used=60130.0MB, alloc=44.3MB, time=717.67
x[1] = 0.6123 2.256
h = 0.003 0.006
y2[1] (numeric) = 13.4883131726 28.6970878143
y2[1] (closed_form) = 18.8960598718 26.4225358203
absolute error = 5.867
relative error = 18.06 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.9482710263 -2.71284392966
y1[1] (closed_form) = 3.9482710263 -2.71284392966
absolute error = 1.005e-62
relative error = 2.098e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.78
Order of pole (three term test) = 45.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.78
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60176.0MB, alloc=44.3MB, time=718.21
memory used=60222.6MB, alloc=44.3MB, time=718.76
x[1] = 0.6153 2.262
h = 0.0001 0.005
y2[1] (numeric) = 13.5022072807 28.7475597839
y2[1] (closed_form) = 18.9542889305 26.4980890447
absolute error = 5.898
relative error = 18.1 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.96313142925 -2.74117780503
y1[1] (closed_form) = 3.96313142925 -2.74117780503
absolute error = 1.005e-62
relative error = 2.086e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.05
Order of pole (three term test) = 45.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.05
Order of pole (three term test) = 32.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60268.7MB, alloc=44.3MB, time=719.30
memory used=60315.4MB, alloc=44.3MB, time=719.85
x[1] = 0.6154 2.267
h = 0.0001 0.003
y2[1] (numeric) = 13.5161827474 28.7980254356
y2[1] (closed_form) = 18.9694281359 26.5676777193
absolute error = 5.892
relative error = 18.05 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.98228997162 -2.75560835439
y1[1] (closed_form) = 3.98228997162 -2.75560835439
absolute error = 1.005e-62
relative error = 2.075e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.28
Order of pole (three term test) = 45.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.28
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60361.4MB, alloc=44.3MB, time=720.39
memory used=60408.3MB, alloc=44.3MB, time=720.96
x[1] = 0.6155 2.27
h = 0.001 0.001
y2[1] (numeric) = 13.5302400005 28.8484845187
y2[1] (closed_form) = 18.9791070287 26.6093657204
absolute error = 5.891
relative error = 18.02 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.9937185519 -2.76445800211
y1[1] (closed_form) = 3.9937185519 -2.76445800211
absolute error = 1.005e-62
relative error = 2.069e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.42
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.42
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60454.8MB, alloc=44.3MB, time=721.52
memory used=60501.0MB, alloc=44.3MB, time=722.06
memory used=60547.7MB, alloc=44.3MB, time=722.63
x[1] = 0.6165 2.271
h = 0.001 0.003
y2[1] (numeric) = 13.5443794696 28.8989367809
y2[1] (closed_form) = 18.9958691151 26.6205921546
absolute error = 5.908
relative error = 18.07 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.99480104389 -2.77119546894
y1[1] (closed_form) = 3.99480104389 -2.77119546894
absolute error = 1.005e-62
relative error = 2.067e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.47
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.47
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60593.6MB, alloc=44.3MB, time=723.17
memory used=60640.2MB, alloc=44.3MB, time=723.72
x[1] = 0.6175 2.274
h = 0.0001 0.004
y2[1] (numeric) = 13.5586015861 28.9493819677
y2[1] (closed_form) = 19.0182005834 26.659812512
absolute error = 5.92
relative error = 18.08 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.00370961631 -2.78362176308
y1[1] (closed_form) = 4.00370961631 -2.78362176308
absolute error = 1.005e-62
relative error = 2.061e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.61
Order of pole (three term test) = 46.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.61
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60686.1MB, alloc=44.3MB, time=724.25
memory used=60732.6MB, alloc=44.3MB, time=724.80
x[1] = 0.6176 2.278
h = 0.003 0.006
y2[1] (numeric) = 13.5729067832 28.9998198231
y2[1] (closed_form) = 19.0307597736 26.7155792304
absolute error = 5.917
relative error = 18.04 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.01913548201 -2.79541043664
y1[1] (closed_form) = 4.01913548201 -2.79541043664
absolute error = 1.020e-62
relative error = 2.083e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.8
Order of pole (three term test) = 46.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.8
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60778.6MB, alloc=44.3MB, time=725.34
memory used=60825.4MB, alloc=44.3MB, time=725.89
x[1] = 0.6206 2.284
h = 0.0001 0.005
y2[1] (numeric) = 13.5872954955 29.0502500893
y2[1] (closed_form) = 19.0896992467 26.7913094541
absolute error = 5.948
relative error = 18.08 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.0341885128 -2.82445603622
y1[1] (closed_form) = 4.0341885128 -2.82445603622
absolute error = 1.020e-62
relative error = 2.071e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.09
Order of pole (three term test) = 46.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.09
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60871.5MB, alloc=44.3MB, time=726.43
memory used=60918.2MB, alloc=44.3MB, time=726.99
memory used=60965.0MB, alloc=44.3MB, time=727.54
x[1] = 0.6207 2.289
h = 0.0001 0.003
y2[1] (numeric) = 13.6017681597 29.1006725065
y2[1] (closed_form) = 19.1052630171 26.8612459613
absolute error = 5.942
relative error = 18.03 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.05370576382 -2.83930703709
y1[1] (closed_form) = 4.05370576382 -2.83930703709
absolute error = 1.020e-62
relative error = 2.061e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.33
Order of pole (three term test) = 46.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.33
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61011.3MB, alloc=44.3MB, time=728.09
memory used=61058.3MB, alloc=44.3MB, time=728.66
x[1] = 0.6208 2.292
h = 0.001 0.001
y2[1] (numeric) = 13.6163252142 29.1510868133
y2[1] (closed_form) = 19.1152005424 26.9031401461
absolute error = 5.941
relative error = 18 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.06534706154 -2.84841294434
y1[1] (closed_form) = 4.06534706154 -2.84841294434
absolute error = 1.020e-62
relative error = 2.054e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.48
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.48
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61104.3MB, alloc=44.3MB, time=729.20
memory used=61151.0MB, alloc=44.3MB, time=729.75
x[1] = 0.6218 2.293
h = 0.001 0.003
y2[1] (numeric) = 13.6309670991 29.2014927462
y2[1] (closed_form) = 19.132118286 26.9143541707
absolute error = 5.958
relative error = 18.04 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.06642015043 -2.85530735073
y1[1] (closed_form) = 4.06642015043 -2.85530735073
absolute error = 1.105e-62
relative error = 2.223e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.53
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.53
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61196.9MB, alloc=44.3MB, time=730.29
memory used=61243.5MB, alloc=44.3MB, time=730.85
x[1] = 0.6228 2.296
h = 0.0001 0.004
y2[1] (numeric) = 13.6456942562 29.2518900401
y2[1] (closed_form) = 19.1547742639 26.9537053187
absolute error = 5.969
relative error = 18.05 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.07546679373 -2.86805770628
y1[1] (closed_form) = 4.07546679373 -2.86805770628
absolute error = 1.105e-62
relative error = 2.216e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.67
Order of pole (three term test) = 46.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.67
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61289.4MB, alloc=44.3MB, time=731.38
memory used=61336.0MB, alloc=44.3MB, time=731.93
x[1] = 0.6229 2.3
h = 0.003 0.006
y2[1] (numeric) = 13.6605071292 29.3022784279
y2[1] (closed_form) = 19.1676790723 27.0097511802
absolute error = 5.965
relative error = 18.01 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.09118041393 -2.88018876856
y1[1] (closed_form) = 4.09118041393 -2.88018876856
absolute error = 1.105e-62
relative error = 2.208e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.87
Order of pole (three term test) = 46.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.87
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61382.0MB, alloc=44.3MB, time=732.47
memory used=61428.6MB, alloc=44.3MB, time=733.02
memory used=61475.3MB, alloc=44.3MB, time=733.57
x[1] = 0.6259 2.306
h = 0.0001 0.005
y2[1] (numeric) = 13.6754061635 29.3526576407
y2[1] (closed_form) = 19.2273458225 27.0856588257
absolute error = 5.997
relative error = 18.05 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.10642616163 -2.90996284553
y1[1] (closed_form) = 4.10642616163 -2.90996284553
absolute error = 1.105e-62
relative error = 2.195e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.17
Order of pole (three term test) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.17
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61521.3MB, alloc=44.3MB, time=734.11
memory used=61568.0MB, alloc=44.3MB, time=734.66
x[1] = 0.626 2.311
h = 0.0001 0.003
y2[1] (numeric) = 13.6903918063 29.4030274077
y2[1] (closed_form) = 19.2433454475 27.1559488586
absolute error = 5.99
relative error = 18 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.12630755614 -2.9252456206
y1[1] (closed_form) = 4.12630755614 -2.9252456206
absolute error = 1.005e-62
relative error = 1.987e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.43
Order of pole (three term test) = 47.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.43
Order of pole (three term test) = 34.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61614.0MB, alloc=44.3MB, time=735.21
memory used=61660.8MB, alloc=44.3MB, time=735.78
x[1] = 0.6261 2.314
h = 0.001 0.001
y2[1] (numeric) = 13.7054645067 29.4533874563
y2[1] (closed_form) = 19.253548454 27.1980525654
absolute error = 5.989
relative error = 17.97 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.13816475517 -2.93461465391
y1[1] (closed_form) = 4.13816475517 -2.93461465391
absolute error = 1.105e-62
relative error = 2.177e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.58
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.58
Order of pole (three term test) = 34.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61706.9MB, alloc=44.3MB, time=736.32
memory used=61753.5MB, alloc=44.3MB, time=736.88
x[1] = 0.6271 2.315
h = 0.001 0.003
y2[1] (numeric) = 13.7206247153 29.503737512
y2[1] (closed_form) = 19.2706252919 27.2092531206
absolute error = 6.006
relative error = 18.01 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.13922732232 -2.94166939345
y1[1] (closed_form) = 4.13922732232 -2.94166939345
absolute error = 1.020e-62
relative error = 2.008e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.63
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.63
Order of pole (three term test) = 34.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61799.3MB, alloc=44.3MB, time=737.42
memory used=61846.0MB, alloc=44.3MB, time=737.98
x[1] = 0.6281 2.318
h = 0.0001 0.004
y2[1] (numeric) = 13.7358728849 29.5540772983
y2[1] (closed_form) = 19.2936137304 27.248736371
absolute error = 6.017
relative error = 18.02 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.14841318746 -2.95475173342
y1[1] (closed_form) = 4.14841318746 -2.95475173342
absolute error = 1.020e-62
relative error = 2.002e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.78
Order of pole (three term test) = 47.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.78
Order of pole (three term test) = 34.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61892.5MB, alloc=44.3MB, time=738.53
memory used=61938.8MB, alloc=44.3MB, time=739.07
memory used=61985.4MB, alloc=44.3MB, time=739.63
x[1] = 0.6282 2.322
h = 0.003 0.006
y2[1] (numeric) = 13.7512094698 29.6044065368
y2[1] (closed_form) = 19.3068733268 27.3050659149
absolute error = 6.013
relative error = 17.98 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.16441889718 -2.96723437995
y1[1] (closed_form) = 4.16441889718 -2.96723437995
absolute error = 1.118e-62
relative error = 2.186e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.99
Order of pole (three term test) = 47.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.99
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62031.4MB, alloc=44.3MB, time=740.17
memory used=62078.3MB, alloc=44.3MB, time=740.73
x[1] = 0.6312 2.328
h = 0.0001 0.005
y2[1] (numeric) = 13.7666349262 29.6547249473
y2[1] (closed_form) = 19.3672845899 27.3811513161
absolute error = 6.045
relative error = 18.02 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.17985736882 -2.99775406456
y1[1] (closed_form) = 4.17985736882 -2.99775406456
absolute error = 1.118e-62
relative error = 2.174e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.31
Order of pole (three term test) = 47.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.31
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62124.3MB, alloc=44.3MB, time=741.26
memory used=62171.1MB, alloc=44.3MB, time=741.82
x[1] = 0.6313 2.333
h = 0.0001 0.003
y2[1] (numeric) = 13.7821497121 29.7050322477
y2[1] (closed_form) = 19.38373164 27.4518006271
absolute error = 6.038
relative error = 17.97 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.20010840701 -3.01348021829
y1[1] (closed_form) = 4.20010840701 -3.01348021829
absolute error = 1.118e-62
relative error = 2.163e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.57
Order of pole (three term test) = 47.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.57
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62217.2MB, alloc=44.3MB, time=742.36
memory used=62264.0MB, alloc=44.3MB, time=742.92
x[1] = 0.6314 2.336
h = 0.001 0.001
y2[1] (numeric) = 13.7977542873 29.755328154
y2[1] (closed_form) = 19.3942071464 27.494117228
absolute error = 6.036
relative error = 17.94 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.21218472829 -3.02311941454
y1[1] (closed_form) = 4.21218472829 -3.02311941454
absolute error = 1.118e-62
relative error = 2.156e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.73
Order of pole (three term test) = 47.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.73
Order of pole (three term test) = 35.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62310.2MB, alloc=44.3MB, time=743.47
memory used=62356.9MB, alloc=44.3MB, time=744.02
x[1] = 0.6324 2.337
h = 0.0001 0.004
y2[1] (numeric) = 13.8134491135 29.8056123799
y2[1] (closed_form) = 19.411446585 27.5053032107
absolute error = 6.052
relative error = 17.98 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.21323561284 -3.03033795145
y1[1] (closed_form) = 4.21323561284 -3.03033795145
absolute error = 1.118e-62
relative error = 2.154e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.78
Order of pole (three term test) = 47.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.78
Order of pole (three term test) = 35.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62403.3MB, alloc=44.3MB, time=744.57
memory used=62449.4MB, alloc=44.3MB, time=745.12
memory used=62495.9MB, alloc=44.3MB, time=745.67
x[1] = 0.6325 2.341
h = 0.003 0.006
y2[1] (numeric) = 13.8292346541 29.8558846377
y2[1] (closed_form) = 19.4250156343 27.5618849886
absolute error = 6.048
relative error = 17.94 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.22950059531 -3.04312721717
y1[1] (closed_form) = 4.22950059531 -3.04312721717
absolute error = 1.118e-62
relative error = 2.146e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27
Order of pole (three term test) = 48.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62541.9MB, alloc=44.3MB, time=746.21
memory used=62588.5MB, alloc=44.3MB, time=746.76
x[1] = 0.6355 2.347
h = 0.0001 0.005
y2[1] (numeric) = 13.8451113746 29.9061446372
y2[1] (closed_form) = 19.4860797206 27.6381327478
absolute error = 6.08
relative error = 17.98 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.24511406388 -3.07430041286
y1[1] (closed_form) = 4.24511406388 -3.07430041286
absolute error = 1.140e-62
relative error = 2.175e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.32
Order of pole (three term test) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.32
Order of pole (three term test) = 35.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62634.6MB, alloc=44.3MB, time=747.30
memory used=62681.3MB, alloc=44.3MB, time=747.86
x[1] = 0.6356 2.352
h = 0.0001 0.003
y2[1] (numeric) = 13.8610797419 29.9563920867
y2[1] (closed_form) = 19.5029170103 27.7091014879
absolute error = 6.073
relative error = 17.92 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.26569320812 -3.09041323113
y1[1] (closed_form) = 4.26569320812 -3.09041323113
absolute error = 1.140e-62
relative error = 2.165e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.6
Order of pole (three term test) = 48.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.6
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62727.3MB, alloc=44.3MB, time=748.40
memory used=62774.1MB, alloc=44.3MB, time=748.96
x[1] = 0.6357 2.355
h = 0.001 0.001
y2[1] (numeric) = 13.8771402253 30.0066266923
y2[1] (closed_form) = 19.5136302372 27.7516074299
absolute error = 6.071
relative error = 17.89 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.27796408543 -3.10028807943
y1[1] (closed_form) = 4.27796408543 -3.10028807943
absolute error = 1.140e-62
relative error = 2.158e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.76
Order of pole (three term test) = 48.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.76
Order of pole (three term test) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62820.4MB, alloc=44.3MB, time=749.52
memory used=62867.0MB, alloc=44.3MB, time=750.07
x[1] = 0.6367 2.356
h = 0.001 0.003
y2[1] (numeric) = 13.8932932954 30.056848158
y2[1] (closed_form) = 19.5310126914 27.7627819469
absolute error = 6.087
relative error = 17.93 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.27900595988 -3.10765059541
memory used=62913.6MB, alloc=44.3MB, time=750.63
y1[1] (closed_form) = 4.27900595988 -3.10765059541
absolute error = 1.118e-62
relative error = 2.114e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.82
Order of pole (three term test) = 48.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.82
Order of pole (three term test) = 36.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62959.7MB, alloc=44.3MB, time=751.16
memory used=63006.5MB, alloc=44.3MB, time=751.72
x[1] = 0.6377 2.359
h = 0.0001 0.004
y2[1] (numeric) = 13.909539425 30.107056186
y2[1] (closed_form) = 19.5546399414 27.8025186326
absolute error = 6.097
relative error = 17.94 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.28845808499 -3.12137071078
y1[1] (closed_form) = 4.28845808499 -3.12137071078
absolute error = 1.118e-62
relative error = 2.108e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.99
Order of pole (three term test) = 48.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.99
Order of pole (three term test) = 36.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63052.4MB, alloc=44.3MB, time=752.26
memory used=63098.9MB, alloc=44.3MB, time=752.81
x[1] = 0.6378 2.363
h = 0.003 0.006
y2[1] (numeric) = 13.9258790888 30.1572504763
y2[1] (closed_form) = 19.568581397 27.8593927791
absolute error = 6.093
relative error = 17.9 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.30502347555 -3.13452923039
y1[1] (closed_form) = 4.30502347555 -3.13452923039
absolute error = 1.217e-62
relative error = 2.284e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.21
Order of pole (three term test) = 48.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.21
Order of pole (three term test) = 36.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63144.9MB, alloc=44.3MB, time=753.35
memory used=63191.6MB, alloc=44.3MB, time=753.90
x[1] = 0.6408 2.369
h = 0.0001 0.005
y2[1] (numeric) = 13.942312763 30.2074307272
y2[1] (closed_form) = 19.6304230863 27.9358188818
absolute error = 6.125
relative error = 17.94 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.3208296641 -3.16648094202
y1[1] (closed_form) = 4.3208296641 -3.16648094202
absolute error = 1.237e-62
relative error = 2.309e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.55
Order of pole (three term test) = 49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.55
Order of pole (three term test) = 36.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63237.7MB, alloc=44.3MB, time=754.44
memory used=63284.3MB, alloc=44.3MB, time=755.00
x[1] = 0.6409 2.374
h = 0.0001 0.003
y2[1] (numeric) = 13.9588409262 30.2575966345
y2[1] (closed_form) = 19.6477300325 28.0071579084
absolute error = 6.118
relative error = 17.88 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.34178900616 -3.18305943739
y1[1] (closed_form) = 4.34178900616 -3.18305943739
absolute error = 1.237e-62
relative error = 2.298e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.84
Order of pole (three term test) = 49.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.84
Order of pole (three term test) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63330.8MB, alloc=44.3MB, time=755.54
memory used=63377.3MB, alloc=44.3MB, time=756.10
memory used=63424.2MB, alloc=44.3MB, time=756.67
x[1] = 0.641 2.377
h = 0.001 0.001
y2[1] (numeric) = 13.9754640584 30.3077478925
y2[1] (closed_form) = 19.6587292442 28.0498831968
absolute error = 6.115
relative error = 17.85 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.354285186 -3.19321797012
y1[1] (closed_form) = 4.354285186 -3.19321797012
absolute error = 1.237e-62
relative error = 2.291e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.01
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.01
Order of pole (three term test) = 36.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63470.1MB, alloc=44.3MB, time=757.21
memory used=63516.7MB, alloc=44.3MB, time=757.77
x[1] = 0.642 2.378
h = 0.001 0.003
y2[1] (numeric) = 13.9921826417 30.3578841931
y2[1] (closed_form) = 19.6762810276 28.0610410128
absolute error = 6.131
relative error = 17.89 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.35531314422 -3.20075093719
y1[1] (closed_form) = 4.35531314422 -3.20075093719
absolute error = 1.237e-62
relative error = 2.289e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.07
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.07
Order of pole (three term test) = 36.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63562.7MB, alloc=44.3MB, time=758.30
memory used=63609.5MB, alloc=44.3MB, time=758.86
x[1] = 0.643 2.381
h = 0.0001 0.004
y2[1] (numeric) = 14.0089971602 30.4080052261
y2[1] (closed_form) = 19.7002644903 28.1009135558
absolute error = 6.141
relative error = 17.89 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.36490780396 -3.21482671857
y1[1] (closed_form) = 4.36490780396 -3.21482671857
absolute error = 1.237e-62
relative error = 2.282e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.25
Order of pole (three term test) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.25
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63655.3MB, alloc=44.3MB, time=759.40
memory used=63701.8MB, alloc=44.3MB, time=759.96
x[1] = 0.6431 2.385
h = 0.003 0.006
y2[1] (numeric) = 14.0259080996 30.4581106796
y2[1] (closed_form) = 19.7145881878 28.158084746
absolute error = 6.136
relative error = 17.85 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.38177808635 -3.22836435468
y1[1] (closed_form) = 4.38177808635 -3.22836435468
absolute error = 1.237e-62
relative error = 2.273e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.48
Order of pole (three term test) = 49.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.48
Order of pole (three term test) = 37.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63747.7MB, alloc=44.3MB, time=760.49
memory used=63794.4MB, alloc=44.3MB, time=761.04
x[1] = 0.6461 2.391
h = 0.0001 0.005
y2[1] (numeric) = 14.0429159477 30.5082002393
y2[1] (closed_form) = 19.7772258284 28.2346892553
absolute error = 6.169
relative error = 17.89 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.39777674958 -3.26111283605
y1[1] (closed_form) = 4.39777674958 -3.26111283605
absolute error = 1.237e-62
relative error = 2.259e-61 %
Correct digits = 63
memory used=63840.9MB, alloc=44.3MB, time=761.59
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.84
Order of pole (three term test) = 49.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.84
Order of pole (three term test) = 37.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63887.1MB, alloc=44.3MB, time=762.13
memory used=63933.9MB, alloc=44.3MB, time=762.69
x[1] = 0.6462 2.396
h = 0.0001 0.003
y2[1] (numeric) = 14.0600211943 30.5582735888
y2[1] (closed_form) = 19.7950148423 28.3064044942
absolute error = 6.161
relative error = 17.84 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.41912197889 -3.27816945511
y1[1] (closed_form) = 4.41912197889 -3.27816945511
absolute error = 1.217e-62
relative error = 2.211e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.14
Order of pole (three term test) = 50.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.14
Order of pole (three term test) = 37.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=63980.0MB, alloc=44.3MB, time=763.24
memory used=64026.7MB, alloc=44.3MB, time=763.80
x[1] = 0.6463 2.399
h = 0.001 0.001
y2[1] (numeric) = 14.0772243308 30.60833041
y2[1] (closed_form) = 19.8063075654 28.3493525987
absolute error = 6.158
relative error = 17.81 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.43184678939 -3.28861921811
y1[1] (closed_form) = 4.43184678939 -3.28861921811
absolute error = 1.217e-62
relative error = 2.204e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.32
Order of pole (three term test) = 50.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.32
Order of pole (three term test) = 37.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64072.7MB, alloc=44.3MB, time=764.34
memory used=64119.4MB, alloc=44.3MB, time=764.90
x[1] = 0.6473 2.4
h = 0.001 0.003
y2[1] (numeric) = 14.0945258507 30.6583703823
y2[1] (closed_form) = 19.8240323911 28.3604924804
absolute error = 6.173
relative error = 17.84 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.43285954324 -3.29632631046
y1[1] (closed_form) = 4.43285954324 -3.29632631046
absolute error = 1.217e-62
relative error = 2.202e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.38
Order of pole (three term test) = 50.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.38
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64165.5MB, alloc=44.3MB, time=765.44
memory used=64212.3MB, alloc=44.3MB, time=766.00
x[1] = 0.6483 2.403
h = 0.0001 0.004
y2[1] (numeric) = 14.1119262495 30.7083931831
y2[1] (closed_form) = 19.8483807443 28.4005021206
absolute error = 6.183
relative error = 17.85 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.4425978293 -3.31076641297
y1[1] (closed_form) = 4.4425978293 -3.31076641297
absolute error = 1.315e-62
relative error = 2.374e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.56
Order of pole (three term test) = 50.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.56
Order of pole (three term test) = 38.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64258.3MB, alloc=44.3MB, time=766.54
memory used=64304.8MB, alloc=44.3MB, time=767.09
x[1] = 0.6484 2.407
h = 0.003 0.006
y2[1] (numeric) = 14.1294260244 30.7583984877
y2[1] (closed_form) = 19.863096763 28.457975076
absolute error = 6.178
relative error = 17.8 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.45977753786 -3.32469327214
y1[1] (closed_form) = 4.45977753786 -3.32469327214
absolute error = 1.217e-62
relative error = 2.187e-61 %
Correct digits = 63
memory used=64351.6MB, alloc=44.3MB, time=767.64
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.81
Order of pole (three term test) = 50.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.81
Order of pole (three term test) = 38.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64397.6MB, alloc=44.3MB, time=768.18
memory used=64444.2MB, alloc=44.3MB, time=768.74
x[1] = 0.6514 2.413
h = 0.0001 0.005
y2[1] (numeric) = 14.1470256749 30.8083859693
y2[1] (closed_form) = 19.9265491076 28.5347579505
absolute error = 6.211
relative error = 17.84 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.47596833239 -3.3582571852
y1[1] (closed_form) = 4.47596833239 -3.3582571852
absolute error = 1.217e-62
relative error = 2.174e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.18
Order of pole (three term test) = 50.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.18
Order of pole (three term test) = 38.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64490.3MB, alloc=44.3MB, time=769.28
memory used=64537.1MB, alloc=44.3MB, time=769.84
x[1] = 0.6515 2.418
h = 0.0001 0.003
y2[1] (numeric) = 14.164725702 30.858355299
y2[1] (closed_form) = 19.9448329081 28.6068553866
absolute error = 6.203
relative error = 17.79 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.49770520283 -3.37580468256
y1[1] (closed_form) = 4.49770520283 -3.37580468256
absolute error = 1.315e-62
relative error = 2.339e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.49
Order of pole (three term test) = 50.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.49
Order of pole (three term test) = 38.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64583.1MB, alloc=44.3MB, time=770.39
memory used=64630.0MB, alloc=44.3MB, time=770.96
x[1] = 0.6516 2.421
h = 0.001 0.001
y2[1] (numeric) = 14.1825266088 30.9083061457
y2[1] (closed_form) = 19.956426855 28.6500298102
absolute error = 6.2
relative error = 17.76 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.51066200847 -3.38655340776
y1[1] (closed_form) = 4.51066200847 -3.38655340776
absolute error = 1.237e-62
relative error = 2.193e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.68
Order of pole (three term test) = 51.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.68
Order of pole (three term test) = 38.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64676.1MB, alloc=44.3MB, time=771.51
memory used=64722.7MB, alloc=44.3MB, time=772.07
x[1] = 0.6526 2.422
h = 0.001 0.003
y2[1] (numeric) = 14.2004289005 30.9582381761
y2[1] (closed_form) = 19.9743285108 28.6611504758
absolute error = 6.214
relative error = 17.79 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.51165822224 -3.39443837542
y1[1] (closed_form) = 4.51165822224 -3.39443837542
absolute error = 1.237e-62
relative error = 2.191e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.75
Order of pole (three term test) = 51.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.75
Order of pole (three term test) = 39.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64768.8MB, alloc=44.3MB, time=772.61
memory used=64815.6MB, alloc=44.3MB, time=773.17
memory used=64862.3MB, alloc=44.3MB, time=773.72
x[1] = 0.6536 2.425
h = 0.0001 0.004
y2[1] (numeric) = 14.2184330842 31.0081510547
y2[1] (closed_form) = 19.9990506307 28.7012984305
absolute error = 6.224
relative error = 17.79 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.52154120685 -3.40925165377
y1[1] (closed_form) = 4.52154120685 -3.40925165377
absolute error = 1.237e-62
relative error = 2.184e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.94
Order of pole (three term test) = 51.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.94
Order of pole (three term test) = 39.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=64908.2MB, alloc=44.3MB, time=774.26
memory used=64954.7MB, alloc=44.3MB, time=774.81
x[1] = 0.6537 2.429
h = 0.003 0.006
y2[1] (numeric) = 14.2365396687 31.0580444439
y2[1] (closed_form) = 20.014169299 28.7590779185
absolute error = 6.218
relative error = 17.75 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.53903492619 -3.42357809219
y1[1] (closed_form) = 4.53903492619 -3.42357809219
absolute error = 1.140e-62
relative error = 2.005e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.19
Order of pole (three term test) = 51.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.19
Order of pole (three term test) = 39.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65000.6MB, alloc=44.3MB, time=775.34
memory used=65047.3MB, alloc=44.3MB, time=775.90
x[1] = 0.6567 2.435
h = 0.0001 0.005
y2[1] (numeric) = 14.2547491651 31.107918004
y2[1] (closed_form) = 20.0784555133 28.8360390083
absolute error = 6.251
relative error = 17.79 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.55541740609 -3.45797651547
y1[1] (closed_form) = 4.55541740609 -3.45797651547
absolute error = 1.237e-62
relative error = 2.163e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.58
Order of pole (three term test) = 51.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.58
Order of pole (three term test) = 39.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65093.3MB, alloc=44.3MB, time=776.44
memory used=65140.1MB, alloc=44.3MB, time=777.00
x[1] = 0.6568 2.44
h = 0.0001 0.003
y2[1] (numeric) = 14.2730620862 31.157771393
y2[1] (closed_form) = 20.097247134 28.9085246856
absolute error = 6.243
relative error = 17.73 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.5775517356 -3.47602796084
y1[1] (closed_form) = 4.5775517356 -3.47602796084
absolute error = 1.237e-62
relative error = 2.152e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.91
Order of pole (three term test) = 51.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.91
Order of pole (three term test) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65186.0MB, alloc=44.3MB, time=777.54
memory used=65232.7MB, alloc=44.3MB, time=778.10
x[1] = 0.6569 2.443
h = 0.001 0.001
y2[1] (numeric) = 14.291478947 31.2076042668
y2[1] (closed_form) = 20.1091502072 28.951928964
absolute error = 6.24
relative error = 17.7 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.59074393688 -3.48708357059
y1[1] (closed_form) = 4.59074393688 -3.48708357059
absolute error = 1.237e-62
relative error = 2.146e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.11
Order of pole (three term test) = 51.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.11
Order of pole (three term test) = 40.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65279.2MB, alloc=44.3MB, time=778.66
memory used=65325.6MB, alloc=44.3MB, time=779.22
memory used=65372.2MB, alloc=44.3MB, time=779.77
x[1] = 0.6579 2.444
h = 0.0001 0.004
y2[1] (numeric) = 14.3100002643 31.2574162788
y2[1] (closed_form) = 20.127232557 28.9630290815
absolute error = 6.253
relative error = 17.73 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.59172222586 -3.49515024083
y1[1] (closed_form) = 4.59172222586 -3.49515024083
absolute error = 1.237e-62
relative error = 2.144e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.17
Order of pole (three term test) = 51.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.17
Order of pole (three term test) = 40.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65418.2MB, alloc=44.3MB, time=780.31
memory used=65464.9MB, alloc=44.3MB, time=780.87
x[1] = 0.658 2.448
h = 0.003 0.006
y2[1] (numeric) = 14.3286265571 31.3072070804
y2[1] (closed_form) = 20.1427025485 29.0210812439
absolute error = 6.247
relative error = 17.68 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.60949487706 -3.50982529582
y1[1] (closed_form) = 4.60949487706 -3.50982529582
absolute error = 1.334e-62
relative error = 2.303e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.44
Order of pole (three term test) = 52.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.44
Order of pole (three term test) = 40.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65511.0MB, alloc=44.3MB, time=781.40
memory used=65557.6MB, alloc=44.3MB, time=781.96
x[1] = 0.661 2.454
h = 0.0001 0.005
y2[1] (numeric) = 14.347358346 31.3569763208
y2[1] (closed_form) = 20.2077200809 29.0982057806
absolute error = 6.281
relative error = 17.73 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.62605217232 -3.54495536553
y1[1] (closed_form) = 4.62605217232 -3.54495536553
absolute error = 1.334e-62
relative error = 2.289e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.84
Order of pole (three term test) = 52.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.84
Order of pole (three term test) = 40.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65603.6MB, alloc=44.3MB, time=782.49
memory used=65650.5MB, alloc=44.3MB, time=783.05
x[1] = 0.6611 2.459
h = 0.0001 0.003
y2[1] (numeric) = 14.3661961541 31.4067236468
y2[1] (closed_form) = 20.2269547752 29.1710367937
absolute error = 6.273
relative error = 17.67 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.64853954973 -3.56344647442
y1[1] (closed_form) = 4.64853954973 -3.56344647442
absolute error = 1.360e-62
relative error = 2.322e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.18
Order of pole (three term test) = 52.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.18
Order of pole (three term test) = 40.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65696.5MB, alloc=44.3MB, time=783.59
memory used=65743.5MB, alloc=44.3MB, time=784.16
x[1] = 0.6612 2.462
h = 0.001 0.001
y2[1] (numeric) = 14.3851405061 31.456448703
y2[1] (closed_form) = 20.2391276147 29.214645594
absolute error = 6.269
relative error = 17.64 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.66194090971 -3.57476987297
y1[1] (closed_form) = 4.66194090971 -3.57476987297
absolute error = 1.360e-62
relative error = 2.315e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.39
Order of pole (three term test) = 52.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.39
Order of pole (three term test) = 41.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65790.1MB, alloc=44.3MB, time=784.71
memory used=65836.3MB, alloc=44.3MB, time=785.26
memory used=65882.9MB, alloc=44.3MB, time=785.81
x[1] = 0.6622 2.463
h = 0.001 0.003
y2[1] (numeric) = 14.4041919288 31.5061511319
y2[1] (closed_form) = 20.2573689205 29.2257291351
absolute error = 6.282
relative error = 17.67 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.66290485018 -3.58299630844
y1[1] (closed_form) = 4.66290485018 -3.58299630844
absolute error = 1.360e-62
relative error = 2.313e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.46
Order of pole (three term test) = 52.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.46
Order of pole (three term test) = 41.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=65928.8MB, alloc=44.3MB, time=786.35
memory used=65975.5MB, alloc=44.3MB, time=786.91
x[1] = 0.6632 2.466
h = 0.0001 0.004
y2[1] (numeric) = 14.4233509513 31.5558305732
y2[1] (closed_form) = 20.2828091739 29.2661423286
absolute error = 6.291
relative error = 17.67 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.67306456932 -3.59852649588
y1[1] (closed_form) = 4.67306456932 -3.59852649588
absolute error = 1.334e-62
relative error = 2.262e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.67
Order of pole (three term test) = 52.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.67
Order of pole (three term test) = 41.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66021.5MB, alloc=44.3MB, time=787.44
memory used=66068.0MB, alloc=44.3MB, time=788.00
x[1] = 0.6633 2.47
h = 0.003 0.006
y2[1] (numeric) = 14.4426181043 31.6054866649
y2[1] (closed_form) = 20.2987016591 29.324510147
absolute error = 6.285
relative error = 17.62 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.69116002563 -3.61362102885
y1[1] (closed_form) = 4.69116002563 -3.61362102885
absolute error = 1.432e-62
relative error = 2.418e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.94
Order of pole (three term test) = 53.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.94
Order of pole (three term test) = 41.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66113.9MB, alloc=44.3MB, time=788.53
memory used=66160.6MB, alloc=44.3MB, time=789.08
x[1] = 0.6663 2.476
h = 0.0001 0.005
y2[1] (numeric) = 14.4619939208 31.6551190423
y2[1] (closed_form) = 20.3645898585 29.4018125552
absolute error = 6.318
relative error = 17.67 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.70790812678 -3.64962225621
y1[1] (closed_form) = 4.70790812678 -3.64962225621
absolute error = 1.432e-62
relative error = 2.404e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.37
Order of pole (three term test) = 53.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.37
Order of pole (three term test) = 42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66206.6MB, alloc=44.3MB, time=789.62
memory used=66253.2MB, alloc=44.3MB, time=790.17
memory used=66299.9MB, alloc=44.3MB, time=790.73
x[1] = 0.6664 2.481
h = 0.0001 0.003
y2[1] (numeric) = 14.4814789358 31.7047273386
y2[1] (closed_form) = 20.3843574148 29.4750433758
absolute error = 6.31
relative error = 17.61 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.73080412314 -3.66864242567
y1[1] (closed_form) = 4.73080412314 -3.66864242567
absolute error = 1.432e-62
relative error = 2.392e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.72
Order of pole (three term test) = 53.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.72
Order of pole (three term test) = 42.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66346.1MB, alloc=44.3MB, time=791.28
memory used=66393.0MB, alloc=44.3MB, time=791.84
x[1] = 0.6665 2.484
h = 0.001 0.001
y2[1] (numeric) = 14.5010736862 31.7543111845
y2[1] (closed_form) = 20.3968545636 29.5188887968
absolute error = 6.305
relative error = 17.57 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.74444740117 -3.68028793084
y1[1] (closed_form) = 4.74444740117 -3.68028793084
absolute error = 1.552e-62
relative error = 2.585e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.94
Order of pole (three term test) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.94
Order of pole (three term test) = 42.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66439.0MB, alloc=44.3MB, time=792.38
memory used=66485.5MB, alloc=44.3MB, time=792.94
x[1] = 0.6675 2.485
h = 0.001 0.003
y2[1] (numeric) = 14.520778711 31.8038702086
y2[1] (closed_form) = 20.4152839782 29.5299492216
absolute error = 6.318
relative error = 17.6 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.74539075231 -3.68870341896
y1[1] (closed_form) = 4.74539075231 -3.68870341896
absolute error = 1.552e-62
relative error = 2.583e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.01
Order of pole (three term test) = 53.85 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.01
Order of pole (three term test) = 42.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66531.6MB, alloc=44.3MB, time=793.48
memory used=66578.3MB, alloc=44.3MB, time=794.03
x[1] = 0.6685 2.488
h = 0.0001 0.004
y2[1] (numeric) = 14.5405945514 31.8534040369
y2[1] (closed_form) = 20.4411245119 29.5705041876
absolute error = 6.327
relative error = 17.6 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.75569822927 -3.70463324263
y1[1] (closed_form) = 4.75569822927 -3.70463324263
absolute error = 1.552e-62
relative error = 2.575e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.22
Order of pole (three term test) = 53.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.22
Order of pole (three term test) = 42.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66624.4MB, alloc=44.3MB, time=794.56
memory used=66670.9MB, alloc=44.3MB, time=795.12
x[1] = 0.6686 2.492
h = 0.003 0.006
y2[1] (numeric) = 14.5605217505 31.9029122932
y2[1] (closed_form) = 20.4574505644 29.6291925631
absolute error = 6.32
relative error = 17.55 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.7741212205 -3.7201583557
y1[1] (closed_form) = 4.7741212205 -3.7201583557
absolute error = 1.581e-62
relative error = 2.612e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.52
Order of pole (three term test) = 54.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.52
Order of pole (three term test) = 42.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66717.1MB, alloc=44.3MB, time=795.66
memory used=66763.8MB, alloc=44.3MB, time=796.21
memory used=66810.6MB, alloc=44.3MB, time=796.76
x[1] = 0.6716 2.498
h = 0.0001 0.005
y2[1] (numeric) = 14.5805608534 31.9523945988
y2[1] (closed_form) = 20.5242298283 29.7066723617
absolute error = 6.354
relative error = 17.6 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.79105936726 -3.75705106045
y1[1] (closed_form) = 4.79105936726 -3.75705106045
absolute error = 1.552e-62
relative error = 2.550e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.96
Order of pole (three term test) = 54.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.96
Order of pole (three term test) = 43.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66856.5MB, alloc=44.3MB, time=797.29
memory used=66903.3MB, alloc=44.3MB, time=797.85
x[1] = 0.6717 2.503
h = 0.0001 0.003
y2[1] (numeric) = 14.6007124074 32.0018505728
y2[1] (closed_form) = 20.544544221 29.7803092042
absolute error = 6.345
relative error = 17.54 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.81436998555 -3.77661430197
y1[1] (closed_form) = 4.81436998555 -3.77661430197
absolute error = 1.581e-62
relative error = 2.584e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.33
Order of pole (three term test) = 54.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.33
Order of pole (three term test) = 43.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=66949.4MB, alloc=44.3MB, time=798.39
memory used=66996.4MB, alloc=44.3MB, time=798.96
x[1] = 0.6718 2.506
h = 0.001 0.001
y2[1] (numeric) = 14.6209769618 32.0512798318
y2[1] (closed_form) = 20.5573741499 29.824394877
absolute error = 6.34
relative error = 17.5 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.82825868595 -3.78859040506
y1[1] (closed_form) = 4.82825868595 -3.78859040506
absolute error = 1.676e-62
relative error = 2.731e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.55
Order of pole (three term test) = 54.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.55
Order of pole (three term test) = 43.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67042.5MB, alloc=44.3MB, time=799.50
memory used=67089.1MB, alloc=44.3MB, time=800.06
x[1] = 0.6728 2.507
h = 0.001 0.003
y2[1] (numeric) = 14.6413550681 32.10068199
y2[1] (closed_form) = 20.5759957637 29.835430703
absolute error = 6.352
relative error = 17.53 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.82917991522 -3.79719900265
y1[1] (closed_form) = 4.82917991522 -3.79719900265
absolute error = 1.676e-62
relative error = 2.729e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.63
Order of pole (three term test) = 54.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.63
Order of pole (three term test) = 43.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67135.1MB, alloc=44.3MB, time=800.60
memory used=67181.8MB, alloc=44.3MB, time=801.16
x[1] = 0.6738 2.51
h = 0.0001 0.004
y2[1] (numeric) = 14.6618472796 32.1500566593
y2[1] (closed_form) = 20.6022462613 29.8761285595
absolute error = 6.361
relative error = 17.53 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.8396361343 -3.8135381292
y1[1] (closed_form) = 4.8396361343 -3.8135381292
absolute error = 1.676e-62
relative error = 2.721e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.85
Order of pole (three term test) = 55.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.85
Order of pole (three term test) = 44.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67228.1MB, alloc=44.3MB, time=801.70
memory used=67274.4MB, alloc=44.3MB, time=802.24
memory used=67321.1MB, alloc=44.3MB, time=802.80
x[1] = 0.6739 2.514
h = 0.003 0.006
y2[1] (numeric) = 14.6824541521 32.1994034489
y2[1] (closed_form) = 20.619017227 29.9351424382
absolute error = 6.354
relative error = 17.48 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.85839143919 -3.8295051972
y1[1] (closed_form) = 4.85839143919 -3.8295051972
absolute error = 1.772e-62
relative error = 2.864e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.16
Order of pole (three term test) = 55.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.16
Order of pole (three term test) = 44.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67367.0MB, alloc=44.3MB, time=803.34
memory used=67413.6MB, alloc=44.3MB, time=803.89
x[1] = 0.6769 2.52
h = 0.0001 0.005
y2[1] (numeric) = 14.703176243 32.2487219658
y2[1] (closed_form) = 20.6867084006 30.0127990191
absolute error = 6.388
relative error = 17.52 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.87551875 -3.86731014983
y1[1] (closed_form) = 4.87551875 -3.86731014983
absolute error = 1.676e-62
relative error = 2.694e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.62
Order of pole (three term test) = 55.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.62
Order of pole (three term test) = 44.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67459.7MB, alloc=44.3MB, time=804.42
memory used=67506.3MB, alloc=44.3MB, time=804.98
x[1] = 0.677 2.525
h = 0.0001 0.003
y2[1] (numeric) = 14.7240141123 32.2980118147
y2[1] (closed_form) = 20.707583948 30.0868481557
absolute error = 6.379
relative error = 17.47 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.89925005558 -3.88743081918
y1[1] (closed_form) = 4.89925005558 -3.88743081918
absolute error = 1.676e-62
relative error = 2.680e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.01
Order of pole (three term test) = 55.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.01
Order of pole (three term test) = 45.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67552.4MB, alloc=44.3MB, time=805.52
memory used=67599.2MB, alloc=44.3MB, time=806.08
x[1] = 0.6771 2.528
h = 0.001 0.001
y2[1] (numeric) = 14.7449683216 32.3472725975
y2[1] (closed_form) = 20.7207553357 30.1311777434
absolute error = 6.373
relative error = 17.43 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.91338771749 -3.89974621946
y1[1] (closed_form) = 4.91338771749 -3.89974621946
absolute error = 1.676e-62
relative error = 2.672e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.24
Order of pole (three term test) = 56.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.24
Order of pole (three term test) = 45.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67645.4MB, alloc=44.3MB, time=806.64
memory used=67691.9MB, alloc=44.3MB, time=807.19
x[1] = 0.6781 2.529
h = 0.001 0.003
y2[1] (numeric) = 14.7660394351 32.3965039138
y2[1] (closed_form) = 20.7395733211 30.1421874322
absolute error = 6.385
relative error = 17.45 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.91428523721 -3.90855206623
y1[1] (closed_form) = 4.91428523721 -3.90855206623
absolute error = 1.581e-62
relative error = 2.518e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.32
Order of pole (three term test) = 56.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.32
Order of pole (three term test) = 45.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67738.3MB, alloc=44.3MB, time=807.74
memory used=67784.6MB, alloc=44.3MB, time=808.28
memory used=67831.3MB, alloc=44.3MB, time=808.84
x[1] = 0.6791 2.532
h = 0.0001 0.004
y2[1] (numeric) = 14.7872280187 32.4457053607
y2[1] (closed_form) = 20.7662436864 30.1830292666
absolute error = 6.393
relative error = 17.45 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.92489115507 -3.92531038362
y1[1] (closed_form) = 4.92489115507 -3.92531038362
absolute error = 1.676e-62
relative error = 2.662e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.56
Order of pole (three term test) = 56.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.56
Order of pole (three term test) = 45.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67877.3MB, alloc=44.3MB, time=809.37
memory used=67923.8MB, alloc=44.3MB, time=809.92
x[1] = 0.6792 2.536
h = 0.003 0.006
y2[1] (numeric) = 14.8085346407 32.494876533
y2[1] (closed_form) = 20.7834711902 30.2423736394
absolute error = 6.385
relative error = 17.4 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.94398360079 -3.94173106036
y1[1] (closed_form) = 4.94398360079 -3.94173106036
absolute error = 1.649e-62
relative error = 2.608e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.87
Order of pole (three term test) = 56.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.87
Order of pole (three term test) = 45.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=67969.9MB, alloc=44.3MB, time=810.46
memory used=68016.5MB, alloc=44.3MB, time=811.01
x[1] = 0.6822 2.542
h = 0.0001 0.005
y2[1] (numeric) = 14.8299598713 32.5440170226
y2[1] (closed_form) = 20.8520955754 30.3202062623
absolute error = 6.42
relative error = 17.45 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.9612990676 -3.9804694914
y1[1] (closed_form) = 4.9612990676 -3.9804694914
absolute error = 1.676e-62
relative error = 2.635e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.36
Order of pole (three term test) = 56.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.36
Order of pole (three term test) = 46.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68062.6MB, alloc=44.3MB, time=811.55
memory used=68109.3MB, alloc=44.3MB, time=812.10
x[1] = 0.6823 2.547
h = 0.0001 0.003
y2[1] (numeric) = 14.8515042832 32.5931264193
y2[1] (closed_form) = 20.8735469481 30.3946740221
absolute error = 6.411
relative error = 17.39 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.9854571876 -4.00116229662
y1[1] (closed_form) = 4.9854571876 -4.00116229662
absolute error = 1.676e-62
relative error = 2.622e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.76
Order of pole (three term test) = 57.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.76
Order of pole (three term test) = 46.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68155.6MB, alloc=44.3MB, time=812.64
memory used=68202.4MB, alloc=44.3MB, time=813.20
x[1] = 0.6824 2.55
h = 0.001 0.001
y2[1] (numeric) = 14.8731684507 32.6422043102
y2[1] (closed_form) = 20.8870686855 30.4392512193
absolute error = 6.405
relative error = 17.35 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.99984738453 -4.01382590613
y1[1] (closed_form) = 4.99984738453 -4.01382590613
absolute error = 1.676e-62
relative error = 2.614e-61 %
Correct digits = 63
memory used=68249.5MB, alloc=44.3MB, time=813.77
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.01
Order of pole (three term test) = 57.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.01
Order of pole (three term test) = 46.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68295.5MB, alloc=44.3MB, time=814.31
memory used=68342.0MB, alloc=44.3MB, time=814.86
x[1] = 0.6834 2.551
h = 0.0001 0.004
y2[1] (numeric) = 14.8949529507 32.6912502798
y2[1] (closed_form) = 20.9060872984 30.4502331747
absolute error = 6.415
relative error = 17.37 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.00071955024 -4.02283322617
y1[1] (closed_form) = 5.00071955024 -4.02283322617
absolute error = 1.676e-62
relative error = 2.612e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.09
Order of pole (three term test) = 57.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.09
Order of pole (three term test) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68388.0MB, alloc=44.3MB, time=815.40
memory used=68434.5MB, alloc=44.3MB, time=815.96
x[1] = 0.6835 2.555
h = 0.003 0.006
y2[1] (numeric) = 14.9168583621 32.7402639101
y2[1] (closed_form) = 20.9237132825 30.5098716879
absolute error = 6.408
relative error = 17.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.02011169522 -4.03964980887
y1[1] (closed_form) = 5.02011169522 -4.03964980887
absolute error = 1.772e-62
relative error = 2.750e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.42
Order of pole (three term test) = 57.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.42
Order of pole (three term test) = 47.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68480.5MB, alloc=44.3MB, time=816.49
memory used=68527.2MB, alloc=44.3MB, time=817.04
x[1] = 0.6865 2.561
h = 0.0001 0.005
y2[1] (numeric) = 14.9388852658 32.7892447808
y2[1] (closed_form) = 20.9931562769 30.5878666149
absolute error = 6.442
relative error = 17.36 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.03759968511 -4.07920688354
y1[1] (closed_form) = 5.03759968511 -4.07920688354
absolute error = 1.676e-62
relative error = 2.586e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.92
Order of pole (three term test) = 57.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.92
Order of pole (three term test) = 47.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68573.3MB, alloc=44.3MB, time=817.58
memory used=68620.1MB, alloc=44.3MB, time=818.14
x[1] = 0.6866 2.566
h = 0.0001 0.003
y2[1] (numeric) = 14.9610342451 32.8381924685
y2[1] (closed_form) = 21.0151102329 30.6627069268
absolute error = 6.433
relative error = 17.31 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.0621372063 -4.10039903231
y1[1] (closed_form) = 5.0621372063 -4.10039903231
absolute error = 1.803e-62
relative error = 2.767e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.34
Order of pole (three term test) = 58.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.34
Order of pole (three term test) = 48.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68666.4MB, alloc=44.3MB, time=818.68
memory used=68712.9MB, alloc=44.3MB, time=819.24
memory used=68759.8MB, alloc=44.3MB, time=819.81
x[1] = 0.6867 2.569
h = 0.001 0.001
y2[1] (numeric) = 14.9833058854 32.8871065478
y2[1] (closed_form) = 21.0289378154 30.7075045619
absolute error = 6.427
relative error = 17.27 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.07675196083 -4.11336660451
y1[1] (closed_form) = 5.07675196083 -4.11336660451
absolute error = 1.803e-62
relative error = 2.759e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.6
Order of pole (three term test) = 58.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.6
Order of pole (three term test) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68805.8MB, alloc=44.3MB, time=820.35
memory used=68852.5MB, alloc=44.3MB, time=820.91
x[1] = 0.6877 2.57
h = 0.001 0.003
y2[1] (numeric) = 15.0057007742 32.9359865902
y2[1] (closed_form) = 21.0481329518 30.7184637822
absolute error = 6.436
relative error = 17.28 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.07760341115 -4.12255112393
y1[1] (closed_form) = 5.07760341115 -4.12255112393
absolute error = 1.803e-62
relative error = 2.756e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.68
Order of pole (three term test) = 58.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.68
Order of pole (three term test) = 48.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68898.4MB, alloc=44.3MB, time=821.44
memory used=68944.9MB, alloc=44.3MB, time=822.00
x[1] = 0.6887 2.573
h = 0.0001 0.004
y2[1] (numeric) = 15.0282195012 32.9848321648
y2[1] (closed_form) = 21.0756099829 30.7595815991
absolute error = 6.444
relative error = 17.28 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.08849560928 -4.14011474387
y1[1] (closed_form) = 5.08849560928 -4.14011474387
absolute error = 1.803e-62
relative error = 2.748e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.94
Order of pole (three term test) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.94
Order of pole (three term test) = 48.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=68990.9MB, alloc=44.3MB, time=822.53
memory used=69037.4MB, alloc=44.3MB, time=823.08
x[1] = 0.6888 2.577
h = 0.003 0.006
y2[1] (numeric) = 15.0508626584 33.0336428382
y2[1] (closed_form) = 21.0937148394 30.8195601571
absolute error = 6.436
relative error = 17.23 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.1082341514 -4.15740732624
y1[1] (closed_form) = 5.1082341514 -4.15740732624
absolute error = 1.803e-62
relative error = 2.737e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.28
Order of pole (three term test) = 58.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 43.28
Order of pole (three term test) = 48.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69083.4MB, alloc=44.3MB, time=823.62
memory used=69130.2MB, alloc=44.3MB, time=824.18
x[1] = 0.6918 2.583
h = 0.0001 0.005
y2[1] (numeric) = 15.0736308398 33.0824181741
y2[1] (closed_form) = 21.1641319457 30.8977296459
absolute error = 6.47
relative error = 17.28 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.12590833246 -4.19793865708
y1[1] (closed_form) = 5.12590833246 -4.19793865708
absolute error = 1.772e-62
relative error = 2.675e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.8
Order of pole (three term test) = 59.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 43.8
Order of pole (three term test) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69176.7MB, alloc=44.3MB, time=824.72
memory used=69223.0MB, alloc=44.3MB, time=825.27
memory used=69269.6MB, alloc=44.3MB, time=825.83
x[1] = 0.6919 2.588
h = 0.0001 0.003
y2[1] (numeric) = 15.0965246418 33.1311577339
y2[1] (closed_form) = 21.1866899129 30.9730006935
absolute error = 6.461
relative error = 17.22 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.15088441702 -4.21973120078
y1[1] (closed_form) = 5.15088441702 -4.21973120078
absolute error = 1.803e-62
relative error = 2.707e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.24
Order of pole (three term test) = 59.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.24
Order of pole (three term test) = 49.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69315.7MB, alloc=44.3MB, time=826.37
memory used=69362.6MB, alloc=44.3MB, time=826.94
x[1] = 0.692 2.591
h = 0.001 0.001
y2[1] (numeric) = 15.1195446629 33.179861076
y2[1] (closed_form) = 21.2008849274 31.0180530075
absolute error = 6.454
relative error = 17.18 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.16575855835 -4.23306410499
y1[1] (closed_form) = 5.16575855835 -4.23306410499
absolute error = 1.803e-62
relative error = 2.699e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.51
Order of pole (three term test) = 59.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.51
Order of pole (three term test) = 50 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69408.6MB, alloc=44.3MB, time=827.48
memory used=69455.3MB, alloc=44.3MB, time=828.04
x[1] = 0.693 2.592
h = 0.001 0.003
y2[1] (numeric) = 15.1426915038 33.2285277564
y2[1] (closed_form) = 21.2202888584 31.028981418
absolute error = 6.463
relative error = 17.19 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.16658149024 -4.24245820896
y1[1] (closed_form) = 5.16658149024 -4.24245820896
absolute error = 1.803e-62
relative error = 2.697e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.6
Order of pole (three term test) = 59.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.6
Order of pole (three term test) = 50.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69501.3MB, alloc=44.3MB, time=828.58
memory used=69548.1MB, alloc=44.3MB, time=829.13
x[1] = 0.694 2.595
h = 0.0001 0.004
y2[1] (numeric) = 15.1659657674 33.2771573281
y2[1] (closed_form) = 21.2482153378 31.0702462664
absolute error = 6.47
relative error = 17.19 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.17762608131 -4.26047056157
y1[1] (closed_form) = 5.17762608131 -4.26047056157
absolute error = 1.709e-62
relative error = 2.548e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.87
Order of pole (three term test) = 59.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.87
Order of pole (three term test) = 50.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69594.1MB, alloc=44.3MB, time=829.67
memory used=69640.7MB, alloc=44.3MB, time=830.22
x[1] = 0.6941 2.599
h = 0.003 0.006
y2[1] (numeric) = 15.1893680588 33.3257493419
y2[1] (closed_form) = 21.2668115245 31.1305699885
absolute error = 6.462
relative error = 17.14 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.19771598689 -4.27825163107
y1[1] (closed_form) = 5.19771598689 -4.27825163107
absolute error = 1.709e-62
relative error = 2.538e-61 %
Correct digits = 63
memory used=69687.3MB, alloc=44.3MB, time=830.78
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.23
Order of pole (three term test) = 60.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 45.23
Order of pole (three term test) = 50.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69733.3MB, alloc=44.3MB, time=831.32
memory used=69780.0MB, alloc=44.3MB, time=831.87
x[1] = 0.6971 2.605
h = 0.0001 0.005
y2[1] (numeric) = 15.2128989856 33.3743033453
y2[1] (closed_form) = 21.338225407 31.2089128972
absolute error = 6.497
relative error = 17.18 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.21557496455 -4.31977981918
y1[1] (closed_form) = 5.21557496455 -4.31977981918
absolute error = 1.709e-62
relative error = 2.523e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.77
Order of pole (three term test) = 60.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 45.77
Order of pole (three term test) = 51.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69825.9MB, alloc=44.3MB, time=832.41
memory used=69872.6MB, alloc=44.3MB, time=832.97
x[1] = 0.6972 2.61
h = 0.0001 0.003
y2[1] (numeric) = 15.2365591572 33.4228188837
y2[1] (closed_form) = 21.3614031081 31.2846211743
absolute error = 6.487
relative error = 17.13 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.24099591723 -4.34218851839
y1[1] (closed_form) = 5.24099591723 -4.34218851839
absolute error = 1.746e-62
relative error = 2.566e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.23
Order of pole (three term test) = 61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.23
Order of pole (three term test) = 51.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=69918.6MB, alloc=44.3MB, time=833.51
memory used=69965.4MB, alloc=44.3MB, time=834.07
x[1] = 0.6973 2.613
h = 0.001 0.001
y2[1] (numeric) = 15.2603491856 33.4712954993
y2[1] (closed_form) = 21.3759750809 31.3299319528
absolute error = 6.48
relative error = 17.08 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.25613311736 -4.3558963023
y1[1] (closed_form) = 5.25613311736 -4.3558963023
absolute error = 1.709e-62
relative error = 2.503e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.51
Order of pole (three term test) = 61.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.51
Order of pole (three term test) = 51.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70011.6MB, alloc=44.3MB, time=834.63
memory used=70058.2MB, alloc=44.3MB, time=835.18
x[1] = 0.6983 2.614
h = 0.001 0.003
y2[1] (numeric) = 15.2842696848 33.5197327318
y2[1] (closed_form) = 21.3955923105 31.3408277834
absolute error = 6.488
relative error = 17.1 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.25692571513 -4.36550446573
y1[1] (closed_form) = 5.25692571513 -4.36550446573
absolute error = 1.709e-62
relative error = 2.501e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.61
Order of pole (three term test) = 61.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.61
Order of pole (three term test) = 51.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70104.2MB, alloc=44.3MB, time=835.72
memory used=70151.0MB, alloc=44.3MB, time=836.28
memory used=70197.7MB, alloc=44.3MB, time=836.83
x[1] = 0.6993 2.617
h = 0.0001 0.004
y2[1] (numeric) = 15.3083212712 33.5681301181
y2[1] (closed_form) = 21.4239790384 31.3822406185
absolute error = 6.495
relative error = 17.09 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.26812353383 -4.38397633904
y1[1] (closed_form) = 5.26812353383 -4.38397633904
absolute error = 1.709e-62
relative error = 2.493e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.89
Order of pole (three term test) = 61.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.89
Order of pole (three term test) = 52.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70243.7MB, alloc=44.3MB, time=837.36
memory used=70290.3MB, alloc=44.3MB, time=837.92
x[1] = 0.6994 2.621
h = 0.003 0.006
y2[1] (numeric) = 15.3325045633 33.6164871922
y2[1] (closed_form) = 21.4430793176 31.4429146671
absolute error = 6.486
relative error = 17.04 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.28856981546 -4.4022586878
y1[1] (closed_form) = 5.28856981546 -4.4022586878
absolute error = 1.709e-62
relative error = 2.483e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.26
Order of pole (three term test) = 61.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 47.26
Order of pole (three term test) = 52.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70336.4MB, alloc=44.3MB, time=838.46
memory used=70383.2MB, alloc=44.3MB, time=839.01
x[1] = 0.7024 2.627
h = 0.0001 0.005
y2[1] (numeric) = 15.3568201822 33.6648034856
y2[1] (closed_form) = 21.5155131359 31.5214297
absolute error = 6.521
relative error = 17.09 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.30661204693 -4.44480683185
y1[1] (closed_form) = 5.30661204693 -4.44480683185
absolute error = 1.746e-62
relative error = 2.523e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.83
Order of pole (three term test) = 62.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 47.83
Order of pole (three term test) = 53.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70429.2MB, alloc=44.3MB, time=839.54
memory used=70476.0MB, alloc=44.3MB, time=840.10
x[1] = 0.7025 2.632
h = 0.0001 0.003
y2[1] (numeric) = 15.3812687508 33.7130785268
y2[1] (closed_form) = 21.5393266777 31.5975817554
absolute error = 6.511
relative error = 17.03 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.33248423162 -4.46784783182
y1[1] (closed_form) = 5.33248423162 -4.46784783182
absolute error = 1.746e-62
relative error = 2.510e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 48.31
Order of pole (three term test) = 62.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 48.31
Order of pole (three term test) = 53.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70522.0MB, alloc=44.3MB, time=840.64
memory used=70568.9MB, alloc=44.3MB, time=841.20
x[1] = 0.7026 2.635
h = 0.001 0.001
y2[1] (numeric) = 15.4058508946 33.7613118417
y2[1] (closed_form) = 21.5542853673 31.6431548137
absolute error = 6.503
relative error = 16.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.34788819504 -4.48194027538
y1[1] (closed_form) = 5.34788819504 -4.48194027538
absolute error = 1.746e-62
relative error = 2.503e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 48.61
Order of pole (three term test) = 62.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 48.61
Order of pole (three term test) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70615.3MB, alloc=44.3MB, time=841.76
memory used=70661.7MB, alloc=44.3MB, time=842.31
memory used=70708.3MB, alloc=44.3MB, time=842.86
x[1] = 0.7036 2.636
h = 0.001 0.003
y2[1] (numeric) = 15.4305672414 33.809502953
y2[1] (closed_form) = 21.5741204892 31.6540162301
absolute error = 6.511
relative error = 17 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.34864857927 -4.49176706371
y1[1] (closed_form) = 5.34864857927 -4.49176706371
absolute error = 1.709e-62
relative error = 2.447e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 48.7
Order of pole (three term test) = 62.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 48.7
Order of pole (three term test) = 53.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70754.3MB, alloc=44.3MB, time=843.40
memory used=70800.8MB, alloc=44.3MB, time=843.96
x[1] = 0.7046 2.639
h = 0.0001 0.004
y2[1] (numeric) = 15.455418421 33.857651381
y2[1] (closed_form) = 21.6029785102 31.695577967
absolute error = 6.517
relative error = 16.99 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.36000042297 -4.510709491
y1[1] (closed_form) = 5.36000042297 -4.510709491
absolute error = 1.746e-62
relative error = 2.493e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49
Order of pole (three term test) = 63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49
Order of pole (three term test) = 54.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70846.6MB, alloc=44.3MB, time=844.49
memory used=70893.2MB, alloc=44.3MB, time=845.05
x[1] = 0.7047 2.643
h = 0.003 0.006
y2[1] (numeric) = 15.4804050657 33.905756643
y2[1] (closed_form) = 21.6225959558 31.7566075466
absolute error = 6.507
relative error = 16.94 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.3808081388 -4.52950622277
y1[1] (closed_form) = 5.3808081388 -4.52950622277
absolute error = 1.746e-62
relative error = 2.483e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.39
Order of pole (three term test) = 63.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49.39
Order of pole (three term test) = 54.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=70939.3MB, alloc=44.3MB, time=845.58
memory used=70986.1MB, alloc=44.3MB, time=846.14
x[1] = 0.7077 2.649
h = 0.0001 0.005
y2[1] (numeric) = 15.5055278101 33.9538182534
y2[1] (closed_form) = 21.6960733745 31.8352932489
absolute error = 6.543
relative error = 16.98 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.39903192696 -4.57309792921
y1[1] (closed_form) = 5.39903192696 -4.57309792921
absolute error = 1.838e-62
relative error = 2.598e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.99
Order of pole (three term test) = 63.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49.99
Order of pole (three term test) = 55.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71032.1MB, alloc=44.3MB, time=846.67
memory used=71078.8MB, alloc=44.3MB, time=847.23
x[1] = 0.7078 2.654
h = 0.0001 0.003
y2[1] (numeric) = 15.5307872912 34.0018357238
y2[1] (closed_form) = 21.7205392573 31.9118956854
absolute error = 6.533
relative error = 16.92 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.42536176581 -4.5967877687
y1[1] (closed_form) = 5.42536176581 -4.5967877687
absolute error = 1.746e-62
relative error = 2.456e-61 %
Correct digits = 63
memory used=71125.5MB, alloc=44.3MB, time=847.78
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.49
Order of pole (three term test) = 64.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.49
Order of pole (three term test) = 55.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71171.8MB, alloc=44.3MB, time=848.34
memory used=71218.7MB, alloc=44.3MB, time=848.90
x[1] = 0.7079 2.657
h = 0.001 0.001
y2[1] (numeric) = 15.5561841479 34.049808563
y2[1] (closed_form) = 21.7358946597 31.9577348681
absolute error = 6.524
relative error = 16.88 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.44103622892 -4.61127488947
y1[1] (closed_form) = 5.44103622892 -4.61127488947
absolute error = 1.838e-62
relative error = 2.578e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.79
Order of pole (three term test) = 64.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.79
Order of pole (three term test) = 55.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71265.0MB, alloc=44.3MB, time=849.45
memory used=71311.7MB, alloc=44.3MB, time=850.00
x[1] = 0.7089 2.658
h = 0.0001 0.004
y2[1] (numeric) = 15.5817190219 34.0977362768
y2[1] (closed_form) = 21.7559523588 31.9685599692
absolute error = 6.531
relative error = 16.89 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.44176245451 -4.62132496028
y1[1] (closed_form) = 5.44176245451 -4.62132496028
absolute error = 1.746e-62
relative error = 2.446e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.89
Order of pole (three term test) = 64.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.89
Order of pole (three term test) = 56.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71357.7MB, alloc=44.3MB, time=850.54
memory used=71404.4MB, alloc=44.3MB, time=851.10
x[1] = 0.709 2.662
h = 0.003 0.006
y2[1] (numeric) = 15.607392557 34.145618368
y2[1] (closed_form) = 21.7760213562 32.0299061556
absolute error = 6.521
relative error = 16.84 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.4628917112 -4.64057080396
y1[1] (closed_form) = 5.4628917112 -4.64057080396
absolute error = 1.746e-62
relative error = 2.436e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.3
Order of pole (three term test) = 64.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 51.3
Order of pole (three term test) = 56.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71450.2MB, alloc=44.3MB, time=851.63
memory used=71496.8MB, alloc=44.3MB, time=852.18
x[1] = 0.712 2.668
h = 0.0001 0.005
y2[1] (numeric) = 15.6332053993 34.1934543367
y2[1] (closed_form) = 21.8504144083 32.1087502978
absolute error = 6.557
relative error = 16.88 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.48128311905 -4.68507794062
y1[1] (closed_form) = 5.48128311905 -4.68507794062
absolute error = 1.746e-62
relative error = 2.422e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.92
Order of pole (three term test) = 65.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 51.92
Order of pole (three term test) = 57.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71542.8MB, alloc=44.3MB, time=852.72
memory used=71589.5MB, alloc=44.3MB, time=853.27
memory used=71636.3MB, alloc=44.3MB, time=853.83
x[1] = 0.7121 2.673
h = 0.0001 0.003
y2[1] (numeric) = 15.6591581973 34.2412436801
y2[1] (closed_form) = 21.8754498517 32.1857537809
absolute error = 6.547
relative error = 16.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.50802008238 -4.70933427373
y1[1] (closed_form) = 5.50802008238 -4.70933427373
absolute error = 1.746e-62
relative error = 2.410e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.44
Order of pole (three term test) = 65.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.44
Order of pole (three term test) = 57.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71682.3MB, alloc=44.3MB, time=854.37
memory used=71729.2MB, alloc=44.3MB, time=854.94
x[1] = 0.7122 2.676
h = 0.001 0.001
y2[1] (numeric) = 15.6852516018 34.2889858921
y2[1] (closed_form) = 21.8911516881 32.2318300276
absolute error = 6.538
relative error = 16.78 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.52393526683 -4.72416604332
y1[1] (closed_form) = 5.52393526683 -4.72416604332
absolute error = 1.746e-62
relative error = 2.403e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.76
Order of pole (three term test) = 65.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.76
Order of pole (three term test) = 57.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71775.2MB, alloc=44.3MB, time=855.48
memory used=71821.7MB, alloc=44.3MB, time=856.03
x[1] = 0.7132 2.677
h = 0.001 0.003
y2[1] (numeric) = 15.711486266 34.3366804641
y2[1] (closed_form) = 21.9114052615 32.2426250243
absolute error = 6.544
relative error = 16.79 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.52463321759 -4.73441254921
y1[1] (closed_form) = 5.52463321759 -4.73441254921
absolute error = 1.709e-62
relative error = 2.349e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.86
Order of pole (three term test) = 65.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.86
Order of pole (three term test) = 57.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71867.9MB, alloc=44.3MB, time=856.58
memory used=71914.8MB, alloc=44.3MB, time=857.14
x[1] = 0.7142 2.68
h = 0.0001 0.004
y2[1] (numeric) = 15.7378628454 34.384326884
y2[1] (closed_form) = 21.941168706 32.2844720597
absolute error = 6.549
relative error = 16.78 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.53627957839 -4.75425893965
y1[1] (closed_form) = 5.53627957839 -4.75425893965
absolute error = 1.746e-62
relative error = 2.393e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 53.18
Order of pole (three term test) = 66.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 53.18
Order of pole (three term test) = 58.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=71960.7MB, alloc=44.3MB, time=857.68
memory used=72007.3MB, alloc=44.3MB, time=858.23
x[1] = 0.7143 2.684
h = 0.003 0.006
y2[1] (numeric) = 15.764381998 34.4319246372
y2[1] (closed_form) = 21.961779988 32.346183736
absolute error = 6.539
relative error = 16.72 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.55777996522 -4.77404434203
y1[1] (closed_form) = 5.55777996522 -4.77404434203
absolute error = 1.803e-62
relative error = 2.461e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 53.61
Order of pole (three term test) = 66.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 53.61
Order of pole (three term test) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72053.5MB, alloc=44.3MB, time=858.77
memory used=72100.0MB, alloc=44.3MB, time=859.32
memory used=72146.8MB, alloc=44.3MB, time=859.88
x[1] = 0.7173 2.69
h = 0.0001 0.005
y2[1] (numeric) = 15.791044384 34.4794732059
y2[1] (closed_form) = 22.0372620772 32.4251956914
absolute error = 6.575
relative error = 16.77 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.57634963541 -4.81964037906
y1[1] (closed_form) = 5.57634963541 -4.81964037906
absolute error = 1.803e-62
relative error = 2.446e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.26
Order of pole (three term test) = 66.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 54.26
Order of pole (three term test) = 59.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72192.8MB, alloc=44.3MB, time=860.42
memory used=72239.5MB, alloc=44.3MB, time=860.97
x[1] = 0.7174 2.695
h = 0.0001 0.003
y2[1] (numeric) = 15.817850666 34.5269720692
y2[1] (closed_form) = 22.062981563 32.5026621909
absolute error = 6.565
relative error = 16.71 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.60355656335 -4.84457732686
y1[1] (closed_form) = 5.60355656335 -4.84457732686
absolute error = 1.803e-62
relative error = 2.434e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.8
Order of pole (three term test) = 67.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 54.8
Order of pole (three term test) = 59.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72285.7MB, alloc=44.3MB, time=861.52
memory used=72332.4MB, alloc=44.3MB, time=862.08
x[1] = 0.7175 2.698
h = 0.001 0.001
y2[1] (numeric) = 15.8448015092 34.5744207033
y2[1] (closed_form) = 22.0790993167 32.5490119183
absolute error = 6.555
relative error = 16.67 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.6197494091 -4.85982301965
y1[1] (closed_form) = 5.6197494091 -4.85982301965
absolute error = 1.803e-62
relative error = 2.426e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 55.13
Order of pole (three term test) = 67.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 55.13
Order of pole (three term test) = 60.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72378.5MB, alloc=44.3MB, time=862.62
memory used=72424.9MB, alloc=44.3MB, time=863.17
x[1] = 0.7185 2.699
h = 0.001 0.003
y2[1] (numeric) = 15.8718975808 34.6218185814
y2[1] (closed_form) = 22.0995844583 32.5597669371
absolute error = 6.56
relative error = 16.67 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.62040945839 -4.87030175086
y1[1] (closed_form) = 5.62040945839 -4.87030175086
absolute error = 1.803e-62
relative error = 2.424e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 55.24
Order of pole (three term test) = 67.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 55.24
Order of pole (three term test) = 60.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72470.7MB, alloc=44.3MB, time=863.71
memory used=72517.3MB, alloc=44.3MB, time=864.27
x[1] = 0.7195 2.702
h = 0.0001 0.004
y2[1] (numeric) = 15.8991395507 34.6691651735
y2[1] (closed_form) = 22.1298521797 32.6017653948
absolute error = 6.565
relative error = 16.66 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.63221204088 -4.89065165251
y1[1] (closed_form) = 5.63221204088 -4.89065165251
absolute error = 1.803e-62
relative error = 2.417e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 55.57
Order of pole (three term test) = 67.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 55.57
Order of pole (three term test) = 60.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72563.9MB, alloc=44.3MB, time=864.82
memory used=72610.2MB, alloc=44.3MB, time=865.37
memory used=72656.7MB, alloc=44.3MB, time=865.92
x[1] = 0.7196 2.706
h = 0.003 0.006
y2[1] (numeric) = 15.926528091 34.7164599466
y2[1] (closed_form) = 22.151019751 32.6638478862
absolute error = 6.554
relative error = 16.61 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.65408874605 -4.91099064848
y1[1] (closed_form) = 5.65408874605 -4.91099064848
absolute error = 1.838e-62
relative error = 2.455e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.02
Order of pole (three term test) = 68.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 56.02
Order of pole (three term test) = 60.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72702.7MB, alloc=44.3MB, time=866.46
memory used=72749.5MB, alloc=44.3MB, time=867.02
x[1] = 0.7226 2.712
h = 0.0001 0.005
y2[1] (numeric) = 15.9540638765 34.7637023646
y2[1] (closed_form) = 22.2276160476 32.7430257156
absolute error = 6.591
relative error = 16.65 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.67283451111 -4.95770070494
y1[1] (closed_form) = 5.67283451111 -4.95770070494
absolute error = 1.803e-62
relative error = 2.393e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.7
Order of pole (three term test) = 68.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 56.7
Order of pole (three term test) = 61.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72795.6MB, alloc=44.3MB, time=867.55
memory used=72842.5MB, alloc=44.3MB, time=868.11
x[1] = 0.7227 2.717
h = 0.0001 0.003
y2[1] (numeric) = 15.9817475841 34.8108918885
y2[1] (closed_form) = 22.2540372516 32.8209619889
absolute error = 6.58
relative error = 16.59 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.70051799219 -4.98333598188
y1[1] (closed_form) = 5.70051799219 -4.98333598188
absolute error = 1.838e-62
relative error = 2.428e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.27
Order of pole (three term test) = 69.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.27
Order of pole (three term test) = 62.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72888.4MB, alloc=44.3MB, time=868.65
memory used=72935.2MB, alloc=44.3MB, time=869.22
x[1] = 0.7228 2.72
h = 0.001 0.001
y2[1] (numeric) = 16.0095798932 34.8580279759
y2[1] (closed_form) = 22.2705816281 32.8675891256
absolute error = 6.57
relative error = 16.55 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.71699232636 -4.99900632519
y1[1] (closed_form) = 5.71699232636 -4.99900632519
absolute error = 1.838e-62
relative error = 2.421e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.61
Order of pole (three term test) = 69.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.61
Order of pole (three term test) = 62.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=72981.5MB, alloc=44.3MB, time=869.77
memory used=73028.1MB, alloc=44.3MB, time=870.32
x[1] = 0.7238 2.721
h = 0.001 0.003
y2[1] (numeric) = 16.0375614857 34.9051100814
y2[1] (closed_form) = 22.2913032946 32.8783020654
absolute error = 6.574
relative error = 16.55 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.71761233128 -5.00972221315
y1[1] (closed_form) = 5.71761233128 -5.00972221315
absolute error = 1.931e-62
relative error = 2.541e-61 %
Correct digits = 63
memory used=73074.5MB, alloc=44.3MB, time=870.87
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.73
Order of pole (three term test) = 69.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.73
Order of pole (three term test) = 62.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73121.0MB, alloc=44.3MB, time=871.42
memory used=73167.8MB, alloc=44.3MB, time=871.98
x[1] = 0.7248 2.724
h = 0.0001 0.004
y2[1] (numeric) = 16.0656930458 34.9521376565
y2[1] (closed_form) = 22.3220873315 32.920452689
absolute error = 6.578
relative error = 16.54 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.72957177056 -5.03058765657
y1[1] (closed_form) = 5.72957177056 -5.03058765657
absolute error = 1.879e-62
relative error = 2.464e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 58.07
Order of pole (three term test) = 69.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 58.07
Order of pole (three term test) = 63.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73213.7MB, alloc=44.3MB, time=872.52
memory used=73260.3MB, alloc=44.3MB, time=873.07
x[1] = 0.7249 2.728
h = 0.003 0.006
y2[1] (numeric) = 16.0939752604 34.9991101496
y2[1] (closed_form) = 22.343825537 32.9829113599
absolute error = 6.567
relative error = 16.48 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.75183002475 -5.05149462117
y1[1] (closed_form) = 5.75183002475 -5.05149462117
absolute error = 1.970e-62
relative error = 2.573e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 58.54
Order of pole (three term test) = 70.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 58.54
Order of pole (three term test) = 63.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73306.2MB, alloc=44.3MB, time=873.61
memory used=73353.0MB, alloc=44.3MB, time=874.16
x[1] = 0.7279 2.734
h = 0.0001 0.005
y2[1] (numeric) = 16.1224088185 35.0460270058
y2[1] (closed_form) = 22.4215617579 33.0622529398
absolute error = 6.604
relative error = 16.53 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.77074953768 -5.09934436508
y1[1] (closed_form) = 5.77074953768 -5.09934436508
absolute error = 1.879e-62
relative error = 2.440e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 59.25
Order of pole (three term test) = 70.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 59.25
Order of pole (three term test) = 64.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73399.0MB, alloc=44.3MB, time=874.70
memory used=73445.8MB, alloc=44.3MB, time=875.25
x[1] = 0.728 2.739
h = 0.0001 0.003
y2[1] (numeric) = 16.1509944118 35.0928876672
y2[1] (closed_form) = 22.4487027856 33.1406657952
absolute error = 6.593
relative error = 16.47 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.79891621483 -5.12569611516
y1[1] (closed_form) = 5.79891621483 -5.12569611516
absolute error = 2.012e-62
relative error = 2.600e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 59.84
Order of pole (three term test) = 71.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 59.84
Order of pole (three term test) = 64.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73492.1MB, alloc=44.3MB, time=875.79
memory used=73538.9MB, alloc=44.3MB, time=876.35
memory used=73585.8MB, alloc=44.3MB, time=876.92
x[1] = 0.7281 2.742
h = 0.001 0.001
y2[1] (numeric) = 16.1797327343 35.1396915725
y2[1] (closed_form) = 22.4656847497 33.1875742965
absolute error = 6.582
relative error = 16.42 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.81567589384 -5.14180209556
y1[1] (closed_form) = 5.81567589384 -5.14180209556
absolute error = 2.012e-62
relative error = 2.592e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 60.2
Order of pole (three term test) = 71.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 60.2
Order of pole (three term test) = 65.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73631.9MB, alloc=44.3MB, time=877.46
memory used=73678.5MB, alloc=44.3MB, time=878.01
x[1] = 0.7291 2.743
h = 0.001 0.003
y2[1] (numeric) = 16.2086244826 35.1864381574
y2[1] (closed_form) = 22.4866479955 33.198242982
absolute error = 6.585
relative error = 16.42 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.81625363793 -5.15276017047
y1[1] (closed_form) = 5.81625363793 -5.15276017047
absolute error = 2.012e-62
relative error = 2.590e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 60.32
Order of pole (three term test) = 71.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 60.32
Order of pole (three term test) = 65.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73724.6MB, alloc=44.3MB, time=878.55
memory used=73771.4MB, alloc=44.3MB, time=879.11
x[1] = 0.7301 2.746
h = 0.0001 0.004
y2[1] (numeric) = 16.2376703556 35.2331268543
y2[1] (closed_form) = 22.5179606577 33.2405464639
absolute error = 6.589
relative error = 16.41 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.8283705204 -5.17415345786
y1[1] (closed_form) = 5.8283705204 -5.17415345786
absolute error = 2.102e-62
relative error = 2.698e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 60.69
Order of pole (three term test) = 71.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 60.69
Order of pole (three term test) = 65.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73817.4MB, alloc=44.3MB, time=879.64
memory used=73863.9MB, alloc=44.3MB, time=880.20
x[1] = 0.7302 2.75
h = 0.003 0.006
y2[1] (numeric) = 16.2668710549 35.2797570923
y2[1] (closed_form) = 22.5402841902 33.3033867173
absolute error = 6.577
relative error = 16.36 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.85101559577 -5.19564311407
y1[1] (closed_form) = 5.85101559577 -5.19564311407
absolute error = 2.102e-62
relative error = 2.687e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.17
Order of pole (three term test) = 72.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 61.17
Order of pole (three term test) = 66.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=73909.9MB, alloc=44.3MB, time=880.73
memory used=73956.6MB, alloc=44.3MB, time=881.28
x[1] = 0.7332 2.756
h = 0.0001 0.005
y2[1] (numeric) = 16.2962272843 35.3263282974
y2[1] (closed_form) = 22.6191866102 33.382889733
absolute error = 6.615
relative error = 16.4 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.87010632302 -5.24465877359
y1[1] (closed_form) = 5.87010632302 -5.24465877359
absolute error = 2.102e-62
relative error = 2.671e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.91
Order of pole (three term test) = 72.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 61.91
Order of pole (three term test) = 66.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74003.0MB, alloc=44.3MB, time=881.82
memory used=74049.5MB, alloc=44.3MB, time=882.38
memory used=74096.1MB, alloc=44.3MB, time=882.94
x[1] = 0.7333 2.761
h = 0.0001 0.003
y2[1] (numeric) = 16.3257397502 35.3728398922
y2[1] (closed_form) = 22.6470660061 33.4617860279
absolute error = 6.604
relative error = 16.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.89876289237 -5.27174558012
y1[1] (closed_form) = 5.89876289237 -5.27174558012
absolute error = 2.012e-62
relative error = 2.544e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.53
Order of pole (three term test) = 73.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 62.53
Order of pole (three term test) = 67.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74142.2MB, alloc=44.3MB, time=883.50
memory used=74189.0MB, alloc=44.3MB, time=884.06
x[1] = 0.7334 2.764
h = 0.001 0.001
y2[1] (numeric) = 16.3554091617 35.4192912962
y2[1] (closed_form) = 22.6644967877 33.5089798757
absolute error = 6.592
relative error = 16.29 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.91581180114 -5.28829844935
y1[1] (closed_form) = 5.91581180114 -5.28829844935
absolute error = 2.012e-62
relative error = 2.536e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.91
Order of pole (three term test) = 73.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 62.91
Order of pole (three term test) = 67.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74235.2MB, alloc=44.3MB, time=884.60
memory used=74281.9MB, alloc=44.3MB, time=885.16
x[1] = 0.7344 2.765
h = 0.0001 0.004
y2[1] (numeric) = 16.3852362301 35.4656819255
y2[1] (closed_form) = 22.6857067672 33.5196020548
absolute error = 6.594
relative error = 16.29 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.91634499219 -5.299503842
y1[1] (closed_form) = 5.91634499219 -5.299503842
absolute error = 2.102e-62
relative error = 2.647e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.04
Order of pole (three term test) = 73.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 63.04
Order of pole (three term test) = 67.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74327.9MB, alloc=44.3MB, time=885.70
memory used=74374.6MB, alloc=44.3MB, time=886.26
x[1] = 0.7345 2.769
h = 0.003 0.006
y2[1] (numeric) = 16.4152216694 35.5120111928
y2[1] (closed_form) = 22.708541533 33.582782334
absolute error = 6.582
relative error = 16.24 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.93933446939 -5.32150242698
y1[1] (closed_form) = 5.93933446939 -5.32150242698
absolute error = 2.102e-62
relative error = 2.636e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.54
Order of pole (three term test) = 74.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 63.54
Order of pole (three term test) = 68.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74420.5MB, alloc=44.3MB, time=886.79
memory used=74467.2MB, alloc=44.3MB, time=887.35
x[1] = 0.7375 2.775
h = 0.0001 0.005
y2[1] (numeric) = 16.4453661959 35.5582785077
y2[1] (closed_form) = 22.7884673712 33.6624366318
absolute error = 6.62
relative error = 16.29 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.95858471973 -5.3715411118
y1[1] (closed_form) = 5.95858471973 -5.3715411118
absolute error = 2.102e-62
relative error = 2.621e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.31
Order of pole (three term test) = 74.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 64.31
Order of pole (three term test) = 69.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74513.8MB, alloc=44.3MB, time=887.89
memory used=74560.2MB, alloc=44.3MB, time=888.44
memory used=74607.0MB, alloc=44.3MB, time=889.00
x[1] = 0.7376 2.78
h = 0.0001 0.003
y2[1] (numeric) = 16.4756705286 35.6044832764
y2[1] (closed_form) = 22.816991652 33.7417636879
absolute error = 6.609
relative error = 16.23 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.98767743931 -5.39926990921
y1[1] (closed_form) = 5.98767743931 -5.39926990921
absolute error = 2.102e-62
relative error = 2.608e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.96
Order of pole (three term test) = 75.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 64.96
Order of pole (three term test) = 69.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74653.1MB, alloc=44.3MB, time=889.54
memory used=74700.2MB, alloc=44.3MB, time=890.11
x[1] = 0.7377 2.783
h = 0.001 0.001
y2[1] (numeric) = 16.5061353891 35.6506249015
y2[1] (closed_form) = 22.8348144962 33.7892118936
absolute error = 6.597
relative error = 16.18 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.00498395025 -5.41621315365
y1[1] (closed_form) = 6.00498395025 -5.41621315365
absolute error = 2.102e-62
relative error = 2.600e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.35
Order of pole (three term test) = 75.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 65.35
Order of pole (three term test) = 70.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74746.2MB, alloc=44.3MB, time=890.65
memory used=74792.9MB, alloc=44.3MB, time=891.21
x[1] = 0.7387 2.784
h = 0.001 0.003
y2[1] (numeric) = 16.5367615013 35.6967027826
y2[1] (closed_form) = 22.8562416527 33.7997952027
absolute error = 6.598
relative error = 16.17 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.00547992763 -5.42763618519
y1[1] (closed_form) = 6.00547992763 -5.42763618519
absolute error = 2.102e-62
relative error = 2.597e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.48
Order of pole (three term test) = 75.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 65.48
Order of pole (three term test) = 70.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74838.9MB, alloc=44.3MB, time=891.75
memory used=74885.6MB, alloc=44.3MB, time=892.30
x[1] = 0.7397 2.787
h = 0.0001 0.004
y2[1] (numeric) = 16.5675495918 35.7427163156
y2[1] (closed_form) = 22.8885698399 33.8423914323
absolute error = 6.6
relative error = 16.16 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.01789780476 -5.4500434746
y1[1] (closed_form) = 6.01789780476 -5.4500434746
absolute error = 2.102e-62
relative error = 2.589e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.87
Order of pole (three term test) = 76.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 65.87
Order of pole (three term test) = 70.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=74931.6MB, alloc=44.3MB, time=892.84
memory used=74978.1MB, alloc=44.3MB, time=893.40
x[1] = 0.7398 2.791
h = 0.003 0.006
y2[1] (numeric) = 16.5985003897 35.7886648932
y2[1] (closed_form) = 22.9120181606 33.9059636316
absolute error = 6.588
relative error = 16.1 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.04128420583 -5.47265303667
y1[1] (closed_form) = 6.04128420583 -5.47265303667
absolute error = 2.102e-62
relative error = 2.579e-61 %
Correct digits = 63
memory used=75024.7MB, alloc=44.3MB, time=893.94
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 66.4
Order of pole (three term test) = 76.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 66.4
Order of pole (three term test) = 71.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75070.9MB, alloc=44.3MB, time=894.48
memory used=75117.7MB, alloc=44.3MB, time=895.04
x[1] = 0.7428 2.797
h = 0.0001 0.005
y2[1] (numeric) = 16.6296146268 35.8345479046
y2[1] (closed_form) = 22.9931606466 33.9857748537
absolute error = 6.627
relative error = 16.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.06070076316 -5.52390800724
y1[1] (closed_form) = 6.06070076316 -5.52390800724
absolute error = 2.012e-62
relative error = 2.454e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.2
Order of pole (three term test) = 77.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 67.2
Order of pole (three term test) = 72.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75163.7MB, alloc=44.3MB, time=895.58
memory used=75210.4MB, alloc=44.3MB, time=896.14
x[1] = 0.7429 2.802
h = 0.0001 0.003
y2[1] (numeric) = 16.6608930371 35.8803647355
y2[1] (closed_form) = 23.022458924 34.0655984706
absolute error = 6.615
relative error = 16.09 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.09029620623 -5.55240756302
y1[1] (closed_form) = 6.09029620623 -5.55240756302
absolute error = 2.102e-62
relative error = 2.551e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.88
Order of pole (three term test) = 77.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 67.88
Order of pole (three term test) = 72.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75256.6MB, alloc=44.3MB, time=896.68
memory used=75303.4MB, alloc=44.3MB, time=897.24
x[1] = 0.743 2.805
h = 0.001 0.001
y2[1] (numeric) = 16.6923363574 35.9261147685
y2[1] (closed_form) = 23.0407521602 34.1133396403
absolute error = 6.602
relative error = 16.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.10789939053 -5.56981931263
y1[1] (closed_form) = 6.10789939053 -5.56981931263
absolute error = 2.147e-62
relative error = 2.597e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 68.29
Order of pole (three term test) = 78.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 68.29
Order of pole (three term test) = 73.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75349.6MB, alloc=44.3MB, time=897.79
memory used=75396.3MB, alloc=44.3MB, time=898.34
x[1] = 0.744 2.806
h = 0.001 0.003
y2[1] (numeric) = 16.7239453272 35.9717973822
y2[1] (closed_form) = 23.0624359425 34.1238721057
absolute error = 6.602
relative error = 16.03 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.1083464043 -5.58149951248
y1[1] (closed_form) = 6.1083464043 -5.58149951248
absolute error = 2.102e-62
relative error = 2.541e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 68.42
Order of pole (three term test) = 78.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 68.42
Order of pole (three term test) = 73.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75442.3MB, alloc=44.3MB, time=898.88
memory used=75489.0MB, alloc=44.3MB, time=899.44
memory used=75535.7MB, alloc=44.3MB, time=900.00
x[1] = 0.745 2.809
h = 0.0001 0.004
y2[1] (numeric) = 16.7557206884 36.0174119523
y2[1] (closed_form) = 23.095329512 34.1666230277
absolute error = 6.604
relative error = 16.01 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.12092326737 -5.60447138662
y1[1] (closed_form) = 6.12092326737 -5.60447138662
absolute error = 2.102e-62
relative error = 2.533e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 68.84
Order of pole (three term test) = 78.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 68.84
Order of pole (three term test) = 73.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75581.7MB, alloc=44.3MB, time=900.53
memory used=75628.4MB, alloc=44.3MB, time=901.08
x[1] = 0.7451 2.813
h = 0.003 0.006
y2[1] (numeric) = 16.7876631855 36.0629578504
y2[1] (closed_form) = 23.1194071196 34.2305926588
absolute error = 6.592
relative error = 15.96 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.14471198176 -5.62770768812
y1[1] (closed_form) = 6.14471198176 -5.62770768812
absolute error = 2.102e-62
relative error = 2.523e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 69.39
Order of pole (three term test) = 78.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 69.39
Order of pole (three term test) = 74.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75674.3MB, alloc=44.3MB, time=901.62
memory used=75721.0MB, alloc=44.3MB, time=902.17
x[1] = 0.7481 2.819
h = 0.0001 0.005
y2[1] (numeric) = 16.8197735655 36.1084344452
y2[1] (closed_form) = 23.201794191 34.3105579105
absolute error = 6.63
relative error = 16.01 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.16429174495 -5.68020684104
y1[1] (closed_form) = 6.16429174495 -5.68020684104
absolute error = 1.970e-62
relative error = 2.350e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.23
Order of pole (three term test) = 79.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 70.23
Order of pole (three term test) = 75.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75767.1MB, alloc=44.3MB, time=902.71
memory used=75813.8MB, alloc=44.3MB, time=903.26
x[1] = 0.7482 2.824
h = 0.0001 0.003
y2[1] (numeric) = 16.8520525783 36.1538411015
y2[1] (closed_form) = 23.231886322 34.3908850858
absolute error = 6.619
relative error = 15.95 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.19439675816 -5.70949705097
y1[1] (closed_form) = 6.19439675816 -5.70949705097
absolute error = 2.012e-62
relative error = 2.389e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.93
Order of pole (three term test) = 80.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 70.93
Order of pole (three term test) = 75.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75859.9MB, alloc=44.3MB, time=903.80
memory used=75906.8MB, alloc=44.3MB, time=904.37
x[1] = 0.7483 2.827
h = 0.001 0.001
y2[1] (numeric) = 16.8845009761 36.1991771807
y2[1] (closed_form) = 23.2506619723 34.4389232749
absolute error = 6.605
relative error = 15.9 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.21230058077 -5.72738934953
y1[1] (closed_form) = 6.21230058077 -5.72738934953
absolute error = 2.012e-62
relative error = 2.382e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 71.36
Order of pole (three term test) = 80.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 71.36
Order of pole (three term test) = 76.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=75953.2MB, alloc=44.3MB, time=904.92
memory used=75999.7MB, alloc=44.3MB, time=905.47
memory used=76046.4MB, alloc=44.3MB, time=906.02
x[1] = 0.7493 2.828
h = 0.001 0.003
y2[1] (numeric) = 16.9171195139 36.2444420407
y2[1] (closed_form) = 23.2726078313 34.4494024145
absolute error = 6.604
relative error = 15.89 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.2126961107 -5.73933214721
y1[1] (closed_form) = 6.2126961107 -5.73933214721
absolute error = 2.012e-62
relative error = 2.379e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 71.5
Order of pole (three term test) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 71.5
Order of pole (three term test) = 76.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76092.4MB, alloc=44.3MB, time=906.56
memory used=76139.0MB, alloc=44.3MB, time=907.12
x[1] = 0.7503 2.831
h = 0.0001 0.004
y2[1] (numeric) = 16.9499089491 36.2896350357
y2[1] (closed_form) = 23.3060801947 34.4923085032
absolute error = 6.605
relative error = 15.87 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.22543233635 -5.76288201264
y1[1] (closed_form) = 6.22543233635 -5.76288201264
absolute error = 2.012e-62
relative error = 2.372e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 71.93
Order of pole (three term test) = 80.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 71.93
Order of pole (three term test) = 76.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76184.9MB, alloc=44.3MB, time=907.65
memory used=76231.3MB, alloc=44.3MB, time=908.20
x[1] = 0.7504 2.835
h = 0.003 0.006
y2[1] (numeric) = 16.9828700421 36.3347555163
y2[1] (closed_form) = 23.3308032009 34.5566811124
absolute error = 6.592
relative error = 15.81 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.24962879076 -5.78676119548
y1[1] (closed_form) = 6.24962879076 -5.78676119548
absolute error = 2.012e-62
relative error = 2.363e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 72.51
Order of pole (three term test) = 81.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 72.51
Order of pole (three term test) = 77.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76277.1MB, alloc=44.3MB, time=908.75
memory used=76323.8MB, alloc=44.3MB, time=909.30
x[1] = 0.7534 2.841
h = 0.0001 0.005
y2[1] (numeric) = 17.0160035554 36.3798028297
y2[1] (closed_form) = 23.4144633983 34.6367972785
absolute error = 6.632
relative error = 15.86 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.26936844293 -5.84053303266
y1[1] (closed_form) = 6.26936844293 -5.84053303266
absolute error = 2.059e-62
relative error = 2.403e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 73.38
Order of pole (three term test) = 82.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 73.38
Order of pole (three term test) = 78.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76369.8MB, alloc=44.3MB, time=909.84
memory used=76416.5MB, alloc=44.3MB, time=910.39
x[1] = 0.7535 2.846
h = 0.0001 0.003
y2[1] (numeric) = 17.0493102547 36.4247763194
y2[1] (closed_form) = 23.4453697197 34.7176350543
absolute error = 6.62
relative error = 15.8 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.29998992085 -5.87063427183
y1[1] (closed_form) = 6.29998992085 -5.87063427183
absolute error = 2.059e-62
relative error = 2.391e-61 %
Correct digits = 63
memory used=76463.0MB, alloc=44.3MB, time=910.94
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 74.12
Order of pole (three term test) = 82.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 74.12
Order of pole (three term test) = 79.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76509.5MB, alloc=44.3MB, time=911.50
memory used=76556.6MB, alloc=44.3MB, time=912.07
x[1] = 0.7536 2.849
h = 0.001 0.001
y2[1] (numeric) = 17.0827909079 36.4696753252
y2[1] (closed_form) = 23.4646400951 34.7659743412
absolute error = 6.605
relative error = 15.75 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.31819837173 -5.88901945234
y1[1] (closed_form) = 6.31819837173 -5.88901945234
absolute error = 2.102e-62
relative error = 2.434e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 74.57
Order of pole (three term test) = 83.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 74.57
Order of pole (three term test) = 79.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76602.6MB, alloc=44.3MB, time=912.61
memory used=76649.2MB, alloc=44.3MB, time=913.17
x[1] = 0.7546 2.85
h = 0.001 0.003
y2[1] (numeric) = 17.1164462858 36.5144991834
y2[1] (closed_form) = 23.486853589 34.7763975874
absolute error = 6.603
relative error = 15.74 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.31853981289 -5.90123038509
y1[1] (closed_form) = 6.31853981289 -5.90123038509
absolute error = 2.147e-62
relative error = 2.483e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 74.72
Order of pole (three term test) = 83.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 74.72
Order of pole (three term test) = 79.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76695.3MB, alloc=44.3MB, time=913.72
memory used=76742.0MB, alloc=44.3MB, time=914.27
x[1] = 0.7556 2.853
h = 0.0001 0.004
y2[1] (numeric) = 17.1502771618 36.5592472265
y2[1] (closed_form) = 23.5209184577 34.8194592529
absolute error = 6.604
relative error = 15.72 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.3314357156 -5.92537194904
y1[1] (closed_form) = 6.3314357156 -5.92537194904
absolute error = 2.147e-62
relative error = 2.476e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.17
Order of pole (three term test) = 83.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 75.17
Order of pole (three term test) = 80.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76788.0MB, alloc=44.3MB, time=914.81
memory used=76834.7MB, alloc=44.3MB, time=915.36
x[1] = 0.7557 2.857
h = 0.003 0.006
y2[1] (numeric) = 17.1842843119 36.6039187834
y2[1] (closed_form) = 23.5463033626 34.8842404195
absolute error = 6.59
relative error = 15.66 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.3560453727 -5.94991054332
y1[1] (closed_form) = 6.3560453727 -5.94991054332
absolute error = 2.102e-62
relative error = 2.415e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.77
Order of pole (three term test) = 84.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 75.77
Order of pole (three term test) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=76880.6MB, alloc=44.3MB, time=915.90
memory used=76927.3MB, alloc=44.3MB, time=916.45
memory used=76974.0MB, alloc=44.3MB, time=917.01
x[1] = 0.7587 2.863
h = 0.0001 0.005
y2[1] (numeric) = 17.2184685148 36.6485131793
y2[1] (closed_form) = 23.6312658424 34.964504157
absolute error = 6.63
relative error = 15.71 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.37594137307 -6.0049841842
y1[1] (closed_form) = 6.37594137307 -6.0049841842
absolute error = 2.147e-62
relative error = 2.451e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 76.69
Order of pole (three term test) = 84.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 76.69
Order of pole (three term test) = 81.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=77020.1MB, alloc=44.3MB, time=917.55
memory used=77066.7MB, alloc=44.3MB, time=918.11
x[1] = 0.7588 2.868
h = 0.0001 0.003
y2[1] (numeric) = 17.252830552 36.6930297358
y2[1] (closed_form) = 23.6630071809 35.0458596182
absolute error = 6.618
relative error = 15.65 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.40708625658 -6.03591731793
y1[1] (closed_form) = 6.40708625658 -6.03591731793
absolute error = 2.147e-62
relative error = 2.439e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 77.46
Order of pole (three term test) = 85.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 77.46
Order of pole (three term test) = 82.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=77112.8MB, alloc=44.3MB, time=918.65
memory used=77159.6MB, alloc=44.3MB, time=919.22
x[1] = 0.7589 2.871
h = 0.001 0.001
y2[1] (numeric) = 17.2873712074 36.7374677705
y2[1] (closed_form) = 23.6827848884 35.0945041033
absolute error = 6.603
relative error = 15.6 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.42560334963 -6.05480800915
y1[1] (closed_form) = 6.42560334963 -6.05480800915
absolute error = 2.236e-62
relative error = 2.533e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 77.92
Order of pole (three term test) = 86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 77.92
Order of pole (three term test) = 82.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=77205.7MB, alloc=44.3MB, time=919.76
memory used=77252.2MB, alloc=44.3MB, time=920.32
x[1] = 0.7599 2.872
h = 0.001 0.003
y2[1] (numeric) = 17.3220912679 36.7818265977
y2[1] (closed_form) = 23.7052716844 35.1048688007
absolute error = 6.6
relative error = 15.58 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.42588800987 -6.06729272384
y1[1] (closed_form) = 6.42588800987 -6.06729272384
absolute error = 2.236e-62
relative error = 2.530e-61 %
Correct digits = 63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 78.08
Order of pole (three term test) = 86.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 78.08
Order of pole (three term test) = 83.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=77298.8MB, alloc=44.3MB, time=920.87
memory used=77347.0MB, alloc=44.3MB, time=921.52
Finished!
Maximum Time Reached before Solution Completed!
diff ( y2 , x , 5 ) = y1 ;
diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 4 ) ) ;
Iterations = 754
Total Elapsed Time = 15 Minutes 21 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 15 Minutes 21 Seconds
> quit
memory used=77366.7MB, alloc=44.3MB, time=921.78