|\^/| 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.
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#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(c(1.0) + sin(c(x)));
> end;
exact_soln_y1 := proc(x) return c(1.0) + sin(c(x)) end proc
> exact_soln_y2 := proc(x)
> return(c(1.0) + sin(c(x)));
> end;
exact_soln_y2 := proc(x) return c(1.0) + sin(c(x)) end proc
> exact_soln_y2p := proc(x)
> return( cos(c(x)));
> end;
exact_soln_y2p := proc(x) return cos(c(x)) 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
> 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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 - 4 - 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 - 4 - 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 - 4 - 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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 - 14;
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 - 14;
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 - 14;
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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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_tmp5,
> 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 sub FULL - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] - array_const_1D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,5]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(4))) * c(factorial_3(0,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[2,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[3,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[4,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[5,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1 order_d = 3
> array_tmp4[1] := array_y2_higher[4,1];
> #emit pre neg FULL $eq_no = 2
> array_tmp5[1] := neg(array_tmp4[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_tmp5[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 sub FULL CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(4))) * c(factorial_3(1,5));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2 order_d = 3
> array_tmp4[2] := array_y2_higher[4,2];
> #emit pre neg FULL $eq_no = 2
> array_tmp5[2] := neg(array_tmp4[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_tmp5[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 sub FULL CONST $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,7]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(4))) * c(factorial_3(2,6));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3 order_d = 3
> array_tmp4[3] := array_y2_higher[4,3];
> #emit pre neg FULL $eq_no = 2
> array_tmp5[3] := neg(array_tmp4[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_tmp5[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 sub FULL CONST $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,8]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(4))) * c(factorial_3(3,7));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4 order_d = 3
> array_tmp4[4] := array_y2_higher[4,4];
> #emit pre neg FULL $eq_no = 2
> array_tmp5[4] := neg(array_tmp4[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_tmp5[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 sub FULL CONST $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,9]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(4))) * c(factorial_3(4,8));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5 order_d = 3
> array_tmp4[5] := array_y2_higher[4,5];
> #emit pre neg FULL $eq_no = 2
> array_tmp5[5] := neg(array_tmp4[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_tmp5[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 FULL - NOT FULL sub $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 4;
> 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_tmp2[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_tmp4[kkk] := array_y2_higher[4,kkk];
> fi;# end if 1;
> #emit neg FULL $eq_no = 2
> array_tmp5[kkk] := neg(array_tmp4[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_tmp5[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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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];
array_tmp2[1] := array_tmp1[1] - array_const_1D0[1];
if not array_y2_set_initial[1, 5] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(4))*c(factorial_3(0, 4));
if 5 <= ATS_MAX_TERMS then
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[2, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[3, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[4, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[5, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp4[1] := array_y2_higher[4, 1];
array_tmp5[1] := neg(array_tmp4[1]);
if not array_y1_set_initial[2, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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];
array_tmp2[2] := array_tmp1[2];
if not array_y2_set_initial[1, 6] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(4))*c(factorial_3(1, 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)
end if
end if;
kkk := 3;
array_tmp4[2] := array_y2_higher[4, 2];
array_tmp5[2] := neg(array_tmp4[2]);
if not array_y1_set_initial[2, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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];
array_tmp2[3] := array_tmp1[3];
if not array_y2_set_initial[1, 7] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(4))*c(factorial_3(2, 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)
end if
end if;
kkk := 4;
array_tmp4[3] := array_y2_higher[4, 3];
array_tmp5[3] := neg(array_tmp4[3]);
if not array_y1_set_initial[2, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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];
array_tmp2[4] := array_tmp1[4];
if not array_y2_set_initial[1, 8] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(4))*c(factorial_3(3, 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)
end if
end if;
kkk := 5;
array_tmp4[4] := array_y2_higher[4, 4];
array_tmp5[4] := neg(array_tmp4[4]);
if not array_y1_set_initial[2, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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];
array_tmp2[5] := array_tmp1[5];
if not array_y2_set_initial[1, 9] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(4))*c(factorial_3(4, 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)
end if
end if;
kkk := 6;
array_tmp4[5] := array_y2_higher[4, 5];
array_tmp5[5] := neg(array_tmp4[5]);
if not array_y1_set_initial[2, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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];
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 4;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[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_tmp4[kkk] := array_y2_higher[4, kkk]
end if;
array_tmp5[kkk] := neg(array_tmp4[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_tmp5[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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
> #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_tmp5,
> 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:=32;
> 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_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y2_higher := Array(0..(5) ,(0..40+ 1),[]);
> array_y2_higher_work := Array(0..(5) ,(0..40+ 1),[]);
> array_y2_higher_work2 := Array(0..(5) ,(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_tmp5[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 <=5) 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 <=5) 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 <=5) 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_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_4);
> array_const_4[1] := c(4);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_1D0);
> array_const_1D0[1] := c(1.0);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_3);
> array_const_3[1] := c(3);
> 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] := false;
> 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/mtest8postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 4 ) = y1 - 1.0 ; ");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> 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,"glob_look_poles := true;");
> 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(c(1.0) + sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(c(1.0) + sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return( cos(c(x)));");
> 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,"");
> omniout_str(ALWAYS,"");
> 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);
> glob_look_poles := true;
> 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 := 4;
> #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 <= 5) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 5 + 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 := 5;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #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 := 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 := 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 := 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 := 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 , 4 ) = y1 - 1.0 ; ");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ; ");
> 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,"2017-11-26T16:05:43-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest8")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 4 ) = y1 - 1.0 ; ")
> ;
> 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,"mtest8 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest8 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 , 3 ) ) ; ")
> ;
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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_tmp5, 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 := 32;
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_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y2_higher := Array(0 .. 5, 0 .. 41, []);
array_y2_higher_work := Array(0 .. 5, 0 .. 41, []);
array_y2_higher_work2 := Array(0 .. 5, 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_tmp5[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 <= 5 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 <= 5 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 <= 5 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_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_4);
array_const_4[1] := c(4);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_1D0);
array_const_1D0[1] := c(1.0);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_3);
array_const_3[1] := c(3);
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] := false;
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/mtest8postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0 ; ");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( diff ( y\
2 , x , 3 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
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, "glob_look_poles := true;");
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(c(1.0) +\tsin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(c(1.0) +\tsin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return(\tcos(c(x)));");
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, "");
omniout_str(ALWAYS, "");
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,");
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omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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);
glob_look_poles := true;
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 := 4;
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 <= 5 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 5 + 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 := 5;
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 := 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 := 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 := 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 := 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 , 4 ) = y1 - 1.0 ; ")
;
omniout_str(INFO, "diff ( y1 , x , 1 ) = neg ( diff ( \
y2 , x , 3 ) ) ; ");
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, "2017-11-26T16:05:43-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest8");
logitem_str(html_log_file,
"diff ( y2 , x , 4 ) = y1 - 1.0 ; ");
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,
"mtest8 diffeq.mxt");
logitem_str(html_log_file, "mtest8 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 , 3 ) ) ; ");
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=3.6MB, alloc=40.3MB, time=0.07
##############ECHO OF PROBLEM#################
##############temp/mtest8postcpx.cpx#################
diff ( y2 , x , 4 ) = y1 - 1.0 ;
diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
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);
glob_look_poles := true;
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(c(1.0) + sin(c(x)));
end;
exact_soln_y2 := proc(x)
return(c(1.0) + sin(c(x)));
end;
exact_soln_y2p := proc(x)
return( cos(c(x)));
end;
exact_soln_y2pp := proc(x)
return(neg(sin(c(x))));
end;
exact_soln_y2ppp := proc(x)
return( neg(cos(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=53.9MB, alloc=40.3MB, time=0.68
x[1] = 0.1 0.1
h = 0.0001 0.005
y2[1] (numeric) = 1.10033299984 0.0996663334921
y2[1] (closed_form) = 1.10033299984 0.0996663334921
absolute error = 0
relative error = 0 %
Correct digits = 30
h = 0.0001 0.005
y1[1] (numeric) = 1.10033299984 0.0996663334921
y1[1] (closed_form) = 1.10033299984 0.0996663334921
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=100.3MB, alloc=40.3MB, time=1.24
memory used=147.2MB, alloc=40.3MB, time=1.82
x[1] = 0.1001 0.105
h = 0.0001 0.003
y2[1] (numeric) = 1.10047384107 0.103666034167
y2[1] (closed_form) = 1.10048430307 0.104666466122
absolute error = 0.001
relative error = 0.0905 %
Correct digits = 3
h = 0.0001 0.003
y1[1] (numeric) = 1.10048430307 0.104666466122
y1[1] (closed_form) = 1.10048430307 0.104666466122
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=193.6MB, alloc=40.3MB, time=2.39
memory used=240.8MB, alloc=40.3MB, time=2.98
x[1] = 0.1002 0.108
h = 0.001 0.001
y2[1] (numeric) = 1.10061637183 0.107667312102
y2[1] (closed_form) = 1.1006163718 0.107667312081
absolute error = 3.192e-11
relative error = 2.886e-09 %
Correct digits = 11
h = 0.001 0.001
y1[1] (numeric) = 1.1006163718 0.107667312081
y1[1] (closed_form) = 1.1006163718 0.107667312081
absolute error = 1e-32
relative error = 9.043e-31 %
Correct digits = 32
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=287.3MB, alloc=40.3MB, time=3.56
memory used=334.1MB, alloc=40.3MB, time=4.13
x[1] = 0.1012 0.109
h = 0.001 0.003
y2[1] (numeric) = 1.10076059763 0.11167023119
y2[1] (closed_form) = 1.10162809688 0.108657179181
absolute error = 0.003135
relative error = 0.2832 %
Correct digits = 3
h = 0.001 0.003
y1[1] (numeric) = 1.10162809688 0.108657179181
y1[1] (closed_form) = 1.10162809688 0.108657179181
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=380.4MB, alloc=40.3MB, time=4.70
x[1] = 0.1022 0.112
h = 0.0001 0.004
y2[1] (numeric) = 1.10090652398 0.115674855325
y2[1] (closed_form) = 1.10266273475 0.111648676907
absolute error = 0.004393
relative error = 0.3963 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.10266273475 0.111648676907
y1[1] (closed_form) = 1.10266273475 0.111648676907
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=426.8MB, alloc=40.3MB, time=5.26
memory used=473.5MB, alloc=40.3MB, time=5.83
x[1] = 0.1023 0.116
h = 0.003 0.006
y2[1] (numeric) = 1.10105415641 0.119681248404
y2[1] (closed_form) = 1.10280950546 0.115652505773
absolute error = 0.004395
relative error = 0.3963 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.10280950546 0.115652505773
y1[1] (closed_form) = 1.10280950546 0.115652505773
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=519.3MB, alloc=40.3MB, time=6.39
memory used=566.2MB, alloc=40.3MB, time=6.96
x[1] = 0.1053 0.122
h = 0.0001 0.005
y2[1] (numeric) = 1.10120350046 0.123689474317
y2[1] (closed_form) = 1.10588867776 0.121625440337
absolute error = 0.00512
relative error = 0.4602 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.10588867776 0.121625440337
y1[1] (closed_form) = 1.10588867776 0.121625440337
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=612.5MB, alloc=40.3MB, time=7.53
memory used=659.5MB, alloc=40.3MB, time=8.10
x[1] = 0.1054 0.127
h = 0.0001 0.003
y2[1] (numeric) = 1.10135456179 0.127699596848
y2[1] (closed_form) = 1.10605452381 0.126634997662
absolute error = 0.004819
relative error = 0.4329 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.10605452381 0.126634997662
y1[1] (closed_form) = 1.10605452381 0.126634997662
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=706.0MB, alloc=40.3MB, time=8.68
x[1] = 0.1055 0.13
h = 0.001 0.001
y2[1] (numeric) = 1.10150734614 0.131711679692
y2[1] (closed_form) = 1.10619547806 0.129641643138
absolute error = 0.005125
relative error = 0.4601 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.10619547806 0.129641643138
y1[1] (closed_form) = 1.10619547806 0.129641643138
absolute error = 1e-31
relative error = 8.979e-30 %
Correct digits = 31
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=752.8MB, alloc=40.3MB, time=9.26
memory used=799.7MB, alloc=40.3MB, time=9.84
x[1] = 0.1065 0.131
h = 0.001 0.003
y2[1] (numeric) = 1.10166185932 0.135725786568
y2[1] (closed_form) = 1.10721219109 0.130630663334
absolute error = 0.007534
relative error = 0.6758 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.10721219109 0.130630663334
y1[1] (closed_form) = 1.10721219109 0.130630663334
absolute error = 1e-31
relative error = 8.969e-30 %
Correct digits = 31
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=846.0MB, alloc=40.3MB, time=10.41
memory used=892.9MB, alloc=40.3MB, time=10.99
x[1] = 0.1075 0.134
h = 0.0001 0.004
y2[1] (numeric) = 1.10181810714 0.139741981202
y2[1] (closed_form) = 1.10825778955 0.133625537144
absolute error = 0.008881
relative error = 0.7956 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.10825778955 0.133625537144
y1[1] (closed_form) = 1.10825778955 0.133625537144
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=939.2MB, alloc=40.3MB, time=11.56
memory used=986.0MB, alloc=40.3MB, time=12.13
x[1] = 0.1076 0.138
h = 0.003 0.006
y2[1] (numeric) = 1.10197609542 0.14376032732
y2[1] (closed_form) = 1.10841670753 0.137637798716
absolute error = 0.008886
relative error = 0.7956 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.10841670753 0.137637798716
y1[1] (closed_form) = 1.10841670753 0.137637798716
absolute error = 1e-31
relative error = 8.953e-30 %
Correct digits = 31
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1032.4MB, alloc=40.3MB, time=12.70
x[1] = 0.1106 0.144
h = 0.0001 0.005
y2[1] (numeric) = 1.10213583 0.147780888645
y2[1] (closed_form) = 1.11152099795 0.143615303875
absolute error = 0.01027
relative error = 0.9162 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.11152099795 0.143615303875
y1[1] (closed_form) = 1.11152099795 0.143615303875
absolute error = 0
relative error = 0 %
Correct digits = 30
memory used=1079.2MB, alloc=40.3MB, time=13.26
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1125.9MB, alloc=40.3MB, time=13.84
x[1] = 0.1107 0.149
h = 0.0001 0.003
y2[1] (numeric) = 1.10229731686 0.151803728786
y2[1] (closed_form) = 1.11170263074 0.148636531188
absolute error = 0.009924
relative error = 0.8848 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.11170263074 0.148636531188
y1[1] (closed_form) = 1.11170263074 0.148636531188
absolute error = 1.005e-31
relative error = 8.960e-30 %
Correct digits = 31
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1172.4MB, alloc=40.3MB, time=14.40
memory used=1219.5MB, alloc=40.3MB, time=14.99
x[1] = 0.1108 0.152
h = 0.001 0.001
y2[1] (numeric) = 1.10246056209 0.155828911257
y2[1] (closed_form) = 1.11185323598 0.151650314108
absolute error = 0.01028
relative error = 0.9161 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.11185323598 0.151650314108
y1[1] (closed_form) = 1.11185323598 0.151650314108
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1266.1MB, alloc=40.3MB, time=15.57
memory used=1313.0MB, alloc=40.3MB, time=16.15
x[1] = 0.1118 0.153
h = 0.001 0.003
y2[1] (numeric) = 1.10262557183 0.159856499603
y2[1] (closed_form) = 1.11287563116 0.152638701201
absolute error = 0.01254
relative error = 1.116 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.11287563116 0.152638701201
y1[1] (closed_form) = 1.11287563116 0.152638701201
absolute error = 1e-31
relative error = 8.902e-30 %
Correct digits = 31
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1359.4MB, alloc=40.3MB, time=16.71
x[1] = 0.1128 0.156
h = 0.0001 0.004
y2[1] (numeric) = 1.10279235224 0.163886557379
y2[1] (closed_form) = 1.1139333654 0.155638072673
absolute error = 0.01386
relative error = 1.232 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.1139333654 0.155638072673
y1[1] (closed_form) = 1.1139333654 0.155638072673
absolute error = 1e-31
relative error = 8.891e-30 %
Correct digits = 31
memory used=1406.4MB, alloc=40.3MB, time=17.30
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1452.9MB, alloc=40.3MB, time=17.86
x[1] = 0.1129 0.16
h = 0.003 0.006
y2[1] (numeric) = 1.1029609095 0.167919148137
y2[1] (closed_form) = 1.11410543881 0.159660559171
absolute error = 0.01387
relative error = 1.232 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.11410543881 0.159660559171
y1[1] (closed_form) = 1.11410543881 0.159660559171
absolute error = 1e-31
relative error = 8.885e-30 %
Correct digits = 31
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1499.2MB, alloc=40.3MB, time=18.43
memory used=1546.1MB, alloc=40.3MB, time=19.01
x[1] = 0.1159 0.166
h = 0.0001 0.005
y2[1] (numeric) = 1.10313124978 0.171954335431
y2[1] (closed_form) = 1.11723765674 0.165644636231
absolute error = 0.01545
relative error = 1.368 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.11723765674 0.165644636231
y1[1] (closed_form) = 1.11723765674 0.165644636231
absolute error = 1e-31
relative error = 8.854e-30 %
Correct digits = 31
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) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1592.5MB, alloc=40.3MB, time=19.58
memory used=1639.5MB, alloc=40.3MB, time=20.16
x[1] = 0.116 0.171
h = 0.0001 0.003
y2[1] (numeric) = 1.10330337944 0.175992182691
y2[1] (closed_form) = 1.11743633012 0.170679780464
absolute error = 0.0151
relative error = 1.336 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.11743633012 0.170679780464
y1[1] (closed_form) = 1.11743633012 0.170679780464
absolute error = 1.005e-31
relative error = 8.891e-30 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1686.2MB, alloc=44.3MB, time=20.74
memory used=1733.4MB, alloc=44.3MB, time=21.33
x[1] = 0.1161 0.174
h = 0.001 0.001
y2[1] (numeric) = 1.10347730495 0.180032753246
y2[1] (closed_form) = 1.11759735788 0.173702039755
absolute error = 0.01547
relative error = 1.368 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.11759735788 0.173702039755
y1[1] (closed_form) = 1.11759735788 0.173702039755
absolute error = 1.005e-31
relative error = 8.886e-30 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1780.0MB, alloc=44.3MB, time=21.90
x[1] = 0.1171 0.175
h = 0.001 0.003
y2[1] (numeric) = 1.10365303286 0.184076110468
y2[1] (closed_form) = 1.11862613185 0.174690005932
absolute error = 0.01767
relative error = 1.561 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.11862613185 0.174690005932
y1[1] (closed_form) = 1.11862613185 0.174690005932
absolute error = 1.005e-31
relative error = 8.877e-30 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1826.3MB, alloc=44.3MB, time=22.46
memory used=1873.2MB, alloc=44.3MB, time=23.04
x[1] = 0.1181 0.178
h = 0.0001 0.004
y2[1] (numeric) = 1.10383056972 0.188122317733
y2[1] (closed_form) = 1.11969718362 0.177694995866
absolute error = 0.01899
relative error = 1.675 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.11969718362 0.177694995866
y1[1] (closed_form) = 1.11969718362 0.177694995866
absolute error = 1.005e-31
relative error = 8.865e-30 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1919.6MB, alloc=44.3MB, time=23.60
memory used=1966.3MB, alloc=44.3MB, time=24.18
x[1] = 0.1182 0.182
h = 0.003 0.006
y2[1] (numeric) = 1.10400992208 0.19217143842
y2[1] (closed_form) = 1.11988342903 0.181729501103
absolute error = 0.019
relative error = 1.675 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.11988342903 0.181729501103
y1[1] (closed_form) = 1.11988342903 0.181729501103
absolute error = 2.002e-31
relative error = 1.765e-29 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2012.6MB, alloc=44.3MB, time=24.74
memory used=2059.4MB, alloc=44.3MB, time=25.32
x[1] = 0.1212 0.188
h = 0.0001 0.005
y2[1] (numeric) = 1.10419109655 0.196223535909
y2[1] (closed_form) = 1.12304639811 0.187722147852
absolute error = 0.02068
relative error = 1.817 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.12304639811 0.187722147852
y1[1] (closed_form) = 1.12304639811 0.187722147852
absolute error = 1.005e-31
relative error = 8.826e-30 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2105.8MB, alloc=44.3MB, time=25.88
x[1] = 0.1213 0.193
h = 0.0001 0.003
y2[1] (numeric) = 1.10437409987 0.200278673446
y2[1] (closed_form) = 1.12326337695 0.192773458308
absolute error = 0.02033
relative error = 1.783 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.12326337695 0.192773458308
y1[1] (closed_form) = 1.12326337695 0.192773458308
absolute error = 1.005e-31
relative error = 8.818e-30 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2152.4MB, alloc=44.3MB, time=26.45
memory used=2199.5MB, alloc=44.3MB, time=27.04
x[1] = 0.1214 0.196
h = 0.001 0.001
y2[1] (numeric) = 1.10455893898 0.204336914179
y2[1] (closed_form) = 1.12343560549 0.195805534333
absolute error = 0.02072
relative error = 1.817 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.12343560549 0.195805534333
y1[1] (closed_form) = 1.12343560549 0.195805534333
absolute error = 2.002e-31
relative error = 1.756e-29 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2246.2MB, alloc=44.3MB, time=27.62
memory used=2293.1MB, alloc=44.3MB, time=28.20
x[1] = 0.1224 0.197
h = 0.0001 0.004
y2[1] (numeric) = 1.10474562085 0.208398321295
y2[1] (closed_form) = 1.1244714577 0.196793290103
absolute error = 0.02289
relative error = 2.005 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.1244714577 0.196793290103
y1[1] (closed_form) = 1.1244714577 0.196793290103
absolute error = 2.002e-31
relative error = 1.754e-29 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2339.4MB, alloc=44.3MB, time=28.76
memory used=2386.1MB, alloc=44.3MB, time=29.34
x[1] = 0.1225 0.201
h = 0.003 0.006
y2[1] (numeric) = 1.10493415248 0.212462957997
y2[1] (closed_form) = 1.12467055071 0.200839764217
absolute error = 0.0229
relative error = 2.005 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.12467055071 0.200839764217
y1[1] (closed_form) = 1.12467055071 0.200839764217
absolute error = 2.002e-31
relative error = 1.753e-29 %
Correct digits = 31
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) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2432.5MB, alloc=44.3MB, time=29.90
x[1] = 0.1255 0.207
h = 0.0001 0.005
y2[1] (numeric) = 1.10512454089 0.216530887494
y2[1] (closed_form) = 1.12786212822 0.206841797121
absolute error = 0.02472
relative error = 2.155 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.12786212822 0.206841797121
y1[1] (closed_form) = 1.12786212822 0.206841797121
absolute error = 2.002e-31
relative error = 1.746e-29 %
Correct digits = 31
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) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2479.2MB, alloc=44.3MB, time=30.48
memory used=2525.9MB, alloc=44.3MB, time=31.04
x[1] = 0.1256 0.212
h = 0.0001 0.003
y2[1] (numeric) = 1.10531679328 0.220602172857
y2[1] (closed_form) = 1.12809565679 0.211909065234
absolute error = 0.02438
relative error = 2.124 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.12809565679 0.211909065234
y1[1] (closed_form) = 1.12809565679 0.211909065234
absolute error = 2.002e-31
relative error = 1.745e-29 %
Correct digits = 31
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) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2572.3MB, alloc=44.3MB, time=31.61
memory used=2619.6MB, alloc=44.3MB, time=32.20
x[1] = 0.1257 0.215
h = 0.001 0.001
y2[1] (numeric) = 1.10551091703 0.22467687705
y2[1] (closed_form) = 1.12827801673 0.214950812089
absolute error = 0.02476
relative error = 2.156 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.12827801673 0.214950812089
y1[1] (closed_form) = 1.12827801673 0.214950812089
absolute error = 2.002e-31
relative error = 1.743e-29 %
Correct digits = 31
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) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2666.1MB, alloc=44.3MB, time=32.78
memory used=2713.1MB, alloc=44.3MB, time=33.36
x[1] = 0.1267 0.216
h = 0.001 0.003
y2[1] (numeric) = 1.1057069196 0.228755063087
y2[1] (closed_form) = 1.1293205233 0.215938649698
absolute error = 0.02687
relative error = 2.337 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.1293205233 0.215938649698
y1[1] (closed_form) = 1.1293205233 0.215938649698
absolute error = 2e-31
relative error = 1.739e-29 %
Correct digits = 31
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) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2759.5MB, alloc=44.3MB, time=33.92
x[1] = 0.1277 0.219
h = 0.0001 0.004
y2[1] (numeric) = 1.10590480843 0.232836793993
y2[1] (closed_form) = 1.13041942861 0.218957267869
absolute error = 0.02817
relative error = 2.447 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.13041942861 0.218957267869
y1[1] (closed_form) = 1.13041942861 0.218957267869
absolute error = 2e-31
relative error = 1.737e-29 %
Correct digits = 31
memory used=2806.3MB, alloc=44.3MB, time=34.49
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) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2852.8MB, alloc=44.3MB, time=35.06
x[1] = 0.1278 0.223
h = 0.003 0.006
y2[1] (numeric) = 1.10610459099 0.236922132793
y2[1] (closed_form) = 1.13063458912 0.223019117204
absolute error = 0.0282
relative error = 2.447 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.13063458912 0.223019117204
y1[1] (closed_form) = 1.13063458912 0.223019117204
absolute error = 2e-31
relative error = 1.735e-29 %
Correct digits = 31
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) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2899.2MB, alloc=44.3MB, time=35.63
memory used=2946.0MB, alloc=44.3MB, time=36.20
x[1] = 0.1308 0.229
h = 0.0001 0.005
y2[1] (numeric) = 1.10630627481 0.241011142517
y2[1] (closed_form) = 1.13386219218 0.229033462834
absolute error = 0.03005
relative error = 2.597 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.13386219218 0.229033462834
y1[1] (closed_form) = 1.13386219218 0.229033462834
absolute error = 1e-31
relative error = 8.645e-30 %
Correct digits = 31
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) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2992.4MB, alloc=44.3MB, time=36.77
memory used=3039.4MB, alloc=44.3MB, time=37.35
x[1] = 0.1309 0.234
h = 0.0001 0.003
y2[1] (numeric) = 1.10650986758 0.24510388605
y2[1] (closed_form) = 1.13411638602 0.234121106838
absolute error = 0.02971
relative error = 2.566 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.13411638602 0.234121106838
y1[1] (closed_form) = 1.13411638602 0.234121106838
absolute error = 2e-31
relative error = 1.727e-29 %
Correct digits = 31
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) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3086.0MB, alloc=44.3MB, time=37.92
memory used=3133.3MB, alloc=44.3MB, time=38.51
x[1] = 0.131 0.237
h = 0.001 0.001
y2[1] (numeric) = 1.10671537723 0.249200426163
y2[1] (closed_form) = 1.13431139908 0.237175179306
absolute error = 0.0301
relative error = 2.598 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.13431139908 0.237175179306
y1[1] (closed_form) = 1.13431139908 0.237175179306
absolute error = 2e-31
relative error = 1.726e-29 %
Correct digits = 31
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) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3179.6MB, alloc=44.3MB, time=39.08
x[1] = 0.132 0.238
h = 0.001 0.003
y2[1] (numeric) = 1.10692281172 0.253300825684
y2[1] (closed_form) = 1.1353622917 0.238163201941
absolute error = 0.03222
relative error = 2.777 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.1353622917 0.238163201941
y1[1] (closed_form) = 1.1353622917 0.238163201941
absolute error = 2e-31
relative error = 1.724e-29 %
Correct digits = 31
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) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3226.0MB, alloc=44.3MB, time=39.65
memory used=3273.0MB, alloc=44.3MB, time=40.22
x[1] = 0.133 0.241
h = 0.0001 0.004
y2[1] (numeric) = 1.10713217907 0.257405147456
y2[1] (closed_form) = 1.13647792542 0.241190657123
absolute error = 0.03353
relative error = 2.886 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.13647792542 0.241190657123
y1[1] (closed_form) = 1.13647792542 0.241190657123
absolute error = 2e-31
relative error = 1.721e-29 %
Correct digits = 31
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) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3319.3MB, alloc=44.3MB, time=40.80
memory used=3366.2MB, alloc=44.3MB, time=41.37
x[1] = 0.1331 0.245
h = 0.003 0.006
y2[1] (numeric) = 1.10734348727 0.261513454317
y2[1] (closed_form) = 1.13671019882 0.245269683389
absolute error = 0.03356
relative error = 2.886 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.13671019882 0.245269683389
y1[1] (closed_form) = 1.13671019882 0.245269683389
absolute error = 2e-31
relative error = 1.720e-29 %
Correct digits = 31
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) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3412.5MB, alloc=44.3MB, time=41.94
memory used=3459.4MB, alloc=44.3MB, time=42.51
x[1] = 0.1361 0.251
h = 0.0001 0.005
y2[1] (numeric) = 1.10755674438 0.265625809117
y2[1] (closed_form) = 1.13997670163 0.251298331088
absolute error = 0.03544
relative error = 3.036 %
Correct digits = 2
h = 0.0001 0.005
y1[1] (numeric) = 1.13997670163 0.251298331088
y1[1] (closed_form) = 1.13997670163 0.251298331088
absolute error = 3e-31
relative error = 2.570e-29 %
Correct digits = 31
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) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3505.8MB, alloc=44.3MB, time=43.08
x[1] = 0.1362 0.256
h = 0.0001 0.003
y2[1] (numeric) = 1.10777195866 0.269742274548
y2[1] (closed_form) = 1.14025286316 0.256408611272
absolute error = 0.03511
relative error = 3.004 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.14025286316 0.256408611272
y1[1] (closed_form) = 1.14025286316 0.256408611272
absolute error = 2e-31
relative error = 1.711e-29 %
Correct digits = 31
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) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3552.3MB, alloc=44.3MB, time=43.64
memory used=3599.5MB, alloc=44.3MB, time=44.24
x[1] = 0.1363 0.259
h = 0.001 0.001
y2[1] (numeric) = 1.10798913862 0.273862913187
y2[1] (closed_form) = 1.14046133051 0.259476356295
absolute error = 0.03552
relative error = 3.037 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.14046133051 0.259476356295
y1[1] (closed_form) = 1.14046133051 0.259476356295
absolute error = 2e-31
relative error = 1.710e-29 %
Correct digits = 31
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) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3646.3MB, alloc=44.3MB, time=44.82
memory used=3693.2MB, alloc=44.3MB, time=45.39
x[1] = 0.1373 0.26
h = 0.001 0.003
y2[1] (numeric) = 1.10820829281 0.277987787674
y2[1] (closed_form) = 1.14152131872 0.26046476933
absolute error = 0.03764
relative error = 3.215 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.14152131872 0.26046476933
y1[1] (closed_form) = 1.14152131872 0.26046476933
absolute error = 2e-31
relative error = 1.708e-29 %
Correct digits = 31
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) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3739.6MB, alloc=44.3MB, time=45.96
memory used=3786.6MB, alloc=44.3MB, time=46.54
x[1] = 0.1383 0.263
h = 0.0001 0.004
y2[1] (numeric) = 1.10842942982 0.28211696066
y2[1] (closed_form) = 1.14265489557 0.263502181622
absolute error = 0.03896
relative error = 3.322 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.14265489557 0.263502181622
y1[1] (closed_form) = 1.14265489557 0.263502181622
absolute error = 2.002e-31
relative error = 1.708e-29 %
Correct digits = 31
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) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3832.8MB, alloc=44.3MB, time=47.10
x[1] = 0.1384 0.267
h = 0.003 0.006
y2[1] (numeric) = 1.10865255824 0.286250494799
y2[1] (closed_form) = 1.14290533905 0.267600190372
absolute error = 0.039
relative error = 3.323 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.14290533905 0.267600190372
y1[1] (closed_form) = 1.14290533905 0.267600190372
absolute error = 2.002e-31
relative error = 1.706e-29 %
Correct digits = 31
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) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3879.4MB, alloc=44.3MB, time=47.67
memory used=3926.2MB, alloc=44.3MB, time=48.24
x[1] = 0.1414 0.273
h = 0.0001 0.005
y2[1] (numeric) = 1.10887768672 0.290388452753
y2[1] (closed_form) = 1.14621363686 0.273645126931
absolute error = 0.04092
relative error = 3.472 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.14621363686 0.273645126931
y1[1] (closed_form) = 1.14621363686 0.273645126931
absolute error = 2.002e-31
relative error = 1.699e-29 %
Correct digits = 31
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) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3972.5MB, alloc=44.3MB, time=48.80
memory used=4019.6MB, alloc=44.3MB, time=49.38
x[1] = 0.1415 0.278
h = 0.0001 0.003
y2[1] (numeric) = 1.10910482414 0.294530897019
y2[1] (closed_form) = 1.14651308381 0.278780308783
absolute error = 0.04059
relative error = 3.44 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.14651308381 0.278780308783
y1[1] (closed_form) = 1.14651308381 0.278780308783
absolute error = 2.002e-31
relative error = 1.697e-29 %
Correct digits = 31
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) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4066.2MB, alloc=44.3MB, time=49.96
memory used=4113.4MB, alloc=44.3MB, time=50.55
x[1] = 0.1416 0.281
h = 0.001 0.001
y2[1] (numeric) = 1.10933397961 0.298677889977
y2[1] (closed_form) = 1.14673581594 0.281863076396
absolute error = 0.04101
relative error = 3.473 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.14673581594 0.281863076396
y1[1] (closed_form) = 1.14673581594 0.281863076396
absolute error = 2.002e-31
relative error = 1.696e-29 %
Correct digits = 31
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) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4159.8MB, alloc=44.3MB, time=51.12
x[1] = 0.1426 0.282
h = 0.001 0.003
y2[1] (numeric) = 1.10956516234 0.30282949407
y2[1] (closed_form) = 1.14780561354 0.282852083264
absolute error = 0.04314
relative error = 3.65 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.14780561354 0.282852083264
y1[1] (closed_form) = 1.14780561354 0.282852083264
absolute error = 2.002e-31
relative error = 1.694e-29 %
Correct digits = 31
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) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4206.5MB, alloc=44.3MB, time=51.69
memory used=4253.2MB, alloc=44.3MB, time=52.26
x[1] = 0.1436 0.285
h = 0.0001 0.004
y2[1] (numeric) = 1.10979838155 0.306985771761
y2[1] (closed_form) = 1.14895835871 0.285900573122
absolute error = 0.04448
relative error = 3.756 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.14895835871 0.285900573122
y1[1] (closed_form) = 1.14895835871 0.285900573122
absolute error = 2.002e-31
relative error = 1.691e-29 %
Correct digits = 31
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) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4299.6MB, alloc=44.3MB, time=52.83
memory used=4346.5MB, alloc=44.3MB, time=53.40
x[1] = 0.1437 0.289
h = 0.003 0.006
y2[1] (numeric) = 1.11003364647 0.31114678551
y2[1] (closed_form) = 1.14922804219 0.290019374322
absolute error = 0.04453
relative error = 3.757 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.14922804219 0.290019374322
y1[1] (closed_form) = 1.14922804219 0.290019374322
absolute error = 2.010e-31
relative error = 1.696e-29 %
Correct digits = 31
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) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4392.9MB, alloc=44.3MB, time=53.97
memory used=4439.9MB, alloc=44.3MB, time=54.55
x[1] = 0.1467 0.295
h = 0.0001 0.005
y2[1] (numeric) = 1.11027096638 0.315312597788
y2[1] (closed_form) = 1.15258105312 0.296082584212
absolute error = 0.04648
relative error = 3.905 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.15258105312 0.296082584212
y1[1] (closed_form) = 1.15258105312 0.296082584212
absolute error = 2.010e-31
relative error = 1.689e-29 %
Correct digits = 31
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) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4486.4MB, alloc=44.3MB, time=55.12
memory used=4533.2MB, alloc=44.3MB, time=55.70
x[1] = 0.1468 0.3
h = 0.0001 0.003
y2[1] (numeric) = 1.11051035083 0.319483270896
y2[1] (closed_form) = 1.15290511962 0.301244939142
absolute error = 0.04615
relative error = 3.873 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.15290511962 0.301244939142
y1[1] (closed_form) = 1.15290511962 0.301244939142
absolute error = 2.010e-31
relative error = 1.687e-29 %
Correct digits = 31
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) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4579.9MB, alloc=44.3MB, time=56.28
x[1] = 0.1469 0.303
h = 0.001 0.001
y2[1] (numeric) = 1.11075180961 0.323658867008
y2[1] (closed_form) = 1.15314293705 0.304344082905
absolute error = 0.04658
relative error = 3.906 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.15314293705 0.304344082905
y1[1] (closed_form) = 1.15314293705 0.304344082905
absolute error = 2.010e-31
relative error = 1.685e-29 %
Correct digits = 31
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) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4626.6MB, alloc=44.3MB, time=56.86
memory used=4673.6MB, alloc=44.3MB, time=57.44
x[1] = 0.1479 0.304
h = 0.0001 0.004
y2[1] (numeric) = 1.11099535262 0.327839448373
y2[1] (closed_form) = 1.15422326242 0.305333885021
absolute error = 0.04874
relative error = 4.082 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.15422326242 0.305333885021
y1[1] (closed_form) = 1.15422326242 0.305333885021
absolute error = 2.022e-31
relative error = 1.694e-29 %
Correct digits = 31
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) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4719.9MB, alloc=44.3MB, time=58.00
memory used=4766.8MB, alloc=44.3MB, time=58.58
x[1] = 0.148 0.308
h = 0.003 0.006
y2[1] (numeric) = 1.11124098976 0.332025077257
y2[1] (closed_form) = 1.15451009707 0.309472283621
absolute error = 0.04879
relative error = 4.082 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.15451009707 0.309472283621
y1[1] (closed_form) = 1.15451009707 0.309472283621
absolute error = 2.022e-31
relative error = 1.692e-29 %
Correct digits = 31
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) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4813.1MB, alloc=44.3MB, time=59.14
memory used=4860.0MB, alloc=44.3MB, time=59.72
x[1] = 0.151 0.314
h = 0.0001 0.005
y2[1] (numeric) = 1.11148873097 0.336215815944
y2[1] (closed_form) = 1.15790370128 0.315553390472
absolute error = 0.05081
relative error = 4.233 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.15790370128 0.315553390472
y1[1] (closed_form) = 1.15790370128 0.315553390472
absolute error = 2.022e-31
relative error = 1.685e-29 %
Correct digits = 31
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) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4906.4MB, alloc=44.3MB, time=60.29
x[1] = 0.1511 0.319
h = 0.0001 0.003
y2[1] (numeric) = 1.11173858647 0.340411726539
y2[1] (closed_form) = 1.15824968056 0.320741274242
absolute error = 0.0505
relative error = 4.202 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.15824968056 0.320741274242
y1[1] (closed_form) = 1.15824968056 0.320741274242
absolute error = 3.015e-31
relative error = 2.509e-29 %
Correct digits = 31
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) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4952.9MB, alloc=44.3MB, time=60.86
memory used=5000.3MB, alloc=44.3MB, time=61.45
x[1] = 0.1512 0.322
h = 0.001 0.001
y2[1] (numeric) = 1.11199056674 0.344612871016
y2[1] (closed_form) = 1.158500931 0.32385579414
absolute error = 0.05093
relative error = 4.234 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.158500931 0.32385579414
y1[1] (closed_form) = 1.158500931 0.32385579414
absolute error = 2.022e-31
relative error = 1.681e-29 %
Correct digits = 31
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) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5047.0MB, alloc=44.3MB, time=62.03
memory used=5093.9MB, alloc=44.3MB, time=62.61
x[1] = 0.1522 0.323
h = 0.001 0.003
y2[1] (numeric) = 1.11224468239 0.348819311429
y2[1] (closed_form) = 1.15959088471 0.324846577615
absolute error = 0.05307
relative error = 4.407 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.15959088471 0.324846577615
y1[1] (closed_form) = 1.15959088471 0.324846577615
absolute error = 2.010e-31
relative error = 1.669e-29 %
Correct digits = 31
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) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5140.3MB, alloc=44.3MB, time=63.17
memory used=5187.2MB, alloc=44.3MB, time=63.76
x[1] = 0.1532 0.326
h = 0.0001 0.004
y2[1] (numeric) = 1.112500944 0.353031109851
y2[1] (closed_form) = 1.16078243448 0.327918927857
absolute error = 0.05442
relative error = 4.512 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.16078243448 0.327918927857
y1[1] (closed_form) = 1.16078243448 0.327918927857
absolute error = 2.010e-31
relative error = 1.666e-29 %
Correct digits = 31
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) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5233.5MB, alloc=44.3MB, time=64.32
x[1] = 0.1533 0.33
h = 0.003 0.006
y2[1] (numeric) = 1.11275936219 0.357248328353
y2[1] (closed_form) = 1.16109051522 0.332081513707
absolute error = 0.05449
relative error = 4.512 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.16109051522 0.332081513707
y1[1] (closed_form) = 1.16109051522 0.332081513707
absolute error = 1.020e-31
relative error = 8.445e-30 %
Correct digits = 31
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) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5279.8MB, alloc=44.3MB, time=64.89
memory used=5326.7MB, alloc=44.3MB, time=65.46
x[1] = 0.1563 0.336
h = 0.0001 0.005
y2[1] (numeric) = 1.11301994764 0.361471029021
y2[1] (closed_form) = 1.16453430587 0.338184616598
absolute error = 0.05653
relative error = 4.662 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.16453430587 0.338184616598
y1[1] (closed_form) = 1.16453430587 0.338184616598
absolute error = 1.020e-31
relative error = 8.410e-30 %
Correct digits = 31
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) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5373.1MB, alloc=44.3MB, time=66.03
memory used=5419.9MB, alloc=44.3MB, time=66.60
x[1] = 0.1564 0.341
h = 0.0001 0.003
y2[1] (numeric) = 1.11328271131 0.365699273753
y2[1] (closed_form) = 1.16490740759 0.343403934662
absolute error = 0.05623
relative error = 4.63 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.16490740759 0.343403934662
y1[1] (closed_form) = 1.16490740759 0.343403934662
absolute error = 1.020e-31
relative error = 8.397e-30 %
Correct digits = 31
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) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5466.5MB, alloc=44.3MB, time=67.18
memory used=5513.7MB, alloc=44.3MB, time=67.77
x[1] = 0.1565 0.344
h = 0.001 0.001
y2[1] (numeric) = 1.11354766448 0.369933124314
y2[1] (closed_form) = 1.16517528284 0.346537370287
absolute error = 0.05668
relative error = 4.663 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.16517528284 0.346537370287
y1[1] (closed_form) = 1.16517528284 0.346537370287
absolute error = 1.020e-31
relative error = 8.389e-30 %
Correct digits = 31
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) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5560.3MB, alloc=44.3MB, time=68.34
x[1] = 0.1575 0.345
h = 0.001 0.003
y2[1] (numeric) = 1.11381481852 0.374172642552
y2[1] (closed_form) = 1.16627711233 0.347529326872
absolute error = 0.05884
relative error = 4.835 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.16627711233 0.347529326872
y1[1] (closed_form) = 1.16627711233 0.347529326872
absolute error = 2.002e-31
relative error = 1.645e-29 %
Correct digits = 31
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) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5606.9MB, alloc=44.3MB, time=68.92
memory used=5653.7MB, alloc=44.3MB, time=69.49
x[1] = 0.1585 0.348
h = 0.0001 0.004
y2[1] (numeric) = 1.11408418479 0.378417890334
y2[1] (closed_form) = 1.16749138741 0.350615979092
absolute error = 0.06021
relative error = 4.939 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.16749138741 0.350615979092
y1[1] (closed_form) = 1.16749138741 0.350615979092
absolute error = 1.005e-31
relative error = 8.244e-30 %
Correct digits = 31
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) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5700.2MB, alloc=44.3MB, time=70.06
memory used=5747.0MB, alloc=44.3MB, time=70.63
x[1] = 0.1586 0.352
h = 0.003 0.006
y2[1] (numeric) = 1.1143557747 0.382668929529
y2[1] (closed_form) = 1.1678218255 0.35480457816
absolute error = 0.06029
relative error = 4.94 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.1678218255 0.35480457816
y1[1] (closed_form) = 1.1678218255 0.35480457816
absolute error = 1.005e-31
relative error = 8.234e-30 %
Correct digits = 31
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) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5793.4MB, alloc=44.3MB, time=71.19
memory used=5840.3MB, alloc=44.3MB, time=71.77
x[1] = 0.1616 0.358
h = 0.0001 0.005
y2[1] (numeric) = 1.11462959972 0.386925822021
y2[1] (closed_form) = 1.17131879605 0.360931656483
absolute error = 0.06236
relative error = 5.088 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.17131879605 0.360931656483
y1[1] (closed_form) = 1.17131879605 0.360931656483
absolute error = 1e-32
relative error = 8.159e-31 %
Correct digits = 32
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) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5886.7MB, alloc=44.3MB, time=72.34
memory used=5933.6MB, alloc=44.3MB, time=72.92
x[1] = 0.1617 0.363
h = 0.0001 0.003
y2[1] (numeric) = 1.1149056716 0.391188629498
y2[1] (closed_form) = 1.17172040754 0.366184701432
absolute error = 0.06207
relative error = 5.056 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.17172040754 0.366184701432
y1[1] (closed_form) = 1.17172040754 0.366184701432
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5980.5MB, alloc=44.3MB, time=73.50
x[1] = 0.1618 0.366
h = 0.001 0.001
y2[1] (numeric) = 1.11518400247 0.395457413506
y2[1] (closed_form) = 1.17200576052 0.369338418916
absolute error = 0.06254
relative error = 5.089 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.17200576052 0.369338418916
y1[1] (closed_form) = 1.17200576052 0.369338418916
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6027.3MB, alloc=44.3MB, time=74.08
memory used=6074.2MB, alloc=44.3MB, time=74.65
x[1] = 0.1628 0.367
h = 0.001 0.003
y2[1] (numeric) = 1.1154646045 0.399732235685
y2[1] (closed_form) = 1.17312019947 0.370331743901
absolute error = 0.06472
relative error = 5.261 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.17312019947 0.370331743901
y1[1] (closed_form) = 1.17312019947 0.370331743901
absolute error = 1e-32
relative error = 8.129e-31 %
Correct digits = 32
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) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6120.7MB, alloc=44.3MB, time=75.22
memory used=6167.7MB, alloc=44.3MB, time=75.80
x[1] = 0.1638 0.37
h = 0.0001 0.004
y2[1] (numeric) = 1.11574748991 0.404013157693
y2[1] (closed_form) = 1.17435847335 0.373433822183
absolute error = 0.06611
relative error = 5.365 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.17435847335 0.373433822183
y1[1] (closed_form) = 1.17435847335 0.373433822183
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6214.0MB, alloc=44.3MB, time=76.37
memory used=6260.8MB, alloc=44.3MB, time=76.95
x[1] = 0.1639 0.374
h = 0.003 0.006
y2[1] (numeric) = 1.11603267093 0.408300241191
y2[1] (closed_form) = 1.17471239629 0.377650267082
absolute error = 0.0662
relative error = 5.365 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.17471239629 0.377650267082
y1[1] (closed_form) = 1.17471239629 0.377650267082
absolute error = 1e-31
relative error = 8.104e-30 %
Correct digits = 31
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) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6307.3MB, alloc=44.3MB, time=77.51
x[1] = 0.1669 0.38
h = 0.0001 0.005
y2[1] (numeric) = 1.11632015986 0.412593547854
y2[1] (closed_form) = 1.17826557003 0.383803298756
absolute error = 0.06831
relative error = 5.512 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.17826557003 0.383803298756
y1[1] (closed_form) = 1.17826557003 0.383803298756
absolute error = 1e-31
relative error = 8.070e-30 %
Correct digits = 31
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) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6353.8MB, alloc=44.3MB, time=78.08
memory used=6400.8MB, alloc=44.3MB, time=78.65
x[1] = 0.167 0.385
h = 0.0001 0.003
y2[1] (numeric) = 1.11660996933 0.416893139155
y2[1] (closed_form) = 1.17869709951 0.389092371911
absolute error = 0.06803
relative error = 5.481 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.17869709951 0.389092371911
y1[1] (closed_form) = 1.17869709951 0.389092371911
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6447.3MB, alloc=44.3MB, time=79.22
memory used=6494.5MB, alloc=44.3MB, time=79.82
x[1] = 0.1671 0.388
h = 0.001 0.001
y2[1] (numeric) = 1.11690211231 0.421199076419
y2[1] (closed_form) = 1.17900079581 0.392267742556
absolute error = 0.06851
relative error = 5.513 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.17900079581 0.392267742556
y1[1] (closed_form) = 1.17900079581 0.392267742556
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6541.2MB, alloc=44.3MB, time=80.39
memory used=6588.1MB, alloc=44.3MB, time=80.97
x[1] = 0.1681 0.389
h = 0.001 0.003
y2[1] (numeric) = 1.11719660189 0.42551142107
y2[1] (closed_form) = 1.18012858398 0.393262628912
absolute error = 0.07071
relative error = 5.685 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.18012858398 0.393262628912
y1[1] (closed_form) = 1.18012858398 0.393262628912
absolute error = 1e-31
relative error = 8.039e-30 %
Correct digits = 31
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) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6634.5MB, alloc=44.3MB, time=81.54
x[1] = 0.1691 0.392
h = 0.0001 0.004
y2[1] (numeric) = 1.11749345117 0.429830234553
y2[1] (closed_form) = 1.18139214467 0.396381258778
absolute error = 0.07212
relative error = 5.788 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.18139214467 0.396381258778
y1[1] (closed_form) = 1.18139214467 0.396381258778
absolute error = 1.005e-31
relative error = 8.065e-30 %
Correct digits = 31
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) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6680.8MB, alloc=44.3MB, time=82.10
memory used=6727.7MB, alloc=44.3MB, time=82.68
x[1] = 0.1692 0.396
h = 0.003 0.006
y2[1] (numeric) = 1.11779267324 0.434155578314
y2[1] (closed_form) = 1.18177069718 0.400627389341
absolute error = 0.07223
relative error = 5.789 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.18177069718 0.400627389341
y1[1] (closed_form) = 1.18177069718 0.400627389341
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6774.1MB, alloc=44.3MB, time=83.24
memory used=6821.1MB, alloc=44.3MB, time=83.82
x[1] = 0.1722 0.402
h = 0.0001 0.005
y2[1] (numeric) = 1.11809428131 0.438487513817
y2[1] (closed_form) = 1.18538312907 0.40680835101
absolute error = 0.07437
relative error = 5.934 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.18538312907 0.40680835101
y1[1] (closed_form) = 1.18538312907 0.40680835101
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6867.5MB, alloc=44.3MB, time=84.38
memory used=6914.5MB, alloc=44.3MB, time=84.96
x[1] = 0.1723 0.407
h = 0.0001 0.003
y2[1] (numeric) = 1.1183982889 0.442826102312
y2[1] (closed_form) = 1.18584600679 0.41213576314
absolute error = 0.0741
relative error = 5.903 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.18584600679 0.41213576314
y1[1] (closed_form) = 1.18584600679 0.41213576314
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6961.1MB, alloc=44.3MB, time=85.54
x[1] = 0.1724 0.41
h = 0.001 0.001
y2[1] (numeric) = 1.11870470994 0.447171404899
y2[1] (closed_form) = 1.18616892543 0.415334163842
absolute error = 0.0746
relative error = 5.936 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.18616892543 0.415334163842
y1[1] (closed_form) = 1.18616892543 0.415334163842
absolute error = 1e-32
relative error = 7.957e-31 %
Correct digits = 32
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) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7007.9MB, alloc=44.3MB, time=86.12
memory used=7054.9MB, alloc=44.3MB, time=86.70
x[1] = 0.1734 0.411
h = 0.0001 0.004
y2[1] (numeric) = 1.11901355842 0.45152348278
y2[1] (closed_form) = 1.18731080903 0.416330802141
absolute error = 0.07683
relative error = 6.106 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.18731080903 0.416330802141
y1[1] (closed_form) = 1.18731080903 0.416330802141
absolute error = 0
relative error = 0 %
Correct digits = 30
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) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7101.2MB, alloc=44.3MB, time=87.26
memory used=7148.0MB, alloc=44.3MB, time=87.83
x[1] = 0.1735 0.415
h = 0.003 0.006
y2[1] (numeric) = 1.11932484839 0.455882397185
y2[1] (closed_form) = 1.18771110875 0.420604276634
absolute error = 0.07695
relative error = 6.107 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.18771110875 0.420604276634
y1[1] (closed_form) = 1.18771110875 0.420604276634
absolute error = 1e-32
relative error = 7.937e-31 %
Correct digits = 32
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) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7194.2MB, alloc=44.3MB, time=88.40
memory used=7241.3MB, alloc=44.3MB, time=88.98
x[1] = 0.1765 0.421
h = 0.0001 0.005
y2[1] (numeric) = 1.11963859392 0.460248209365
y2[1] (closed_form) = 1.19137665525 0.426811617548
absolute error = 0.07915
relative error = 6.254 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.19137665525 0.426811617548
y1[1] (closed_form) = 1.19137665525 0.426811617548
absolute error = 1.005e-31
relative error = 7.941e-30 %
Correct digits = 31
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) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7287.7MB, alloc=44.3MB, time=89.54
x[1] = 0.1766 0.426
h = 0.0001 0.003
y2[1] (numeric) = 1.11995480946 0.464620980352
y2[1] (closed_form) = 1.19186718516 0.43217428577
absolute error = 0.07889
relative error = 6.223 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.19186718516 0.43217428577
y1[1] (closed_form) = 1.19186718516 0.43217428577
absolute error = 1.020e-31
relative error = 8.044e-30 %
Correct digits = 31
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) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7334.5MB, alloc=44.3MB, time=90.11
memory used=7381.5MB, alloc=44.3MB, time=90.70
x[1] = 0.1767 0.429
h = 0.001 0.001
y2[1] (numeric) = 1.12027350985 0.469000771022
y2[1] (closed_form) = 1.19220706764 0.43539386063
absolute error = 0.0794
relative error = 6.256 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.19220706764 0.43539386063
y1[1] (closed_form) = 1.19220706764 0.43539386063
absolute error = 1.020e-31
relative error = 8.035e-30 %
Correct digits = 31
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) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7428.1MB, alloc=44.3MB, time=91.28
memory used=7475.0MB, alloc=44.3MB, time=91.86
x[1] = 0.1777 0.43
h = 0.001 0.003
y2[1] (numeric) = 1.12059471005 0.473387642357
y2[1] (closed_form) = 1.19336166296 0.436392337778
absolute error = 0.08163
relative error = 6.424 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.19336166296 0.436392337778
y1[1] (closed_form) = 1.19336166296 0.436392337778
absolute error = 1.020e-31
relative error = 8.026e-30 %
Correct digits = 31
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) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7521.3MB, alloc=44.3MB, time=92.42
memory used=7568.3MB, alloc=44.3MB, time=93.00
x[1] = 0.1787 0.433
h = 0.0001 0.004
y2[1] (numeric) = 1.12091842501 0.477781655365
y2[1] (closed_form) = 1.19467552906 0.439545105871
absolute error = 0.08308
relative error = 6.526 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.19467552906 0.439545105871
y1[1] (closed_form) = 1.19467552906 0.439545105871
absolute error = 1e-32
relative error = 7.856e-31 %
Correct digits = 32
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) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7614.7MB, alloc=44.3MB, time=93.56
x[1] = 0.1788 0.437
h = 0.003 0.006
y2[1] (numeric) = 1.12124466972 0.482182871057
y2[1] (closed_form) = 1.19510261529 0.44385172486
absolute error = 0.08321
relative error = 6.527 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.19510261529 0.44385172486
y1[1] (closed_form) = 1.19510261529 0.44385172486
absolute error = 1e-32
relative error = 7.844e-31 %
Correct digits = 32
memory used=7661.5MB, alloc=44.3MB, time=94.14
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) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7708.1MB, alloc=44.3MB, time=94.70
x[1] = 0.1818 0.443
h = 0.0001 0.005
y2[1] (numeric) = 1.12157345925 0.486591350463
y2[1] (closed_form) = 1.19883317169 0.450090708459
absolute error = 0.08545
relative error = 6.673 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.19883317169 0.450090708459
y1[1] (closed_form) = 1.19883317169 0.450090708459
absolute error = 2e-32
relative error = 1.562e-30 %
Correct digits = 32
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) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7754.6MB, alloc=44.3MB, time=95.27
memory used=7801.7MB, alloc=44.3MB, time=95.85
x[1] = 0.1819 0.448
h = 0.0001 0.003
y2[1] (numeric) = 1.12190480905 0.491007154382
y2[1] (closed_form) = 1.19935774612 0.455496060783
absolute error = 0.08521
relative error = 6.641 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.19935774612 0.455496060783
y1[1] (closed_form) = 1.19935774612 0.455496060783
absolute error = 2e-32
relative error = 1.559e-30 %
Correct digits = 32
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) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7848.2MB, alloc=44.3MB, time=96.42
memory used=7895.4MB, alloc=44.3MB, time=97.01
x[1] = 0.182 0.451
h = 0.001 0.001
y2[1] (numeric) = 1.12223873499 0.495430343452
y2[1] (closed_form) = 1.19971850818 0.458741255002
absolute error = 0.08573
relative error = 6.674 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.19971850818 0.458741255002
y1[1] (closed_form) = 1.19971850818 0.458741255002
absolute error = 2e-32
relative error = 1.557e-30 %
Correct digits = 32
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) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7942.0MB, alloc=44.3MB, time=97.59
x[1] = 0.183 0.452
h = 0.001 0.003
y2[1] (numeric) = 1.12257525305 0.499860978425
y2[1] (closed_form) = 1.20088860374 0.459741841098
absolute error = 0.08799
relative error = 6.843 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.20088860374 0.459741841098
y1[1] (closed_form) = 1.20088860374 0.459741841098
absolute error = 2e-32
relative error = 1.555e-30 %
Correct digits = 32
memory used=7989.0MB, alloc=44.3MB, time=98.17
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) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8035.4MB, alloc=44.3MB, time=98.73
x[1] = 0.184 0.455
h = 0.0001 0.004
y2[1] (numeric) = 1.12291437923 0.50429912008
y2[1] (closed_form) = 1.20223151582 0.462914406448
absolute error = 0.08946
relative error = 6.945 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.20223151582 0.462914406448
y1[1] (closed_form) = 1.20223151582 0.462914406448
absolute error = 2e-32
relative error = 1.552e-30 %
Correct digits = 32
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) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8081.6MB, alloc=44.3MB, time=99.30
memory used=8128.5MB, alloc=44.3MB, time=99.87
x[1] = 0.1841 0.459
h = 0.003 0.006
y2[1] (numeric) = 1.12325612955 0.508744829196
y2[1] (closed_form) = 1.20268658765 0.467256033816
absolute error = 0.08961
relative error = 6.945 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.20268658765 0.467256033816
y1[1] (closed_form) = 1.20268658765 0.467256033816
absolute error = 2e-32
relative error = 1.550e-30 %
Correct digits = 32
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) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8174.7MB, alloc=44.3MB, time=100.44
memory used=8221.6MB, alloc=44.3MB, time=101.01
x[1] = 0.1871 0.465
h = 0.0001 0.005
y2[1] (numeric) = 1.12360052011 0.513198166576
y2[1] (closed_form) = 1.20648530983 0.473528634562
absolute error = 0.09189
relative error = 7.09 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.20648530983 0.473528634562
y1[1] (closed_form) = 1.20648530983 0.473528634562
absolute error = 3e-32
relative error = 2.315e-30 %
Correct digits = 32
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) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8268.0MB, alloc=44.3MB, time=101.58
memory used=8314.9MB, alloc=44.3MB, time=102.16
x[1] = 0.1872 0.47
h = 0.0001 0.003
y2[1] (numeric) = 1.12394756743 0.517659192781
y2[1] (closed_form) = 1.20704542858 0.478979013072
absolute error = 0.09166
relative error = 7.058 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.20704542858 0.478979013072
y1[1] (closed_form) = 1.20704542858 0.478979013072
absolute error = 1.044e-31
relative error = 8.040e-30 %
Correct digits = 31
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) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8361.7MB, alloc=44.3MB, time=102.74
x[1] = 0.1873 0.473
h = 0.001 0.001
y2[1] (numeric) = 1.12429728845 0.522127968205
y2[1] (closed_form) = 1.20742799154 0.482251222072
absolute error = 0.0922
relative error = 7.091 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.20742799154 0.482251222072
y1[1] (closed_form) = 1.20742799154 0.482251222072
absolute error = 3e-32
relative error = 2.307e-30 %
Correct digits = 32
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) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8408.5MB, alloc=44.3MB, time=103.32
memory used=8455.4MB, alloc=44.3MB, time=103.90
x[1] = 0.1883 0.474
h = 0.001 0.003
y2[1] (numeric) = 1.12464970023 0.526604553362
y2[1] (closed_form) = 1.20861435416 0.483254100418
absolute error = 0.0945
relative error = 7.26 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.20861435416 0.483254100418
y1[1] (closed_form) = 1.20861435416 0.483254100418
absolute error = 1.044e-31
relative error = 8.021e-30 %
Correct digits = 31
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) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8501.8MB, alloc=44.3MB, time=104.46
memory used=8548.6MB, alloc=44.3MB, time=105.04
x[1] = 0.1893 0.477
h = 0.0001 0.004
y2[1] (numeric) = 1.12500481987 0.531089008795
y2[1] (closed_form) = 1.20998766437 0.48644759628
absolute error = 0.09599
relative error = 7.361 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.20998766437 0.48644759628
y1[1] (closed_form) = 1.20998766437 0.48644759628
absolute error = 1.077e-31
relative error = 8.259e-30 %
Correct digits = 31
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) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8595.0MB, alloc=44.3MB, time=105.60
memory used=8641.8MB, alloc=44.3MB, time=106.18
x[1] = 0.1894 0.481
h = 0.003 0.006
y2[1] (numeric) = 1.12536266447 0.535581395047
y2[1] (closed_form) = 1.21047194183 0.490826105342
absolute error = 0.09616
relative error = 7.362 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.21047194183 0.490826105342
y1[1] (closed_form) = 1.21047194183 0.490826105342
absolute error = 1.077e-31
relative error = 8.246e-30 %
Correct digits = 31
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) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8688.2MB, alloc=44.3MB, time=106.75
x[1] = 0.1924 0.487
h = 0.0001 0.005
y2[1] (numeric) = 1.12572325122 0.540081772687
y2[1] (closed_form) = 1.2143420246 0.497134297128
absolute error = 0.09848
relative error = 7.505 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.2143420246 0.497134297128
y1[1] (closed_form) = 1.2143420246 0.497134297128
absolute error = 1.077e-31
relative error = 8.208e-30 %
Correct digits = 31
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) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8734.8MB, alloc=44.3MB, time=107.31
memory used=8781.5MB, alloc=44.3MB, time=107.89
x[1] = 0.1925 0.492
h = 0.0001 0.003
y2[1] (numeric) = 1.12608659776 0.54459020203
y2[1] (closed_form) = 1.21493921416 0.502632056145
absolute error = 0.09826
relative error = 7.473 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.21493921416 0.502632056145
y1[1] (closed_form) = 1.21493921416 0.502632056145
absolute error = 4e-32
relative error = 3.042e-30 %
Correct digits = 32
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) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8828.0MB, alloc=44.3MB, time=108.46
memory used=8875.3MB, alloc=44.3MB, time=109.05
x[1] = 0.1926 0.495
h = 0.001 0.001
y2[1] (numeric) = 1.12645272215 0.54910674322
y2[1] (closed_form) = 1.21534451557 0.50593268258
absolute error = 0.09882
relative error = 7.507 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.21534451557 0.50593268258
y1[1] (closed_form) = 1.21534451557 0.50593268258
absolute error = 3e-32
relative error = 2.279e-30 %
Correct digits = 32
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) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8922.0MB, alloc=44.3MB, time=109.63
memory used=8968.8MB, alloc=44.3MB, time=110.20
x[1] = 0.1936 0.496
h = 0.001 0.003
y2[1] (numeric) = 1.12682164261 0.553631456528
y2[1] (closed_form) = 1.21654792004 0.506938033732
absolute error = 0.1011
relative error = 7.675 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.21654792004 0.506938033732
y1[1] (closed_form) = 1.21654792004 0.506938033732
absolute error = 4e-32
relative error = 3.035e-30 %
Correct digits = 32
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) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9015.2MB, alloc=44.3MB, time=110.77
x[1] = 0.1946 0.499
h = 0.0001 0.004
y2[1] (numeric) = 1.12719337735 0.558164402251
y2[1] (closed_form) = 1.21795299929 0.510153595812
absolute error = 0.1027
relative error = 7.776 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.21795299929 0.510153595812
y1[1] (closed_form) = 1.21795299929 0.510153595812
absolute error = 1.077e-31
relative error = 8.156e-30 %
Correct digits = 31
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) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9061.9MB, alloc=44.3MB, time=111.34
memory used=9108.5MB, alloc=44.3MB, time=111.91
x[1] = 0.1947 0.503
h = 0.003 0.006
y2[1] (numeric) = 1.12756794463 0.562705640691
y2[1] (closed_form) = 1.21846772431 0.514570869889
absolute error = 0.1029
relative error = 7.777 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.21846772431 0.514570869889
y1[1] (closed_form) = 1.21846772431 0.514570869889
absolute error = 1.077e-31
relative error = 8.143e-30 %
Correct digits = 31
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) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9154.9MB, alloc=44.3MB, time=112.47
memory used=9201.9MB, alloc=44.3MB, time=113.05
x[1] = 0.1977 0.509
h = 0.0001 0.005
y2[1] (numeric) = 1.12794536278 0.567255232174
y2[1] (closed_form) = 1.22241240331 0.520916626191
absolute error = 0.1052
relative error = 7.919 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.22241240331 0.520916626191
y1[1] (closed_form) = 1.22241240331 0.520916626191
absolute error = 1.077e-31
relative error = 8.105e-30 %
Correct digits = 31
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) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9248.3MB, alloc=44.3MB, time=113.62
memory used=9295.4MB, alloc=44.3MB, time=114.20
x[1] = 0.1978 0.514
h = 0.0001 0.003
y2[1] (numeric) = 1.12832565059 0.571813236766
y2[1] (closed_form) = 1.22304821813 0.526464132994
absolute error = 0.105
relative error = 7.887 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.22304821813 0.526464132994
y1[1] (closed_form) = 1.22304821813 0.526464132994
absolute error = 1.077e-31
relative error = 8.089e-30 %
Correct digits = 31
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) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9342.0MB, alloc=44.3MB, time=114.77
x[1] = 0.1979 0.517
h = 0.001 0.001
y2[1] (numeric) = 1.12870882734 0.576379714351
y2[1] (closed_form) = 1.22347721254 0.529794587172
absolute error = 0.1056
relative error = 7.92 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.22347721254 0.529794587172
y1[1] (closed_form) = 1.22347721254 0.529794587172
absolute error = 1.077e-31
relative error = 8.078e-30 %
Correct digits = 31
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) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9389.1MB, alloc=44.3MB, time=115.36
memory used=9435.6MB, alloc=44.3MB, time=115.93
x[1] = 0.1989 0.518
h = 0.0001 0.004
y2[1] (numeric) = 1.12909491242 0.580954724948
y2[1] (closed_form) = 1.22469844199 0.530802588836
absolute error = 0.108
relative error = 8.088 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.22469844199 0.530802588836
y1[1] (closed_form) = 1.22469844199 0.530802588836
absolute error = 1.077e-31
relative error = 8.069e-30 %
Correct digits = 31
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) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9482.1MB, alloc=44.3MB, time=116.49
memory used=9529.0MB, alloc=44.3MB, time=117.07
x[1] = 0.199 0.522
h = 0.003 0.006
y2[1] (numeric) = 1.12948392524 0.58553832861
y2[1] (closed_form) = 1.22523989476 0.535255129962
absolute error = 0.1082
relative error = 8.089 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.22523989476 0.535255129962
y1[1] (closed_form) = 1.22523989476 0.535255129962
absolute error = 2.040e-31
relative error = 1.525e-29 %
Correct digits = 31
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) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9575.2MB, alloc=44.3MB, time=117.63
memory used=9622.2MB, alloc=44.3MB, time=118.22
x[1] = 0.202 0.528
h = 0.0001 0.005
y2[1] (numeric) = 1.12987588529 0.590130585423
y2[1] (closed_form) = 1.22925092786 0.541635742479
absolute error = 0.1106
relative error = 8.232 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.22925092786 0.541635742479
y1[1] (closed_form) = 1.22925092786 0.541635742479
absolute error = 2.040e-31
relative error = 1.518e-29 %
Correct digits = 31
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) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9668.6MB, alloc=44.3MB, time=118.78
memory used=9715.5MB, alloc=44.3MB, time=119.36
x[1] = 0.2021 0.533
h = 0.0001 0.003
y2[1] (numeric) = 1.13027081251 0.594731555199
y2[1] (closed_form) = 1.22992062582 0.547228462435
absolute error = 0.1104
relative error = 8.201 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.22992062582 0.547228462435
y1[1] (closed_form) = 1.22992062582 0.547228462435
absolute error = 1.077e-31
relative error = 8.001e-30 %
Correct digits = 31
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) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9762.2MB, alloc=44.3MB, time=119.94
x[1] = 0.2022 0.536
h = 0.001 0.001
y2[1] (numeric) = 1.13066872735 0.599341297568
y2[1] (closed_form) = 1.23037041397 0.550586024862
absolute error = 0.111
relative error = 8.234 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.23037041397 0.550586024862
y1[1] (closed_form) = 1.23037041397 0.550586024862
absolute error = 1.077e-31
relative error = 7.990e-30 %
Correct digits = 31
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) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9808.9MB, alloc=44.3MB, time=120.52
memory used=9855.9MB, alloc=44.3MB, time=121.09
x[1] = 0.2032 0.537
h = 0.001 0.003
y2[1] (numeric) = 1.13106965039 0.603959872298
y2[1] (closed_form) = 1.23160758594 0.551596673241
absolute error = 0.1134
relative error = 8.4 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.23160758594 0.551596673241
y1[1] (closed_form) = 1.23160758594 0.551596673241
absolute error = 2.040e-31
relative error = 1.511e-29 %
Correct digits = 31
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) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9902.3MB, alloc=44.3MB, time=121.66
memory used=9949.2MB, alloc=44.3MB, time=122.24
x[1] = 0.2042 0.54
h = 0.0001 0.004
y2[1] (numeric) = 1.13147360223 0.608587339188
y2[1] (closed_form) = 1.23307520164 0.554856745278
absolute error = 0.1149
relative error = 8.5 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.23307520164 0.554856745278
y1[1] (closed_form) = 1.23307520164 0.554856745278
absolute error = 2.040e-31
relative error = 1.508e-29 %
Correct digits = 31
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) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9995.5MB, alloc=44.3MB, time=122.80
memory used=10042.3MB, alloc=44.3MB, time=123.38
x[1] = 0.2043 0.544
h = 0.003 0.006
y2[1] (numeric) = 1.13188060349 0.61322375804
y2[1] (closed_form) = 1.23364945198 0.55935159987
absolute error = 0.1151
relative error = 8.501 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.23364945198 0.55935159987
y1[1] (closed_form) = 1.23364945198 0.55935159987
absolute error = 2.062e-31
relative error = 1.522e-29 %
Correct digits = 31
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) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10088.7MB, alloc=44.3MB, time=123.94
x[1] = 0.2073 0.55
h = 0.0001 0.005
y2[1] (numeric) = 1.1322906749 0.617869188682
y2[1] (closed_form) = 1.23774119391 0.565773488247
absolute error = 0.1176
relative error = 8.642 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.23774119391 0.565773488247
y1[1] (closed_form) = 1.23774119391 0.565773488247
absolute error = 2.040e-31
relative error = 1.499e-29 %
Correct digits = 31
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) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10135.2MB, alloc=44.3MB, time=124.50
memory used=10182.1MB, alloc=44.3MB, time=125.08
x[1] = 0.2074 0.555
h = 0.0001 0.003
y2[1] (numeric) = 1.13270383767 0.622523690665
y2[1] (closed_form) = 1.23845245972 0.571420417242
absolute error = 0.1174
relative error = 8.611 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.23845245972 0.571420417242
y1[1] (closed_form) = 1.23845245972 0.571420417242
absolute error = 3.027e-31
relative error = 2.219e-29 %
Correct digits = 31
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) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10228.7MB, alloc=44.3MB, time=125.65
memory used=10275.9MB, alloc=44.3MB, time=126.24
x[1] = 0.2075 0.558
h = 0.001 0.001
y2[1] (numeric) = 1.13312011354 0.627187323346
y2[1] (closed_form) = 1.23892774789 0.574810465358
absolute error = 0.1181
relative error = 8.644 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.23892774789 0.574810465358
y1[1] (closed_form) = 1.23892774789 0.574810465358
absolute error = 3.041e-31
relative error = 2.227e-29 %
Correct digits = 31
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) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10322.6MB, alloc=44.3MB, time=126.82
memory used=10369.6MB, alloc=44.3MB, time=127.39
x[1] = 0.2085 0.559
h = 0.001 0.003
y2[1] (numeric) = 1.13353952439 0.631860146228
y2[1] (closed_form) = 1.24018422359 0.575824096575
absolute error = 0.1205
relative error = 8.811 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.24018422359 0.575824096575
y1[1] (closed_form) = 1.24018422359 0.575824096575
absolute error = 3.041e-31
relative error = 2.224e-29 %
Correct digits = 31
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) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10416.0MB, alloc=44.3MB, time=127.96
x[1] = 0.2095 0.562
h = 0.0001 0.004
y2[1] (numeric) = 1.1339620921 0.636542218844
y2[1] (closed_form) = 1.24168762801 0.579109516289
absolute error = 0.1221
relative error = 8.91 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.24168762801 0.579109516289
y1[1] (closed_form) = 1.24168762801 0.579109516289
absolute error = 3.041e-31
relative error = 2.220e-29 %
Correct digits = 31
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) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10462.5MB, alloc=44.3MB, time=128.53
memory used=10509.3MB, alloc=44.3MB, time=129.10
x[1] = 0.2096 0.566
h = 0.003 0.006
y2[1] (numeric) = 1.13438783859 0.641233600734
y2[1] (closed_form) = 1.24229598602 0.583648599727
absolute error = 0.1223
relative error = 8.911 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.24229598602 0.583648599727
y1[1] (closed_form) = 1.24229598602 0.583648599727
absolute error = 3.027e-31
relative error = 2.205e-29 %
Correct digits = 31
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) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10555.5MB, alloc=44.3MB, time=129.67
memory used=10602.4MB, alloc=44.3MB, time=130.24
x[1] = 0.2126 0.572
h = 0.0001 0.005
y2[1] (numeric) = 1.1348167859 0.645934351464
y2[1] (closed_form) = 1.24647179999 0.590113737583
absolute error = 0.1248
relative error = 9.052 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.24647179999 0.590113737583
y1[1] (closed_form) = 1.24647179999 0.590113737583
absolute error = 3.027e-31
relative error = 2.195e-29 %
Correct digits = 31
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) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10648.8MB, alloc=44.3MB, time=130.81
memory used=10695.8MB, alloc=44.3MB, time=131.39
x[1] = 0.2127 0.577
h = 0.0001 0.003
y2[1] (numeric) = 1.13524895655 0.650644530311
y2[1] (closed_form) = 1.2472262749 0.595817284301
absolute error = 0.1247
relative error = 9.02 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.2472262749 0.595817284301
y1[1] (closed_form) = 1.2472262749 0.595817284301
absolute error = 3.027e-31
relative error = 2.190e-29 %
Correct digits = 31
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) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10742.5MB, alloc=44.3MB, time=131.96
x[1] = 0.2128 0.58
h = 0.001 0.001
y2[1] (numeric) = 1.13568437364 0.655364196352
y2[1] (closed_form) = 1.2477280704 0.59924125286
absolute error = 0.1253
relative error = 9.053 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.2477280704 0.59924125286
y1[1] (closed_form) = 1.2477280704 0.59924125286
absolute error = 3.041e-31
relative error = 2.197e-29 %
Correct digits = 31
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) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10789.6MB, alloc=44.3MB, time=132.55
memory used=10836.3MB, alloc=44.3MB, time=133.12
x[1] = 0.2138 0.581
h = 0.001 0.003
y2[1] (numeric) = 1.13612306038 0.660093408815
y2[1] (closed_form) = 1.24900465909 0.60025803602
absolute error = 0.1278
relative error = 9.219 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.24900465909 0.60025803602
y1[1] (closed_form) = 1.24900465909 0.60025803602
absolute error = 3.041e-31
relative error = 2.195e-29 %
Correct digits = 31
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) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10882.8MB, alloc=44.3MB, time=133.69
memory used=10929.9MB, alloc=44.3MB, time=134.27
x[1] = 0.2148 0.584
h = 0.0001 0.004
y2[1] (numeric) = 1.13656504 0.664832226963
y2[1] (closed_form) = 1.25054530389 0.603569950688
absolute error = 0.1294
relative error = 9.319 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.25054530389 0.603569950688
y1[1] (closed_form) = 1.25054530389 0.603569950688
absolute error = 3.041e-31
relative error = 2.190e-29 %
Correct digits = 31
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) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10976.2MB, alloc=44.3MB, time=134.83
memory used=11023.0MB, alloc=44.3MB, time=135.40
x[1] = 0.2149 0.588
h = 0.003 0.006
y2[1] (numeric) = 1.13701033579 0.669580710061
y2[1] (closed_form) = 1.25118910551 0.608155190564
absolute error = 0.1297
relative error = 9.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.25118910551 0.608155190564
y1[1] (closed_form) = 1.25118910551 0.608155190564
absolute error = 3.041e-31
relative error = 2.186e-29 %
Correct digits = 31
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) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11069.5MB, alloc=44.3MB, time=135.99
memory used=11116.5MB, alloc=44.3MB, time=136.56
x[1] = 0.2179 0.594
h = 0.0001 0.005
y2[1] (numeric) = 1.13745897113 0.674338917407
y2[1] (closed_form) = 1.25545240316 0.61466555163
absolute error = 0.1322
relative error = 9.459 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.25545240316 0.61466555163
y1[1] (closed_form) = 1.25545240316 0.61466555163
absolute error = 3.041e-31
relative error = 2.176e-29 %
Correct digits = 31
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) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11163.0MB, alloc=44.3MB, time=137.14
x[1] = 0.218 0.599
h = 0.0001 0.003
y2[1] (numeric) = 1.13791096994 0.679106907994
y2[1] (closed_form) = 1.25625176132 0.62042814049
absolute error = 0.1321
relative error = 9.428 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.25625176132 0.62042814049
y1[1] (closed_form) = 1.25625176132 0.62042814049
absolute error = 3.041e-31
relative error = 2.171e-29 %
Correct digits = 31
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) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11209.4MB, alloc=44.3MB, time=137.70
memory used=11256.8MB, alloc=44.3MB, time=138.30
x[1] = 0.2181 0.602
h = 0.001 0.001
y2[1] (numeric) = 1.13836635668 0.683884740612
y2[1] (closed_form) = 1.25678109146 0.623887473529
absolute error = 0.1327
relative error = 9.461 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.25678109146 0.623887473529
y1[1] (closed_form) = 1.25678109146 0.623887473529
absolute error = 3.041e-31
relative error = 2.168e-29 %
Correct digits = 31
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) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11303.5MB, alloc=44.3MB, time=138.87
memory used=11350.4MB, alloc=44.3MB, time=139.45
x[1] = 0.2191 0.603
h = 0.001 0.003
y2[1] (numeric) = 1.13882515599 0.688672474205
y2[1] (closed_form) = 1.2580786123 0.624907574485
absolute error = 0.1352
relative error = 9.627 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.2580786123 0.624907574485
y1[1] (closed_form) = 1.2580786123 0.624907574485
absolute error = 2.062e-31
relative error = 1.468e-29 %
Correct digits = 31
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) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11396.9MB, alloc=44.3MB, time=140.01
memory used=11443.7MB, alloc=44.3MB, time=140.59
x[1] = 0.2201 0.606
h = 0.0001 0.004
y2[1] (numeric) = 1.13928739252 0.693470167755
y2[1] (closed_form) = 1.25965797228 0.628247134777
absolute error = 0.1369
relative error = 9.726 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.25965797228 0.628247134777
y1[1] (closed_form) = 1.25965797228 0.628247134777
absolute error = 2.088e-31
relative error = 1.483e-29 %
Correct digits = 31
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) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11490.0MB, alloc=44.3MB, time=141.16
x[1] = 0.2202 0.61
h = 0.003 0.006
y2[1] (numeric) = 1.13975309094 0.698277880248
y2[1] (closed_form) = 1.26033858041 0.632880471461
absolute error = 0.1372
relative error = 9.727 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.26033858041 0.632880471461
y1[1] (closed_form) = 1.26033858041 0.632880471461
absolute error = 2.088e-31
relative error = 1.481e-29 %
Correct digits = 31
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) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11536.3MB, alloc=44.3MB, time=141.72
memory used=11583.2MB, alloc=44.3MB, time=142.29
x[1] = 0.2232 0.616
h = 0.0001 0.005
y2[1] (numeric) = 1.14022227605 0.7030956707
y2[1] (closed_form) = 1.2646928238 0.639438029682
absolute error = 0.1398
relative error = 9.865 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.2646928238 0.639438029682
y1[1] (closed_form) = 1.2646928238 0.639438029682
absolute error = 3.059e-31
relative error = 2.159e-29 %
Correct digits = 31
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) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11629.7MB, alloc=44.3MB, time=142.87
memory used=11676.7MB, alloc=44.3MB, time=143.44
x[1] = 0.2233 0.621
h = 0.0001 0.003
y2[1] (numeric) = 1.1406949732 0.707923597815
y2[1] (closed_form) = 1.26553877359 0.645262101556
absolute error = 0.1397
relative error = 9.833 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.26553877359 0.645262101556
y1[1] (closed_form) = 1.26553877359 0.645262101556
absolute error = 2.088e-31
relative error = 1.470e-29 %
Correct digits = 31
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) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11723.3MB, alloc=44.3MB, time=144.02
memory used=11770.7MB, alloc=44.3MB, time=144.61
x[1] = 0.2234 0.624
h = 0.001 0.001
y2[1] (numeric) = 1.14117120833 0.712761720082
y2[1] (closed_form) = 1.26609668649 0.648758252816
absolute error = 0.1404
relative error = 9.867 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.26609668649 0.648758252816
y1[1] (closed_form) = 1.26609668649 0.648758252816
absolute error = 2.088e-31
relative error = 1.468e-29 %
Correct digits = 31
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) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11817.3MB, alloc=44.3MB, time=145.19
x[1] = 0.2244 0.625
h = 0.0001 0.004
y2[1] (numeric) = 1.14165100751 0.717610096157
y2[1] (closed_form) = 1.26741596895 0.649781834048
absolute error = 0.1429
relative error = 10.03 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.26741596895 0.649781834048
y1[1] (closed_form) = 1.26741596895 0.649781834048
absolute error = 3.041e-31
relative error = 2.135e-29 %
Correct digits = 31
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) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11863.7MB, alloc=44.3MB, time=145.75
memory used=11910.7MB, alloc=44.3MB, time=146.33
x[1] = 0.2245 0.629
h = 0.003 0.006
y2[1] (numeric) = 1.14213439687 0.722468784736
y2[1] (closed_form) = 1.26812876697 0.654458595881
absolute error = 0.1432
relative error = 10.03 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.26812876697 0.654458595881
y1[1] (closed_form) = 1.26812876697 0.654458595881
absolute error = 3.041e-31
relative error = 2.131e-29 %
Correct digits = 31
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) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11957.1MB, alloc=44.3MB, time=146.89
memory used=12003.9MB, alloc=44.3MB, time=147.47
x[1] = 0.2275 0.635
h = 0.0001 0.005
y2[1] (numeric) = 1.14262140259 0.727337844555
y2[1] (closed_form) = 1.27256351154 0.661059501194
absolute error = 0.1459
relative error = 10.17 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.27256351154 0.661059501194
y1[1] (closed_form) = 1.27256351154 0.661059501194
absolute error = 3.059e-31
relative error = 2.133e-29 %
Correct digits = 31
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) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12050.3MB, alloc=44.3MB, time=148.03
memory used=12097.3MB, alloc=44.3MB, time=148.61
x[1] = 0.2276 0.64
h = 0.0001 0.003
y2[1] (numeric) = 1.14311205144 0.732217334026
y2[1] (closed_form) = 1.27345018874 0.666939046621
absolute error = 0.1458
relative error = 10.14 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.27345018874 0.666939046621
y1[1] (closed_form) = 1.27345018874 0.666939046621
absolute error = 2.088e-31
relative error = 1.453e-29 %
Correct digits = 31
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) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12144.1MB, alloc=44.3MB, time=149.19
x[1] = 0.2277 0.643
h = 0.001 0.001
y2[1] (numeric) = 1.14360637079 0.737107311343
y2[1] (closed_form) = 1.27403309817 0.670468419478
absolute error = 0.1465
relative error = 10.17 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.27403309817 0.670468419478
y1[1] (closed_form) = 1.27403309817 0.670468419478
absolute error = 2.088e-31
relative error = 1.450e-29 %
Correct digits = 31
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) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12191.1MB, alloc=44.3MB, time=149.77
memory used=12237.9MB, alloc=44.3MB, time=150.34
x[1] = 0.2287 0.644
h = 0.001 0.003
y2[1] (numeric) = 1.14410438817 0.742007834867
y2[1] (closed_form) = 1.27537174069 0.671495396738
absolute error = 0.149
relative error = 10.34 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.27537174069 0.671495396738
y1[1] (closed_form) = 1.27537174069 0.671495396738
absolute error = 2.088e-31
relative error = 1.449e-29 %
Correct digits = 31
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) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12284.5MB, alloc=44.3MB, time=150.92
memory used=12331.6MB, alloc=44.3MB, time=151.50
x[1] = 0.2297 0.647
h = 0.0001 0.004
y2[1] (numeric) = 1.14460613113 0.746918962998
y2[1] (closed_form) = 1.27702678727 0.674889977815
absolute error = 0.1507
relative error = 10.44 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.27702678727 0.674889977815
y1[1] (closed_form) = 1.27702678727 0.674889977815
absolute error = 2.088e-31
relative error = 1.446e-29 %
Correct digits = 31
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) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12378.1MB, alloc=44.3MB, time=152.06
memory used=12424.8MB, alloc=44.3MB, time=152.64
x[1] = 0.2298 0.651
h = 0.003 0.006
y2[1] (numeric) = 1.14511162727 0.751840754142
y2[1] (closed_form) = 1.27777897965 0.679618500022
absolute error = 0.1511
relative error = 10.44 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.27777897965 0.679618500022
y1[1] (closed_form) = 1.27777897965 0.679618500022
absolute error = 2.088e-31
relative error = 1.443e-29 %
Correct digits = 31
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) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12471.2MB, alloc=44.3MB, time=153.20
x[1] = 0.2328 0.657
h = 0.0001 0.005
y2[1] (numeric) = 1.14562090428 0.756773266737
y2[1] (closed_form) = 1.28231122977 0.686270319178
absolute error = 0.1538
relative error = 10.57 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.28231122977 0.686270319178
y1[1] (closed_form) = 1.28231122977 0.686270319178
absolute error = 2.119e-31
relative error = 1.457e-29 %
Correct digits = 31
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) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12518.1MB, alloc=44.3MB, time=153.77
memory used=12564.8MB, alloc=44.3MB, time=154.34
x[1] = 0.2329 0.662
h = 0.0001 0.003
y2[1] (numeric) = 1.14613399048 0.761716558888
y2[1] (closed_form) = 1.28324774368 0.692215957118
absolute error = 0.1537
relative error = 10.54 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.28324774368 0.692215957118
y1[1] (closed_form) = 1.28324774368 0.692215957118
absolute error = 1.221e-31
relative error = 8.372e-30 %
Correct digits = 31
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) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12611.2MB, alloc=44.3MB, time=154.91
memory used=12658.5MB, alloc=44.3MB, time=155.50
x[1] = 0.233 0.665
h = 0.001 0.001
y2[1] (numeric) = 1.14665091479 0.766670688471
y2[1] (closed_form) = 1.28386122671 0.695784893628
absolute error = 0.1544
relative error = 10.58 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.28386122671 0.695784893628
y1[1] (closed_form) = 1.28386122671 0.695784893628
absolute error = 2.119e-31
relative error = 1.451e-29 %
Correct digits = 31
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) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12705.1MB, alloc=44.3MB, time=156.08
memory used=12752.0MB, alloc=44.3MB, time=156.65
x[1] = 0.234 0.666
h = 0.001 0.003
y2[1] (numeric) = 1.14717170632 0.771635713539
y2[1] (closed_form) = 1.28522320137 0.696815654319
absolute error = 0.157
relative error = 10.74 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.28522320137 0.696815654319
y1[1] (closed_form) = 1.28522320137 0.696815654319
absolute error = 2.119e-31
relative error = 1.449e-29 %
Correct digits = 31
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) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12798.4MB, alloc=44.3MB, time=157.22
x[1] = 0.235 0.669
h = 0.0001 0.004
y2[1] (numeric) = 1.14769639418 0.776611692184
y2[1] (closed_form) = 1.28692130472 0.700241211747
absolute error = 0.1588
relative error = 10.84 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.28692130472 0.700241211747
y1[1] (closed_form) = 1.28692130472 0.700241211747
absolute error = 1.221e-31
relative error = 8.332e-30 %
Correct digits = 31
memory used=12845.2MB, alloc=44.3MB, time=157.79
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) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12891.7MB, alloc=44.3MB, time=158.36
x[1] = 0.2351 0.673
h = 0.003 0.006
y2[1] (numeric) = 1.14822500754 0.781598682504
y2[1] (closed_form) = 1.28771433718 0.705023474745
absolute error = 0.1591
relative error = 10.84 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.28771433718 0.705023474745
y1[1] (closed_form) = 1.28771433718 0.705023474745
absolute error = 2.119e-31
relative error = 1.443e-29 %
Correct digits = 31
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) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12938.0MB, alloc=44.3MB, time=158.92
memory used=12984.9MB, alloc=44.3MB, time=159.50
x[1] = 0.2381 0.679
h = 0.0001 0.005
y2[1] (numeric) = 1.14875757568 0.786596742629
y2[1] (closed_form) = 1.29234771052 0.711728183458
absolute error = 0.1619
relative error = 10.98 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.29234771052 0.711728183458
y1[1] (closed_form) = 1.29234771052 0.711728183458
absolute error = 1.221e-31
relative error = 8.274e-30 %
Correct digits = 31
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) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13031.5MB, alloc=44.3MB, time=160.07
memory used=13078.5MB, alloc=44.3MB, time=160.64
x[1] = 0.2382 0.684
h = 0.0001 0.003
y2[1] (numeric) = 1.14929412849 0.791605930346
y2[1] (closed_form) = 1.29333587474 0.717742406252
absolute error = 0.1619
relative error = 10.94 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.29333587474 0.717742406252
y1[1] (closed_form) = 1.29333587474 0.717742406252
absolute error = 1.281e-31
relative error = 8.658e-30 %
Correct digits = 31
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) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13125.0MB, alloc=44.3MB, time=161.22
memory used=13172.4MB, alloc=44.3MB, time=161.81
x[1] = 0.2383 0.687
h = 0.001 0.001
y2[1] (numeric) = 1.14983469655 0.796626303205
y2[1] (closed_form) = 1.29398104342 0.7213523905
absolute error = 0.1626
relative error = 10.98 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.29398104342 0.7213523905
y1[1] (closed_form) = 1.29398104342 0.7213523905
absolute error = 7e-32
relative error = 4.725e-30 %
Correct digits = 31
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) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13218.9MB, alloc=44.3MB, time=162.38
x[1] = 0.2393 0.688
h = 0.001 0.003
y2[1] (numeric) = 1.15037931056 0.801657918939
y2[1] (closed_form) = 1.29536721156 0.722387086932
absolute error = 0.1652
relative error = 11.14 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.29536721156 0.722387086932
y1[1] (closed_form) = 1.29536721156 0.722387086932
absolute error = 8e-32
relative error = 5.394e-30 %
Correct digits = 31
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) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13265.3MB, alloc=44.3MB, time=162.95
memory used=13312.3MB, alloc=44.3MB, time=163.52
x[1] = 0.2403 0.691
h = 0.0001 0.004
y2[1] (numeric) = 1.15092800128 0.806700835321
y2[1] (closed_form) = 1.29710994479 0.725844786474
absolute error = 0.1671
relative error = 11.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.29710994479 0.725844786474
y1[1] (closed_form) = 1.29710994479 0.725844786474
absolute error = 8e-32
relative error = 5.382e-30 %
Correct digits = 31
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) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13358.7MB, alloc=44.3MB, time=164.09
memory used=13405.6MB, alloc=44.3MB, time=164.66
x[1] = 0.2404 0.695
h = 0.003 0.006
y2[1] (numeric) = 1.1514807995 0.811755110129
y2[1] (closed_form) = 1.2979452942 0.730682785655
absolute error = 0.1674
relative error = 11.24 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.2979452942 0.730682785655
y1[1] (closed_form) = 1.2979452942 0.730682785655
absolute error = 8e-32
relative error = 5.371e-30 %
Correct digits = 31
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) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13451.8MB, alloc=44.3MB, time=165.22
memory used=13498.8MB, alloc=44.3MB, time=165.80
x[1] = 0.2434 0.701
h = 0.0001 0.005
y2[1] (numeric) = 1.15203773614 0.816820801177
y2[1] (closed_form) = 1.30268346688 0.73744236017
absolute error = 0.1703
relative error = 11.38 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.30268346688 0.73744236017
y1[1] (closed_form) = 1.30268346688 0.73744236017
absolute error = 9e-32
relative error = 6.012e-30 %
Correct digits = 31
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) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13545.1MB, alloc=44.3MB, time=166.36
x[1] = 0.2435 0.706
h = 0.0001 0.003
y2[1] (numeric) = 1.15259884274 0.821897965924
y2[1] (closed_form) = 1.30372513456 0.743527679381
absolute error = 0.1702
relative error = 11.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.30372513456 0.743527679381
y1[1] (closed_form) = 1.30372513456 0.743527679381
absolute error = 8e-32
relative error = 5.330e-30 %
Correct digits = 31
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) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13591.6MB, alloc=44.3MB, time=166.92
memory used=13638.9MB, alloc=44.3MB, time=167.52
x[1] = 0.2436 0.709
h = 0.001 0.001
y2[1] (numeric) = 1.15316415155 0.826986661579
y2[1] (closed_form) = 1.30440312495 0.747180206777
absolute error = 0.171
relative error = 11.38 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.30440312495 0.747180206777
y1[1] (closed_form) = 1.30440312495 0.747180206777
absolute error = 9e-32
relative error = 5.987e-30 %
Correct digits = 31
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) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13685.7MB, alloc=44.3MB, time=168.10
memory used=13732.6MB, alloc=44.3MB, time=168.68
x[1] = 0.2446 0.71
h = 0.001 0.003
y2[1] (numeric) = 1.15373369497 0.832086945546
y2[1] (closed_form) = 1.30581435986 0.748218987413
absolute error = 0.1737
relative error = 11.54 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.30581435986 0.748218987413
y1[1] (closed_form) = 1.30581435986 0.748218987413
absolute error = 9e-32
relative error = 5.980e-30 %
Correct digits = 31
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) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13779.1MB, alloc=44.3MB, time=169.24
memory used=13826.0MB, alloc=44.3MB, time=169.82
x[1] = 0.2456 0.713
h = 0.0001 0.004
y2[1] (numeric) = 1.15430750545 0.837198875266
y2[1] (closed_form) = 1.30760332392 0.751709999076
absolute error = 0.1755
relative error = 11.64 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.30760332392 0.751709999076
y1[1] (closed_form) = 1.30760332392 0.751709999076
absolute error = 9e-32
relative error = 5.967e-30 %
Correct digits = 31
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) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13872.4MB, alloc=44.3MB, time=170.38
x[1] = 0.2457 0.717
h = 0.003 0.006
y2[1] (numeric) = 1.15488561545 0.84232250819
y2[1] (closed_form) = 1.30848249944 0.756605745377
absolute error = 0.1759
relative error = 11.64 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.30848249944 0.756605745377
y1[1] (closed_form) = 1.30848249944 0.756605745377
absolute error = 9e-32
relative error = 5.954e-30 %
Correct digits = 31
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) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13918.9MB, alloc=44.3MB, time=170.95
memory used=13965.7MB, alloc=44.3MB, time=171.52
x[1] = 0.2487 0.723
h = 0.0001 0.005
y2[1] (numeric) = 1.15546805759 0.847457901802
y2[1] (closed_form) = 1.31332920816 0.763422162512
absolute error = 0.1788
relative error = 11.77 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.31332920816 0.763422162512
y1[1] (closed_form) = 1.31332920816 0.763422162512
absolute error = 1.345e-31
relative error = 8.856e-30 %
Correct digits = 31
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) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14012.2MB, alloc=44.3MB, time=172.09
memory used=14059.3MB, alloc=44.3MB, time=172.67
x[1] = 0.2488 0.728
h = 0.0001 0.003
y2[1] (numeric) = 1.15605486514 0.852605113219
y2[1] (closed_form) = 1.31442627342 0.769581109641
absolute error = 0.1788
relative error = 11.74 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.31442627342 0.769581109641
y1[1] (closed_form) = 1.31442627342 0.769581109641
absolute error = 1.345e-31
relative error = 8.833e-30 %
Correct digits = 31
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) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14105.9MB, alloc=44.3MB, time=173.24
memory used=14153.3MB, alloc=44.3MB, time=173.83
x[1] = 0.2489 0.731
h = 0.001 0.001
y2[1] (numeric) = 1.15664607208 0.857764199303
y2[1] (closed_form) = 1.31513824646 0.773277687335
absolute error = 0.1796
relative error = 11.77 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.31513824646 0.773277687335
y1[1] (closed_form) = 1.31513824646 0.773277687335
absolute error = 1.345e-31
relative error = 8.818e-30 %
Correct digits = 31
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) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14199.9MB, alloc=44.3MB, time=174.41
x[1] = 0.2499 0.732
h = 0.0001 0.004
y2[1] (numeric) = 1.15724171255 0.862935217113
y2[1] (closed_form) = 1.31657543382 0.774320696654
absolute error = 0.1823
relative error = 11.94 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.31657543382 0.774320696654
y1[1] (closed_form) = 1.31657543382 0.774320696654
absolute error = 1.345e-31
relative error = 8.808e-30 %
Correct digits = 31
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) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14246.6MB, alloc=44.3MB, time=174.99
memory used=14293.2MB, alloc=44.3MB, time=175.57
x[1] = 0.25 0.736
h = 0.003 0.006
y2[1] (numeric) = 1.15784182073 0.868118223757
y2[1] (closed_form) = 1.31749284662 0.779268319478
absolute error = 0.1827
relative error = 11.94 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.31749284662 0.779268319478
y1[1] (closed_form) = 1.31749284662 0.779268319478
absolute error = 1.345e-31
relative error = 8.789e-30 %
Correct digits = 31
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) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14339.5MB, alloc=44.3MB, time=176.14
memory used=14386.6MB, alloc=44.3MB, time=176.71
x[1] = 0.253 0.742
h = 0.0001 0.005
y2[1] (numeric) = 1.15844643093 0.873313276392
y2[1] (closed_form) = 1.32243531047 0.786136602907
absolute error = 0.1857
relative error = 12.07 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.32243531047 0.786136602907
y1[1] (closed_form) = 1.32243531047 0.786136602907
absolute error = 1.281e-31
relative error = 8.324e-30 %
Correct digits = 31
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) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14433.2MB, alloc=44.3MB, time=177.27
memory used=14480.0MB, alloc=44.3MB, time=177.86
x[1] = 0.2531 0.747
h = 0.0001 0.003
y2[1] (numeric) = 1.15905557808 0.878520431789
y2[1] (closed_form) = 1.32358069077 0.792361660785
absolute error = 0.1857
relative error = 12.04 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.32358069077 0.792361660785
y1[1] (closed_form) = 1.32358069077 0.792361660785
absolute error = 1.281e-31
relative error = 8.302e-30 %
Correct digits = 31
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) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14526.6MB, alloc=44.3MB, time=178.43
x[1] = 0.2532 0.75
h = 0.001 0.001
y2[1] (numeric) = 1.15966929787 0.883739746462
y2[1] (closed_form) = 1.32432231487 0.796097795764
absolute error = 0.1865
relative error = 12.07 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.32432231487 0.796097795764
y1[1] (closed_form) = 1.32432231487 0.796097795764
absolute error = 2.193e-31
relative error = 1.419e-29 %
Correct digits = 31
memory used=14573.9MB, alloc=44.3MB, time=179.02
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) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14620.6MB, alloc=44.3MB, time=179.59
x[1] = 0.2542 0.751
h = 0.001 0.003
y2[1] (numeric) = 1.16028762618 0.888971277125
y2[1] (closed_form) = 1.3257825076 0.797144881281
absolute error = 0.1893
relative error = 12.23 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.3257825076 0.797144881281
y1[1] (closed_form) = 1.3257825076 0.797144881281
absolute error = 2.154e-31
relative error = 1.392e-29 %
Correct digits = 31
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) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14667.0MB, alloc=44.3MB, time=180.16
memory used=14714.1MB, alloc=44.3MB, time=180.74
x[1] = 0.2552 0.754
h = 0.0001 0.004
y2[1] (numeric) = 1.1609105989 0.894215080537
y2[1] (closed_form) = 1.32766142705 0.800701605346
absolute error = 0.1912
relative error = 12.33 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.32766142705 0.800701605346
y1[1] (closed_form) = 1.32766142705 0.800701605346
absolute error = 2.154e-31
relative error = 1.389e-29 %
Correct digits = 31
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) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14760.4MB, alloc=44.3MB, time=181.30
memory used=14807.3MB, alloc=44.3MB, time=181.88
x[1] = 0.2553 0.758
h = 0.0001 0.004
y2[1] (numeric) = 1.16153825196 0.899471213463
y2[1] (closed_form) = 1.32862553967 0.805710779413
absolute error = 0.1916
relative error = 12.33 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.32862553967 0.805710779413
y1[1] (closed_form) = 1.32862553967 0.805710779413
absolute error = 1.281e-31
relative error = 8.242e-30 %
Correct digits = 31
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) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14853.7MB, alloc=44.3MB, time=182.44
memory used=14900.5MB, alloc=44.3MB, time=183.01
x[1] = 0.2554 0.762
h = 0.003 0.006
y2[1] (numeric) = 1.16217062141 0.904739732761
y2[1] (closed_form) = 1.32959555158 0.810732573911
absolute error = 0.192
relative error = 12.33 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.32959555158 0.810732573911
y1[1] (closed_form) = 1.32959555158 0.810732573911
absolute error = 2.154e-31
relative error = 1.383e-29 %
Correct digits = 31
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) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14946.9MB, alloc=44.3MB, time=183.58
x[1] = 0.2584 0.768
h = 0.0001 0.005
y2[1] (numeric) = 1.16280774343 0.910020695425
y2[1] (closed_form) = 1.33467173681 0.817676484628
absolute error = 0.1951
relative error = 12.46 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.33467173681 0.817676484628
y1[1] (closed_form) = 1.33467173681 0.817676484628
absolute error = 2.154e-31
relative error = 1.376e-29 %
Correct digits = 31
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) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14993.3MB, alloc=44.3MB, time=184.14
memory used=15040.2MB, alloc=44.3MB, time=184.72
x[1] = 0.2585 0.773
h = 0.0001 0.003
y2[1] (numeric) = 1.16344965491 0.91531415806
y2[1] (closed_form) = 1.33588355128 0.823996016976
absolute error = 0.1951
relative error = 12.43 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.33588355128 0.823996016976
y1[1] (closed_form) = 1.33588355128 0.823996016976
absolute error = 1.345e-31
relative error = 8.572e-30 %
Correct digits = 31
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) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15086.7MB, alloc=44.3MB, time=185.28
memory used=15134.2MB, alloc=44.3MB, time=185.88
x[1] = 0.2586 0.776
h = 0.001 0.001
y2[1] (numeric) = 1.16409639351 0.920620177
y2[1] (closed_form) = 1.33666597153 0.827788691023
absolute error = 0.196
relative error = 12.46 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.33666597153 0.827788691023
y1[1] (closed_form) = 1.33666597153 0.827788691023
absolute error = 1.281e-31
relative error = 8.145e-30 %
Correct digits = 31
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) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15180.8MB, alloc=44.3MB, time=186.46
memory used=15227.7MB, alloc=44.3MB, time=187.04
x[1] = 0.2596 0.777
h = 0.001 0.003
y2[1] (numeric) = 1.16474799707 0.925938808792
y2[1] (closed_form) = 1.33815849726 0.828842113114
absolute error = 0.1987
relative error = 12.63 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.33815849726 0.828842113114
y1[1] (closed_form) = 1.33815849726 0.828842113114
absolute error = 2.154e-31
relative error = 1.368e-29 %
Correct digits = 31
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) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15274.0MB, alloc=44.3MB, time=187.60
x[1] = 0.2606 0.78
h = 0.0001 0.004
y2[1] (numeric) = 1.16540450344 0.931270110026
y2[1] (closed_form) = 1.34009596661 0.832443939954
absolute error = 0.2007
relative error = 12.72 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.34009596661 0.832443939954
y1[1] (closed_form) = 1.34009596661 0.832443939954
absolute error = 2.154e-31
relative error = 1.365e-29 %
Correct digits = 31
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) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15320.5MB, alloc=44.3MB, time=188.17
memory used=15367.2MB, alloc=44.3MB, time=188.74
x[1] = 0.2607 0.784
h = 0.003 0.006
y2[1] (numeric) = 1.16606595057 0.936614137299
y2[1] (closed_form) = 1.34111449093 0.837529762931
absolute error = 0.2011
relative error = 12.72 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.34111449093 0.837529762931
y1[1] (closed_form) = 1.34111449093 0.837529762931
absolute error = 1.281e-31
relative error = 8.099e-30 %
Correct digits = 31
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) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15413.5MB, alloc=44.3MB, time=189.30
memory used=15460.5MB, alloc=44.3MB, time=189.88
x[1] = 0.2637 0.79
h = 0.0001 0.005
y2[1] (numeric) = 1.1667323765 0.941970947252
y2[1] (closed_form) = 1.34631084392 0.844536711474
absolute error = 0.2043
relative error = 12.86 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.34631084392 0.844536711474
y1[1] (closed_form) = 1.34631084392 0.844536711474
absolute error = 1.281e-31
relative error = 8.058e-30 %
Correct digits = 31
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) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15506.9MB, alloc=44.3MB, time=190.44
memory used=15553.8MB, alloc=44.3MB, time=191.02
x[1] = 0.2638 0.795
h = 0.0001 0.003
y2[1] (numeric) = 1.16740382003 0.947340596112
y2[1] (closed_form) = 1.34758393995 0.850937781192
absolute error = 0.2043
relative error = 12.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.34758393995 0.850937781192
y1[1] (closed_form) = 1.34758393995 0.850937781192
absolute error = 1.281e-31
relative error = 8.035e-30 %
Correct digits = 31
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) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15600.5MB, alloc=44.3MB, time=191.60
x[1] = 0.2639 0.798
h = 0.001 0.001
y2[1] (numeric) = 1.16808032074 0.952723139829
y2[1] (closed_form) = 1.34840395003 0.85477921536
absolute error = 0.2052
relative error = 12.85 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.34840395003 0.85477921536
y1[1] (closed_form) = 1.34840395003 0.85477921536
absolute error = 1.281e-31
relative error = 8.021e-30 %
Correct digits = 31
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) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15647.5MB, alloc=44.3MB, time=192.18
memory used=15694.3MB, alloc=44.3MB, time=192.76
x[1] = 0.2649 0.799
h = 0.001 0.003
y2[1] (numeric) = 1.1687619184 0.958118634569
y2[1] (closed_form) = 1.34992518895 0.85583732432
absolute error = 0.208
relative error = 13.02 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.34992518895 0.85583732432
y1[1] (closed_form) = 1.34992518895 0.85583732432
absolute error = 8e-32
relative error = 5.005e-30 %
Correct digits = 31
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) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15740.6MB, alloc=44.3MB, time=193.33
memory used=15787.6MB, alloc=44.3MB, time=193.91
x[1] = 0.2659 0.802
h = 0.0001 0.004
y2[1] (numeric) = 1.16944865281 0.963527136546
y2[1] (closed_form) = 1.35191559174 0.859477314253
absolute error = 0.21
relative error = 13.11 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.35191559174 0.859477314253
y1[1] (closed_form) = 1.35191559174 0.859477314253
absolute error = 8e-32
relative error = 4.994e-30 %
Correct digits = 31
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) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15833.9MB, alloc=44.3MB, time=194.48
memory used=15880.9MB, alloc=44.3MB, time=195.05
x[1] = 0.266 0.806
h = 0.003 0.006
y2[1] (numeric) = 1.17014056382 0.968948701979
y2[1] (closed_form) = 1.35298427893 0.864629246913
absolute error = 0.2105
relative error = 13.11 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.35298427893 0.864629246913
y1[1] (closed_form) = 1.35298427893 0.864629246913
absolute error = 1.281e-31
relative error = 7.976e-30 %
Correct digits = 31
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) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15927.2MB, alloc=44.3MB, time=195.62
x[1] = 0.269 0.812
h = 0.0001 0.005
y2[1] (numeric) = 1.17083769143 0.974383387133
y2[1] (closed_form) = 1.35830480296 0.871701216028
absolute error = 0.2137
relative error = 13.24 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.35830480296 0.871701216028
y1[1] (closed_form) = 1.35830480296 0.871701216028
absolute error = 1.345e-31
relative error = 8.336e-30 %
Correct digits = 31
memory used=15974.2MB, alloc=44.3MB, time=196.20
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) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16020.6MB, alloc=44.3MB, time=196.76
x[1] = 0.2691 0.817
h = 0.0001 0.003
y2[1] (numeric) = 1.17154007641 0.979831247845
y2[1] (closed_form) = 1.35964125383 0.878186444601
absolute error = 0.2138
relative error = 13.21 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.35964125383 0.878186444601
y1[1] (closed_form) = 1.35964125383 0.878186444601
absolute error = 1.281e-31
relative error = 7.912e-30 %
Correct digits = 31
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) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16067.1MB, alloc=44.3MB, time=197.34
memory used=16114.4MB, alloc=44.3MB, time=197.93
x[1] = 0.2692 0.82
h = 0.001 0.001
y2[1] (numeric) = 1.17224776031 0.985292339666
y2[1] (closed_form) = 1.36050012349 0.882078199046
absolute error = 0.2147
relative error = 13.24 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.36050012349 0.882078199046
y1[1] (closed_form) = 1.36050012349 0.882078199046
absolute error = 9e-32
relative error = 5.551e-30 %
Correct digits = 31
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) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16161.0MB, alloc=44.3MB, time=198.51
memory used=16207.9MB, alloc=44.3MB, time=199.09
x[1] = 0.2702 0.821
h = 0.001 0.003
y2[1] (numeric) = 1.1729607849 0.990766718367
y2[1] (closed_form) = 1.36205101595 0.883141122511
absolute error = 0.2176
relative error = 13.4 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.36205101595 0.883141122511
y1[1] (closed_form) = 1.36205101595 0.883141122511
absolute error = 9e-32
relative error = 5.544e-30 %
Correct digits = 31
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) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16254.4MB, alloc=44.3MB, time=199.65
memory used=16301.3MB, alloc=44.3MB, time=200.23
x[1] = 0.2712 0.824
h = 0.0001 0.004
y2[1] (numeric) = 1.17367919198 0.996254439772
y2[1] (closed_form) = 1.36409610854 0.886820470894
absolute error = 0.2196
relative error = 13.5 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.36409610854 0.886820470894
y1[1] (closed_form) = 1.36409610854 0.886820470894
absolute error = 9e-32
relative error = 5.532e-30 %
Correct digits = 31
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) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16347.6MB, alloc=44.3MB, time=200.80
x[1] = 0.2713 0.828
h = 0.003 0.006
y2[1] (numeric) = 1.17440302339 1.00175555971
y2[1] (closed_form) = 1.36521664737 0.892040612884
absolute error = 0.2201
relative error = 13.5 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.36521664737 0.892040612884
y1[1] (closed_form) = 1.36521664737 0.892040612884
absolute error = 1.345e-31
relative error = 8.250e-30 %
Correct digits = 31
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) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16393.9MB, alloc=44.3MB, time=201.36
memory used=16440.9MB, alloc=44.3MB, time=201.93
x[1] = 0.2743 0.834
h = 0.0001 0.005
y2[1] (numeric) = 1.17513232114 1.00727013405
y2[1] (closed_form) = 1.37066541749 0.899179586003
absolute error = 0.2234
relative error = 13.63 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.37066541749 0.899179586003
y1[1] (closed_form) = 1.37066541749 0.899179586003
absolute error = 9e-32
relative error = 5.490e-30 %
Correct digits = 31
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) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16487.3MB, alloc=44.3MB, time=202.50
memory used=16534.3MB, alloc=44.3MB, time=203.08
x[1] = 0.2744 0.839
h = 0.0001 0.003
y2[1] (numeric) = 1.17586712801 1.01279821823
y2[1] (closed_form) = 1.372067345 0.90575161851
absolute error = 0.2235
relative error = 13.59 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.372067345 0.90575161851
y1[1] (closed_form) = 1.372067345 0.90575161851
absolute error = 9e-32
relative error = 5.474e-30 %
Correct digits = 31
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) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16581.0MB, alloc=44.3MB, time=203.65
memory used=16628.4MB, alloc=44.3MB, time=204.24
x[1] = 0.2745 0.842
h = 0.001 0.001
y2[1] (numeric) = 1.17660748762 1.01833986739
y2[1] (closed_form) = 1.37296637343 0.909695267268
absolute error = 0.2244
relative error = 13.63 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.37296637343 0.909695267268
y1[1] (closed_form) = 1.37296637343 0.909695267268
absolute error = 9e-32
relative error = 5.465e-30 %
Correct digits = 31
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) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16674.8MB, alloc=44.3MB, time=204.82
x[1] = 0.2755 0.843
h = 0.001 0.003
y2[1] (numeric) = 1.17735344377 1.02389513688
y2[1] (closed_form) = 1.37454787441 0.910763128154
absolute error = 0.2273
relative error = 13.79 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.37454787441 0.910763128154
y1[1] (closed_form) = 1.37454787441 0.910763128154
absolute error = 9e-32
relative error = 5.458e-30 %
Correct digits = 31
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) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16721.2MB, alloc=44.3MB, time=205.38
memory used=16768.2MB, alloc=44.3MB, time=205.96
x[1] = 0.2765 0.846
h = 0.0001 0.004
y2[1] (numeric) = 1.17810504034 1.02946408213
y2[1] (closed_form) = 1.37664944731 0.914483035533
absolute error = 0.2294
relative error = 13.88 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.37664944731 0.914483035533
y1[1] (closed_form) = 1.37664944731 0.914483035533
absolute error = 1.0e-31
relative error = 6.051e-30 %
Correct digits = 31
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) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16814.6MB, alloc=44.3MB, time=206.52
memory used=16861.5MB, alloc=44.3MB, time=207.10
x[1] = 0.2766 0.85
h = 0.003 0.006
y2[1] (numeric) = 1.17886232123 1.03504675856
y2[1] (closed_form) = 1.37782356608 0.919773505505
absolute error = 0.2299
relative error = 13.88 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.37782356608 0.919773505505
y1[1] (closed_form) = 1.37782356608 0.919773505505
absolute error = 1.0e-31
relative error = 6.036e-30 %
Correct digits = 31
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) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16907.8MB, alloc=44.3MB, time=207.66
memory used=16954.8MB, alloc=44.3MB, time=208.24
x[1] = 0.2796 0.856
h = 0.0001 0.005
y2[1] (numeric) = 1.1796253305 1.04064322163
y2[1] (closed_form) = 1.38340473144 0.9269814667
absolute error = 0.2333
relative error = 14.01 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.38340473144 0.9269814667
y1[1] (closed_form) = 1.38340473144 0.9269814667
absolute error = 9e-32
relative error = 5.405e-30 %
Correct digits = 31
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) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17001.4MB, alloc=44.3MB, time=208.81
x[1] = 0.2797 0.861
h = 0.0001 0.003
y2[1] (numeric) = 1.18039411304 1.04625352636
y2[1] (closed_form) = 1.38487430748 0.933642972525
absolute error = 0.2334
relative error = 13.98 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.38487430748 0.933642972525
y1[1] (closed_form) = 1.38487430748 0.933642972525
absolute error = 1.345e-31
relative error = 8.055e-30 %
Correct digits = 31
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) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17048.0MB, alloc=44.3MB, time=209.38
memory used=17095.1MB, alloc=44.3MB, time=209.97
x[1] = 0.2798 0.864
h = 0.001 0.001
y2[1] (numeric) = 1.18116871455 1.05187772746
y2[1] (closed_form) = 1.38581482431 0.937640103926
absolute error = 0.2344
relative error = 14.01 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.38581482431 0.937640103926
y1[1] (closed_form) = 1.38581482431 0.937640103926
absolute error = 1.345e-31
relative error = 8.041e-30 %
Correct digits = 31
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) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17141.9MB, alloc=44.3MB, time=210.55
memory used=17188.8MB, alloc=44.3MB, time=211.12
x[1] = 0.2808 0.865
h = 0.0001 0.004
y2[1] (numeric) = 1.181949181 1.05751587987
y2[1] (closed_form) = 1.38742790388 0.938713020261
absolute error = 0.2374
relative error = 14.17 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.38742790388 0.938713020261
y1[1] (closed_form) = 1.38742790388 0.938713020261
absolute error = 1.414e-31
relative error = 8.442e-30 %
Correct digits = 31
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) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17235.3MB, alloc=44.3MB, time=211.69
memory used=17282.0MB, alloc=44.3MB, time=212.26
x[1] = 0.2809 0.869
h = 0.003 0.006
y2[1] (numeric) = 1.18273555836 1.06316803859
y2[1] (closed_form) = 1.38864868516 0.944066404719
absolute error = 0.2379
relative error = 14.17 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.38864868516 0.944066404719
y1[1] (closed_form) = 1.38864868516 0.944066404719
absolute error = 1.345e-31
relative error = 8.012e-30 %
Correct digits = 31
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) = 33.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17328.5MB, alloc=44.3MB, time=212.83
x[1] = 0.2839 0.875
h = 0.0001 0.005
y2[1] (numeric) = 1.18352789272 1.06883425868
y2[1] (closed_form) = 1.39434633881 0.951336983551
absolute error = 0.2414
relative error = 14.3 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.39434633881 0.951336983551
y1[1] (closed_form) = 1.39434633881 0.951336983551
absolute error = 1.345e-31
relative error = 7.970e-30 %
Correct digits = 31
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) = 33.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17375.3MB, alloc=44.3MB, time=213.40
memory used=17422.0MB, alloc=44.3MB, time=213.98
x[1] = 0.284 0.88
h = 0.0001 0.003
y2[1] (numeric) = 1.18432623102 1.07451459473
y2[1] (closed_form) = 1.39587481352 0.958078503676
absolute error = 0.2415
relative error = 14.26 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.39587481352 0.958078503676
y1[1] (closed_form) = 1.39587481352 0.958078503676
absolute error = 1.345e-31
relative error = 7.946e-30 %
Correct digits = 31
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) = 33.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17468.5MB, alloc=44.3MB, time=214.55
memory used=17515.8MB, alloc=44.3MB, time=215.14
x[1] = 0.2841 0.883
h = 0.001 0.001
y2[1] (numeric) = 1.18513062105 1.08020910101
y2[1] (closed_form) = 1.39685146774 0.96212347061
absolute error = 0.2424
relative error = 14.29 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.39685146774 0.96212347061
y1[1] (closed_form) = 1.39685146774 0.96212347061
absolute error = 1.345e-31
relative error = 7.932e-30 %
Correct digits = 31
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) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17562.4MB, alloc=44.3MB, time=215.72
memory used=17609.5MB, alloc=44.3MB, time=216.30
x[1] = 0.2851 0.884
h = 0.001 0.003
y2[1] (numeric) = 1.18594111082 1.08591783205
y2[1] (closed_form) = 1.39849245578 0.96320122134
absolute error = 0.2454
relative error = 14.45 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.39849245578 0.96320122134
y1[1] (closed_form) = 1.39849245578 0.96320122134
absolute error = 2.193e-31
relative error = 1.292e-29 %
Correct digits = 31
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) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17655.9MB, alloc=44.3MB, time=216.87
x[1] = 0.2861 0.887
h = 0.0001 0.004
y2[1] (numeric) = 1.1867577484 1.09164084242
y2[1] (closed_form) = 1.40070349508 0.967000537974
absolute error = 0.2476
relative error = 14.55 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.40070349508 0.967000537974
y1[1] (closed_form) = 1.40070349508 0.967000537974
absolute error = 2.193e-31
relative error = 1.289e-29 %
Correct digits = 31
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) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17702.7MB, alloc=44.3MB, time=217.44
memory used=17749.3MB, alloc=44.3MB, time=218.01
x[1] = 0.2862 0.891
h = 0.003 0.006
y2[1] (numeric) = 1.1875805819 1.09737818669
y2[1] (closed_form) = 1.40198115614 0.972428267003
absolute error = 0.2482
relative error = 14.54 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.40198115614 0.972428267003
y1[1] (closed_form) = 1.40198115614 0.972428267003
absolute error = 2.154e-31
relative error = 1.262e-29 %
Correct digits = 31
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) = 33.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17795.5MB, alloc=44.3MB, time=218.57
memory used=17842.5MB, alloc=44.3MB, time=219.15
x[1] = 0.2892 0.897
h = 0.0001 0.005
y2[1] (numeric) = 1.1884096596 1.10312991948
y2[1] (closed_form) = 1.40781910731 0.979771578895
absolute error = 0.2517
relative error = 14.68 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.40781910731 0.979771578895
y1[1] (closed_form) = 1.40781910731 0.979771578895
absolute error = 2.193e-31
relative error = 1.279e-29 %
Correct digits = 31
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) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17888.9MB, alloc=44.3MB, time=219.72
memory used=17935.8MB, alloc=44.3MB, time=220.30
x[1] = 0.2893 0.902
h = 0.0001 0.003
y2[1] (numeric) = 1.18924503063 1.10889609495
y2[1] (closed_form) = 1.40941937827 0.986607633921
absolute error = 0.2519
relative error = 14.64 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.40941937827 0.986607633921
y1[1] (closed_form) = 1.40941937827 0.986607633921
absolute error = 1.345e-31
relative error = 7.820e-30 %
Correct digits = 31
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) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17982.5MB, alloc=44.3MB, time=220.87
x[1] = 0.2894 0.905
h = 0.001 0.001
y2[1] (numeric) = 1.19008674502 1.1146767669
y2[1] (closed_form) = 1.41044005995 0.990709095211
absolute error = 0.2528
relative error = 14.67 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.41044005995 0.990709095211
y1[1] (closed_form) = 1.41044005995 0.990709095211
absolute error = 1.345e-31
relative error = 7.805e-30 %
Correct digits = 31
memory used=18029.9MB, alloc=44.3MB, time=221.47
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) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18076.4MB, alloc=44.3MB, time=222.04
x[1] = 0.2904 0.906
h = 0.001 0.003
y2[1] (numeric) = 1.19093485305 1.12047198939
y2[1] (closed_form) = 1.41211447225 0.991792119412
absolute error = 0.2559
relative error = 14.83 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.41211447225 0.991792119412
y1[1] (closed_form) = 1.41211447225 0.991792119412
absolute error = 1.345e-31
relative error = 7.796e-30 %
Correct digits = 31
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) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18122.9MB, alloc=44.3MB, time=222.61
memory used=18169.8MB, alloc=44.3MB, time=223.18
x[1] = 0.2914 0.909
h = 0.0001 0.004
y2[1] (numeric) = 1.191789405 1.12628181656
y2[1] (closed_form) = 1.41438729779 0.995635482114
absolute error = 0.2581
relative error = 14.92 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.41438729779 0.995635482114
y1[1] (closed_form) = 1.41438729779 0.995635482114
absolute error = 1.345e-31
relative error = 7.778e-30 %
Correct digits = 31
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) = 33.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18216.1MB, alloc=44.3MB, time=223.75
memory used=18263.0MB, alloc=44.3MB, time=224.32
x[1] = 0.2915 0.913
h = 0.003 0.006
y2[1] (numeric) = 1.19265045125 1.13210630252
y2[1] (closed_form) = 1.415723687 1.00113973237
absolute error = 0.2587
relative error = 14.92 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.415723687 1.00113973237
y1[1] (closed_form) = 1.415723687 1.00113973237
absolute error = 1.414e-31
relative error = 8.156e-30 %
Correct digits = 31
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) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18309.5MB, alloc=44.3MB, time=224.89
memory used=18356.5MB, alloc=44.3MB, time=225.48
x[1] = 0.2945 0.919
h = 0.0001 0.005
y2[1] (numeric) = 1.19351804232 1.13794550146
y2[1] (closed_form) = 1.42170630992 1.00855776379
absolute error = 0.2623
relative error = 15.05 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.42170630992 1.00855776379
y1[1] (closed_form) = 1.42170630992 1.00855776379
absolute error = 1e-31
relative error = 5.737e-30 %
Correct digits = 31
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) = 33.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18403.0MB, alloc=44.3MB, time=226.05
x[1] = 0.2946 0.924
h = 0.0001 0.003
y2[1] (numeric) = 1.19439222962 1.14379946704
y2[1] (closed_form) = 1.42338070103 1.01549109722
absolute error = 0.2625
relative error = 15.01 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.42338070103 1.01549109722
y1[1] (closed_form) = 1.42338070103 1.01549109722
absolute error = 1.414e-31
relative error = 8.088e-30 %
Correct digits = 31
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) = 33.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18449.5MB, alloc=44.3MB, time=226.61
memory used=18496.8MB, alloc=44.3MB, time=227.21
x[1] = 0.2947 0.927
h = 0.001 0.001
y2[1] (numeric) = 1.19527306549 1.1496682526
y2[1] (closed_form) = 1.42444683205 1.01965068477
absolute error = 0.2635
relative error = 15.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.42444683205 1.01965068477
y1[1] (closed_form) = 1.42444683205 1.01965068477
absolute error = 1e-31
relative error = 5.708e-30 %
Correct digits = 31
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) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18543.4MB, alloc=44.3MB, time=227.78
memory used=18590.4MB, alloc=44.3MB, time=228.36
x[1] = 0.2957 0.928
h = 0.001 0.003
y2[1] (numeric) = 1.19616060251 1.15555191175
y2[1] (closed_form) = 1.42615568461 1.02073908572
absolute error = 0.2666
relative error = 15.2 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.42615568461 1.02073908572
y1[1] (closed_form) = 1.42615568461 1.02073908572
absolute error = 1e-31
relative error = 5.702e-30 %
Correct digits = 31
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) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18636.9MB, alloc=44.3MB, time=228.94
memory used=18683.9MB, alloc=44.3MB, time=229.51
x[1] = 0.2967 0.931
h = 0.0001 0.004
y2[1] (numeric) = 1.19705489328 1.16145049813
y2[1] (closed_form) = 1.42849222895 1.0246277167
absolute error = 0.2689
relative error = 15.29 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.42849222895 1.0246277167
y1[1] (closed_form) = 1.42849222895 1.0246277167
absolute error = 1e-31
relative error = 5.688e-30 %
Correct digits = 31
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) = 33.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18730.2MB, alloc=44.3MB, time=230.08
x[1] = 0.2968 0.935
h = 0.003 0.006
y2[1] (numeric) = 1.19795599049 1.16736406539
y2[1] (closed_form) = 1.42988923929 1.03021068602
absolute error = 0.2695
relative error = 15.29 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.42988923929 1.03021068602
y1[1] (closed_form) = 1.42988923929 1.03021068602
absolute error = 1e-31
relative error = 5.674e-30 %
Correct digits = 31
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) = 33.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18776.6MB, alloc=44.3MB, time=230.64
memory used=18823.4MB, alloc=44.3MB, time=231.22
x[1] = 0.2998 0.941
h = 0.0001 0.005
y2[1] (numeric) = 1.19886394698 1.17329266725
y2[1] (closed_form) = 1.43602099159 1.03770542376
absolute error = 0.2732
relative error = 15.42 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.43602099159 1.03770542376
y1[1] (closed_form) = 1.43602099159 1.03770542376
absolute error = 1e-31
relative error = 5.644e-30 %
Correct digits = 31
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) = 33.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18869.8MB, alloc=44.3MB, time=231.78
memory used=18916.8MB, alloc=44.3MB, time=232.36
x[1] = 0.2999 0.946
h = 0.0001 0.003
y2[1] (numeric) = 1.1997788165 1.1792363569
y2[1] (closed_form) = 1.43777188321 1.04473880616
absolute error = 0.2734
relative error = 15.38 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.43777188321 1.04473880616
y1[1] (closed_form) = 1.43777188321 1.04473880616
absolute error = 1e-31
relative error = 5.627e-30 %
Correct digits = 31
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) = 33.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18963.6MB, alloc=44.3MB, time=232.94
memory used=19010.9MB, alloc=44.3MB, time=233.53
x[1] = 0.3 0.949
h = 0.001 0.001
y2[1] (numeric) = 1.20070065377 1.18519518719
y2[1] (closed_form) = 1.43888491975 1.04895816779
absolute error = 0.2744
relative error = 15.41 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.43888491975 1.04895816779
y1[1] (closed_form) = 1.43888491975 1.04895816779
absolute error = 1e-31
relative error = 5.616e-30 %
Correct digits = 31
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) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19057.5MB, alloc=44.3MB, time=234.10
x[1] = 0.301 0.95
h = 0.001 0.003
y2[1] (numeric) = 1.20162951373 1.19116921121
y2[1] (closed_form) = 1.44062924549 1.05005204317
absolute error = 0.2776
relative error = 15.57 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.44062924549 1.05005204317
y1[1] (closed_form) = 1.44062924549 1.05005204317
absolute error = 1.414e-31
relative error = 7.933e-30 %
Correct digits = 31
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) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19104.1MB, alloc=44.3MB, time=234.67
memory used=19151.1MB, alloc=44.3MB, time=235.25
x[1] = 0.302 0.953
h = 0.0001 0.004
y2[1] (numeric) = 1.20256545139 1.19715848213
y2[1] (closed_form) = 1.44303148082 1.05398717043
absolute error = 0.2799
relative error = 15.66 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.44303148082 1.05398717043
y1[1] (closed_form) = 1.44303148082 1.05398717043
absolute error = 1.414e-31
relative error = 7.914e-30 %
Correct digits = 31
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) = 33.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19197.5MB, alloc=44.3MB, time=235.81
memory used=19244.4MB, alloc=44.3MB, time=236.39
x[1] = 0.3021 0.957
h = 0.003 0.006
y2[1] (numeric) = 1.20350852179 1.20316305313
y2[1] (closed_form) = 1.44449105127 1.05965107841
absolute error = 0.2805
relative error = 15.66 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.44449105127 1.05965107841
y1[1] (closed_form) = 1.44449105127 1.05965107841
absolute error = 1e-31
relative error = 5.582e-30 %
Correct digits = 31
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) = 33.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19290.8MB, alloc=44.3MB, time=236.96
memory used=19337.7MB, alloc=44.3MB, time=237.54
x[1] = 0.3051 0.963
h = 0.0001 0.005
y2[1] (numeric) = 1.20445878018 1.20918297742
y2[1] (closed_form) = 1.45077647646 1.06722450947
absolute error = 0.2843
relative error = 15.79 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.45077647646 1.06722450947
y1[1] (closed_form) = 1.45077647646 1.06722450947
absolute error = 1.414e-31
relative error = 7.852e-30 %
Correct digits = 31
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) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19384.0MB, alloc=44.3MB, time=238.10
x[1] = 0.3052 0.968
h = 0.0001 0.003
y2[1] (numeric) = 1.20541628271 1.21521830771
y2[1] (closed_form) = 1.45260630718 1.07436073918
absolute error = 0.2845
relative error = 15.75 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.45260630718 1.07436073918
y1[1] (closed_form) = 1.45260630718 1.07436073918
absolute error = 1.414e-31
relative error = 7.827e-30 %
Correct digits = 31
memory used=19431.1MB, alloc=44.3MB, time=238.68
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) = 33.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19477.9MB, alloc=44.3MB, time=239.26
x[1] = 0.3053 0.971
h = 0.001 0.001
y2[1] (numeric) = 1.20638108654 1.22126909631
y2[1] (closed_form) = 1.45376774071 1.07864153901
absolute error = 0.2856
relative error = 15.77 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.45376774071 1.07864153901
y1[1] (closed_form) = 1.45376774071 1.07864153901
absolute error = 1.414e-31
relative error = 7.812e-30 %
Correct digits = 31
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) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19524.6MB, alloc=44.3MB, time=239.84
memory used=19571.7MB, alloc=44.3MB, time=240.42
x[1] = 0.3063 0.972
h = 0.0001 0.004
y2[1] (numeric) = 1.20735324906 1.22733539582
y2[1] (closed_form) = 1.45554859003 1.07974098074
absolute error = 0.2888
relative error = 15.93 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.45554859003 1.07974098074
y1[1] (closed_form) = 1.45554859003 1.07974098074
absolute error = 2.236e-31
relative error = 1.234e-29 %
Correct digits = 31
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) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19618.2MB, alloc=44.3MB, time=240.99
memory used=19665.1MB, alloc=44.3MB, time=241.57
x[1] = 0.3064 0.976
h = 0.003 0.006
y2[1] (numeric) = 1.20833282773 1.23341725892
y2[1] (closed_form) = 1.45706259844 1.08547712996
absolute error = 0.2894
relative error = 15.93 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.45706259844 1.08547712996
y1[1] (closed_form) = 1.45706259844 1.08547712996
absolute error = 2.236e-31
relative error = 1.231e-29 %
Correct digits = 31
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) = 33.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19711.6MB, alloc=44.3MB, time=242.14
memory used=19758.6MB, alloc=44.3MB, time=242.71
x[1] = 0.3094 0.982
h = 0.0001 0.005
y2[1] (numeric) = 1.20931988013 1.23951473833
y2[1] (closed_form) = 1.46348303628 1.09312179461
absolute error = 0.2933
relative error = 16.06 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.46348303628 1.09312179461
y1[1] (closed_form) = 1.46348303628 1.09312179461
absolute error = 2.236e-31
relative error = 1.224e-29 %
Correct digits = 31
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) = 34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19805.1MB, alloc=44.3MB, time=243.28
x[1] = 0.3095 0.987
h = 0.0001 0.003
y2[1] (numeric) = 1.21031446477 1.24562788624
y2[1] (closed_form) = 1.46538154263 1.10034979538
absolute error = 0.2935
relative error = 16.02 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.46538154263 1.10034979538
y1[1] (closed_form) = 1.46538154263 1.10034979538
absolute error = 2.236e-31
relative error = 1.220e-29 %
Correct digits = 31
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) = 34.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19851.6MB, alloc=44.3MB, time=243.85
memory used=19899.0MB, alloc=44.3MB, time=244.44
x[1] = 0.3096 0.99
h = 0.001 0.001
y2[1] (numeric) = 1.2113166412 1.25175675447
y2[1] (closed_form) = 1.46658509766 1.10468542586
absolute error = 0.2946
relative error = 16.05 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.46658509766 1.10468542586
y1[1] (closed_form) = 1.46658509766 1.10468542586
absolute error = 2.236e-31
relative error = 1.218e-29 %
Correct digits = 31
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) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19945.8MB, alloc=44.3MB, time=245.02
memory used=19992.8MB, alloc=44.3MB, time=245.60
x[1] = 0.3106 0.991
h = 0.001 0.003
y2[1] (numeric) = 1.2123264692 1.2579013951
y2[1] (closed_form) = 1.46839817238 1.10579018039
absolute error = 0.2978
relative error = 16.2 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.46839817238 1.10579018039
y1[1] (closed_form) = 1.46839817238 1.10579018039
absolute error = 2e-31
relative error = 1.088e-29 %
Correct digits = 31
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) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20039.2MB, alloc=44.3MB, time=246.17
memory used=20086.1MB, alloc=44.3MB, time=246.75
x[1] = 0.3116 0.994
h = 0.0001 0.004
y2[1] (numeric) = 1.21334400862 1.26406186029
y2[1] (closed_form) = 1.47092744429 1.10981595482
absolute error = 0.3002
relative error = 16.29 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.47092744429 1.10981595482
y1[1] (closed_form) = 1.47092744429 1.10981595482
absolute error = 2.236e-31
relative error = 1.214e-29 %
Correct digits = 31
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) = 34.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20132.5MB, alloc=44.3MB, time=247.32
x[1] = 0.3117 0.998
h = 0.003 0.006
y2[1] (numeric) = 1.21436931934 1.27023820218
y2[1] (closed_form) = 1.47250772094 1.11563725712
absolute error = 0.3009
relative error = 16.29 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.47250772094 1.11563725712
y1[1] (closed_form) = 1.47250772094 1.11563725712
absolute error = 2e-31
relative error = 1.083e-29 %
Correct digits = 31
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) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20178.8MB, alloc=44.3MB, time=247.88
memory used=20225.9MB, alloc=44.3MB, time=248.46
x[1] = 0.3147 1.004
h = 0.0001 0.005
y2[1] (numeric) = 1.21540246148 1.276430473
y2[1] (closed_form) = 1.47909049971 1.12336436903
absolute error = 0.3049
relative error = 16.42 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.47909049971 1.12336436903
y1[1] (closed_form) = 1.47909049971 1.12336436903
absolute error = 3.162e-31
relative error = 1.703e-29 %
Correct digits = 31
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) = 34.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20272.3MB, alloc=44.3MB, time=249.03
memory used=20319.3MB, alloc=44.3MB, time=249.60
x[1] = 0.3148 1.009
h = 0.0001 0.003
y2[1] (numeric) = 1.21644349608 1.28263872438
y2[1] (closed_form) = 1.48107260964 1.13070053128
absolute error = 0.3051
relative error = 16.38 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.48107260964 1.13070053128
y1[1] (closed_form) = 1.48107260964 1.13070053128
absolute error = 3.162e-31
relative error = 1.697e-29 %
Correct digits = 31
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) = 34.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20366.0MB, alloc=44.3MB, time=250.18
memory used=20413.2MB, alloc=44.3MB, time=250.78
x[1] = 0.3149 1.012
h = 0.001 0.001
y2[1] (numeric) = 1.21749248525 1.2888630076
y2[1] (closed_form) = 1.48232741437 1.13510076014
absolute error = 0.3062
relative error = 16.4 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.48232741437 1.13510076014
y1[1] (closed_form) = 1.48232741437 1.13510076014
absolute error = 3.162e-31
relative error = 1.694e-29 %
Correct digits = 31
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) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20459.7MB, alloc=44.3MB, time=251.34
x[1] = 0.3159 1.013
h = 0.001 0.003
y2[1] (numeric) = 1.21854949137 1.29510337419
y2[1] (closed_form) = 1.48417901444 1.13621124901
absolute error = 0.3095
relative error = 16.56 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.48417901444 1.13621124901
y1[1] (closed_form) = 1.48417901444 1.13621124901
absolute error = 3.162e-31
relative error = 1.692e-29 %
Correct digits = 31
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) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20506.0MB, alloc=44.3MB, time=251.91
memory used=20552.9MB, alloc=44.3MB, time=252.48
x[1] = 0.3169 1.016
h = 0.0001 0.004
y2[1] (numeric) = 1.21961457685 1.30135987577
y2[1] (closed_form) = 1.48677983384 1.14028709067
absolute error = 0.312
relative error = 16.65 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.48677983384 1.14028709067
y1[1] (closed_form) = 1.48677983384 1.14028709067
absolute error = 3.606e-31
relative error = 1.924e-29 %
Correct digits = 31
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) = 34.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20599.4MB, alloc=44.3MB, time=253.05
memory used=20646.3MB, alloc=44.3MB, time=253.63
x[1] = 0.317 1.02
h = 0.003 0.006
y2[1] (numeric) = 1.22068780417 1.30763256395
y2[1] (closed_form) = 1.48842845687 1.14619583156
absolute error = 0.3126
relative error = 16.64 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.48842845687 1.14619583156
y1[1] (closed_form) = 1.48842845687 1.14619583156
absolute error = 3.606e-31
relative error = 1.919e-29 %
Correct digits = 31
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) = 34.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20692.7MB, alloc=44.3MB, time=254.19
memory used=20739.8MB, alloc=44.3MB, time=254.77
x[1] = 0.32 1.026
h = 0.0001 0.005
y2[1] (numeric) = 1.22176923601 1.3139214904
y2[1] (closed_form) = 1.4951783799 1.15400737847
absolute error = 0.3167
relative error = 16.77 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.4951783799 1.15400737847
y1[1] (closed_form) = 1.4951783799 1.15400737847
absolute error = 4.472e-31
relative error = 2.368e-29 %
Correct digits = 31
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) = 34.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20786.3MB, alloc=44.3MB, time=255.34
x[1] = 0.3201 1.031
h = 0.0001 0.003
y2[1] (numeric) = 1.22285893605 1.32022670621
y2[1] (closed_form) = 1.49724670802 1.16145458467
absolute error = 0.317
relative error = 16.73 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.49724670802 1.16145458467
y1[1] (closed_form) = 1.49724670802 1.16145458467
absolute error = 4.472e-31
relative error = 2.360e-29 %
Correct digits = 31
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) = 34.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20833.0MB, alloc=44.3MB, time=255.91
memory used=20880.2MB, alloc=44.3MB, time=256.50
x[1] = 0.3202 1.034
h = 0.001 0.001
y2[1] (numeric) = 1.22395696904 1.32654826207
y2[1] (closed_form) = 1.49855436076 1.16592112543
absolute error = 0.3181
relative error = 16.76 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.49855436076 1.16592112543
y1[1] (closed_form) = 1.49855436076 1.16592112543
absolute error = 4.472e-31
relative error = 2.355e-29 %
Correct digits = 31
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) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20927.0MB, alloc=44.3MB, time=257.08
memory used=20974.0MB, alloc=44.3MB, time=257.66
x[1] = 0.3212 1.035
h = 0.001 0.003
y2[1] (numeric) = 1.2250634 1.33288620895
y2[1] (closed_form) = 1.50044558935 1.1670374231
absolute error = 0.3215
relative error = 16.91 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.50044558935 1.1670374231
y1[1] (closed_form) = 1.50044558935 1.1670374231
absolute error = 4.472e-31
relative error = 2.353e-29 %
Correct digits = 31
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) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21020.4MB, alloc=44.3MB, time=258.23
memory used=21067.4MB, alloc=44.3MB, time=258.81
x[1] = 0.3222 1.038
h = 0.0001 0.004
y2[1] (numeric) = 1.22617829399 1.33924059791
y2[1] (closed_form) = 1.50312009257 1.1711645837
absolute error = 0.324
relative error = 17 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.50312009257 1.1711645837
y1[1] (closed_form) = 1.50312009257 1.1711645837
absolute error = 4.472e-31
relative error = 2.347e-29 %
Correct digits = 31
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) = 34.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21113.8MB, alloc=44.3MB, time=259.37
x[1] = 0.3223 1.042
h = 0.003 0.006
y2[1] (numeric) = 1.22730171614 1.34561148
y2[1] (closed_form) = 1.50483919164 1.17716307263
absolute error = 0.3247
relative error = 16.99 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.50483919164 1.17716307263
y1[1] (closed_form) = 1.50483919164 1.17716307263
absolute error = 5.385e-31
relative error = 2.819e-29 %
Correct digits = 31
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) = 34.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21160.5MB, alloc=44.3MB, time=259.94
memory used=21207.2MB, alloc=44.3MB, time=260.51
x[1] = 0.3253 1.048
h = 0.0001 0.005
y2[1] (numeric) = 1.22843373181 1.35199890632
y2[1] (closed_form) = 1.51176115817 1.18506104181
absolute error = 0.3289
relative error = 17.12 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.51176115817 1.18506104181
y1[1] (closed_form) = 1.51176115817 1.18506104181
absolute error = 5.385e-31
relative error = 2.803e-29 %
Correct digits = 31
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) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21253.7MB, alloc=44.3MB, time=261.08
memory used=21300.7MB, alloc=44.3MB, time=261.66
x[1] = 0.3254 1.053
h = 0.0001 0.003
y2[1] (numeric) = 1.22957440735 1.35840292738
y2[1] (closed_form) = 1.5139183843 1.19262220492
absolute error = 0.3291
relative error = 17.08 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.5139183843 1.19262220492
y1[1] (closed_form) = 1.5139183843 1.19262220492
absolute error = 5.385e-31
relative error = 2.794e-29 %
Correct digits = 31
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) = 34.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21347.1MB, alloc=44.3MB, time=262.23
memory used=21394.5MB, alloc=44.3MB, time=262.82
x[1] = 0.3255 1.056
h = 0.001 0.001
y2[1] (numeric) = 1.23072381022 1.36482359328
y2[1] (closed_form) = 1.51528052292 1.19715678901
absolute error = 0.3303
relative error = 17.1 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.51528052292 1.19715678901
y1[1] (closed_form) = 1.51528052292 1.19715678901
absolute error = 5.385e-31
relative error = 2.789e-29 %
Correct digits = 31
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) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21441.1MB, alloc=44.3MB, time=263.40
x[1] = 0.3265 1.057
h = 0.001 0.003
y2[1] (numeric) = 1.23188200817 1.37126095441
y2[1] (closed_form) = 1.51721250261 1.19827896336
absolute error = 0.3337
relative error = 17.26 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.51721250261 1.19827896336
y1[1] (closed_form) = 1.51721250261 1.19827896336
absolute error = 5.831e-31
relative error = 3.016e-29 %
Correct digits = 31
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) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21487.9MB, alloc=44.3MB, time=263.98
memory used=21534.6MB, alloc=44.3MB, time=264.55
x[1] = 0.3275 1.06
h = 0.0001 0.004
y2[1] (numeric) = 1.23304906899 1.37771506123
y2[1] (closed_form) = 1.51996287155 1.20245870083
absolute error = 0.3362
relative error = 17.35 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.51996287155 1.20245870083
y1[1] (closed_form) = 1.51996287155 1.20245870083
absolute error = 4.472e-31
relative error = 2.307e-29 %
Correct digits = 31
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) = 34.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21581.0MB, alloc=44.3MB, time=265.12
memory used=21627.8MB, alloc=44.3MB, time=265.69
x[1] = 0.3276 1.064
h = 0.003 0.006
y2[1] (numeric) = 1.23422506053 1.38418596421
y2[1] (closed_form) = 1.52175462939 1.20854927172
absolute error = 0.3369
relative error = 17.34 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.52175462939 1.20854927172
y1[1] (closed_form) = 1.52175462939 1.20854927172
absolute error = 5.385e-31
relative error = 2.771e-29 %
Correct digits = 31
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) = 34.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21674.3MB, alloc=44.3MB, time=266.26
memory used=21721.4MB, alloc=44.3MB, time=266.84
x[1] = 0.3306 1.07
h = 0.0001 0.005
y2[1] (numeric) = 1.23541005088 1.39067371386
y2[1] (closed_form) = 1.52885363725 1.21653564971
absolute error = 0.3412
relative error = 17.46 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.52885363725 1.21653564971
y1[1] (closed_form) = 1.52885363725 1.21653564971
absolute error = 4.472e-31
relative error = 2.289e-29 %
Correct digits = 31
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) = 34.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21767.9MB, alloc=44.3MB, time=267.40
memory used=21814.8MB, alloc=44.3MB, time=267.98
x[1] = 0.3307 1.075
h = 0.0001 0.003
y2[1] (numeric) = 1.23660410914 1.39717836011
y2[1] (closed_form) = 1.53110250831 1.22421371394
absolute error = 0.3415
relative error = 17.42 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.53110250831 1.22421371394
y1[1] (closed_form) = 1.53110250831 1.22421371394
absolute error = 4.472e-31
relative error = 2.281e-29 %
Correct digits = 31
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) = 34.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21861.5MB, alloc=44.3MB, time=268.56
x[1] = 0.3308 1.078
h = 0.001 0.001
y2[1] (numeric) = 1.23780730558 1.40369995241
y2[1] (closed_form) = 1.53252081138 1.22881809111
absolute error = 0.3427
relative error = 17.45 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.53252081138 1.22881809111
y1[1] (closed_form) = 1.53252081138 1.22881809111
absolute error = 4.472e-31
relative error = 2.277e-29 %
Correct digits = 31
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) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21908.2MB, alloc=44.3MB, time=269.14
memory used=21955.3MB, alloc=44.3MB, time=269.72
x[1] = 0.3318 1.079
h = 0.0001 0.004
y2[1] (numeric) = 1.23901971073 1.41023854056
y2[1] (closed_form) = 1.53449468473 1.2299462032
absolute error = 0.3461
relative error = 17.6 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.53449468473 1.2299462032
y1[1] (closed_form) = 1.53449468473 1.2299462032
absolute error = 4.472e-31
relative error = 2.274e-29 %
Correct digits = 31
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) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22001.6MB, alloc=44.3MB, time=270.28
memory used=22048.5MB, alloc=44.3MB, time=270.86
x[1] = 0.3319 1.083
h = 0.003 0.006
y2[1] (numeric) = 1.24024139518 1.41679417442
y2[1] (closed_form) = 1.53634963915 1.23611882512
absolute error = 0.3469
relative error = 17.59 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.53634963915 1.23611882512
y1[1] (closed_form) = 1.53634963915 1.23611882512
absolute error = 4.472e-31
relative error = 2.268e-29 %
Correct digits = 31
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) = 34.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22094.9MB, alloc=44.3MB, time=271.42
memory used=22142.0MB, alloc=44.3MB, time=272.00
x[1] = 0.3349 1.089
h = 0.0001 0.005
y2[1] (numeric) = 1.2414724297 1.42336690392
y2[1] (closed_form) = 1.5436040324 1.2441850843
absolute error = 0.3513
relative error = 17.72 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.5436040324 1.2441850843
y1[1] (closed_form) = 1.5436040324 1.2441850843
absolute error = 4.123e-31
relative error = 2.080e-29 %
Correct digits = 31
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) = 34.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22188.5MB, alloc=44.3MB, time=272.57
x[1] = 0.335 1.094
h = 0.0001 0.003
y2[1] (numeric) = 1.24271288608 1.42995677836
y2[1] (closed_form) = 1.54593259985 1.2519672926
absolute error = 0.3516
relative error = 17.67 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.54593259985 1.2519672926
y1[1] (closed_form) = 1.54593259985 1.2519672926
absolute error = 3.162e-31
relative error = 1.590e-29 %
Correct digits = 31
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) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22235.0MB, alloc=44.3MB, time=273.14
memory used=22282.4MB, alloc=44.3MB, time=273.73
x[1] = 0.3351 1.097
h = 0.001 0.001
y2[1] (numeric) = 1.24396283731 1.4365638466
y2[1] (closed_form) = 1.54739976343 1.25663385777
absolute error = 0.3528
relative error = 17.7 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.54739976343 1.25663385777
y1[1] (closed_form) = 1.54739976343 1.25663385777
absolute error = 3.162e-31
relative error = 1.586e-29 %
Correct digits = 31
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) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22329.1MB, alloc=44.3MB, time=274.30
memory used=22376.1MB, alloc=44.3MB, time=274.88
x[1] = 0.3361 1.098
h = 0.001 0.003
y2[1] (numeric) = 1.24522235665 1.4431881578
y2[1] (closed_form) = 1.5494105564 1.25776764231
absolute error = 0.3562
relative error = 17.85 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.5494105564 1.25776764231
y1[1] (closed_form) = 1.5494105564 1.25776764231
absolute error = 4.123e-31
relative error = 2.066e-29 %
Correct digits = 31
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) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22422.5MB, alloc=44.3MB, time=275.45
memory used=22469.5MB, alloc=44.3MB, time=276.03
x[1] = 0.3371 1.101
h = 0.0001 0.004
y2[1] (numeric) = 1.24649151743 1.44982976121
y2[1] (closed_form) = 1.5523074004 1.2620495499
absolute error = 0.3589
relative error = 17.94 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.5523074004 1.2620495499
y1[1] (closed_form) = 1.5523074004 1.2620495499
absolute error = 4.123e-31
relative error = 2.061e-29 %
Correct digits = 31
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) = 34.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22515.9MB, alloc=44.3MB, time=276.59
x[1] = 0.3372 1.105
h = 0.003 0.006
y2[1] (numeric) = 1.24777039302 1.45648870608
y2[1] (closed_form) = 1.55423919315 1.26831869129
absolute error = 0.3596
relative error = 17.93 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.55423919315 1.26831869129
y1[1] (closed_form) = 1.55423919315 1.26831869129
absolute error = 4.123e-31
relative error = 2.055e-29 %
Correct digits = 31
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) = 34.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22562.3MB, alloc=44.3MB, time=277.16
memory used=22609.4MB, alloc=44.3MB, time=277.73
x[1] = 0.3402 1.111
h = 0.0001 0.005
y2[1] (numeric) = 1.24905905707 1.46316504171
y2[1] (closed_form) = 1.56168017573 1.27647711538
absolute error = 0.3641
relative error = 18.05 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.56168017573 1.27647711538
y1[1] (closed_form) = 1.56168017573 1.27647711538
absolute error = 5.099e-31
relative error = 2.528e-29 %
Correct digits = 31
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) = 34.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22655.8MB, alloc=44.3MB, time=278.30
memory used=22702.8MB, alloc=44.3MB, time=278.88
x[1] = 0.3403 1.116
h = 0.0001 0.003
y2[1] (numeric) = 1.25035758426 1.46985881675
y2[1] (closed_form) = 1.5641056488 1.28438182348
absolute error = 0.3645
relative error = 18.01 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.5641056488 1.28438182348
y1[1] (closed_form) = 1.5641056488 1.28438182348
absolute error = 5.099e-31
relative error = 2.519e-29 %
Correct digits = 31
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) = 34.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22749.6MB, alloc=44.3MB, time=279.45
memory used=22797.0MB, alloc=44.3MB, time=280.04
x[1] = 0.3404 1.119
h = 0.001 0.001
y2[1] (numeric) = 1.25166605052 1.47657007939
y2[1] (closed_form) = 1.56563219128 1.28912150893
absolute error = 0.3657
relative error = 18.03 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.56563219128 1.28912150893
y1[1] (closed_form) = 1.56563219128 1.28912150893
absolute error = 4.123e-31
relative error = 2.033e-29 %
Correct digits = 31
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) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22843.5MB, alloc=44.3MB, time=280.61
x[1] = 0.3414 1.12
h = 0.001 0.003
y2[1] (numeric) = 1.25298453204 1.48329887816
y2[1] (closed_form) = 1.56768705832 1.29026134001
absolute error = 0.3692
relative error = 18.18 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.56768705832 1.29026134001
y1[1] (closed_form) = 1.56768705832 1.29026134001
absolute error = 5.385e-31
relative error = 2.652e-29 %
Correct digits = 31
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) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22890.2MB, alloc=44.3MB, time=281.18
memory used=22937.2MB, alloc=44.3MB, time=281.76
x[1] = 0.3424 1.123
h = 0.0001 0.004
y2[1] (numeric) = 1.25431310508 1.49004526163
y2[1] (closed_form) = 1.57066625793 1.29459948589
absolute error = 0.3719
relative error = 18.27 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.57066625793 1.29459948589
y1[1] (closed_form) = 1.57066625793 1.29459948589
absolute error = 5.099e-31
relative error = 2.505e-29 %
Correct digits = 31
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) = 34.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22983.7MB, alloc=44.3MB, time=282.32
memory used=23030.6MB, alloc=44.3MB, time=282.90
x[1] = 0.3425 1.127
h = 0.003 0.006
y2[1] (numeric) = 1.25565184598 1.49680927841
y2[1] (closed_form) = 1.57267723182 1.30096755446
absolute error = 0.3726
relative error = 18.26 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.57267723182 1.30096755446
y1[1] (closed_form) = 1.57267723182 1.30096755446
absolute error = 5.099e-31
relative error = 2.498e-29 %
Correct digits = 31
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) = 34.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23077.0MB, alloc=44.3MB, time=283.46
memory used=23124.0MB, alloc=44.3MB, time=284.04
x[1] = 0.3455 1.133
h = 0.0001 0.005
y2[1] (numeric) = 1.2570008313 1.50359097715
y2[1] (closed_form) = 1.58031009893 1.30922012769
absolute error = 0.3772
relative error = 18.38 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.58031009893 1.30922012769
y1[1] (closed_form) = 1.58031009893 1.30922012769
absolute error = 5.099e-31
relative error = 2.485e-29 %
Correct digits = 31
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) = 34.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23170.4MB, alloc=44.3MB, time=284.61
x[1] = 0.3456 1.138
h = 0.0001 0.003
y2[1] (numeric) = 1.25836013873 1.51039040583
y2[1] (closed_form) = 1.58283542697 1.31725037387
absolute error = 0.3776
relative error = 18.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.58283542697 1.31725037387
y1[1] (closed_form) = 1.58283542697 1.31725037387
absolute error = 5.099e-31
relative error = 2.476e-29 %
Correct digits = 31
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) = 34.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23217.2MB, alloc=44.3MB, time=285.18
memory used=23264.4MB, alloc=44.3MB, time=285.76
x[1] = 0.3457 1.141
h = 0.001 0.001
y2[1] (numeric) = 1.25972984717 1.51720761195
y2[1] (closed_form) = 1.58442314971 1.3220649845
absolute error = 0.3788
relative error = 18.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.58442314971 1.3220649845
y1[1] (closed_form) = 1.58442314971 1.3220649845
absolute error = 5.099e-31
relative error = 2.471e-29 %
Correct digits = 31
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) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23311.1MB, alloc=44.3MB, time=286.34
memory used=23358.0MB, alloc=44.3MB, time=286.92
x[1] = 0.3467 1.142
h = 0.001 0.003
y2[1] (numeric) = 1.26111003586 1.52404264334
y2[1] (closed_form) = 1.58652329352 1.32321090258
absolute error = 0.3824
relative error = 18.51 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.58652329352 1.32321090258
y1[1] (closed_form) = 1.58652329352 1.32321090258
absolute error = 5.099e-31
relative error = 2.468e-29 %
Correct digits = 31
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) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23404.5MB, alloc=44.3MB, time=287.49
memory used=23451.5MB, alloc=44.3MB, time=288.08
x[1] = 0.3477 1.145
h = 0.0001 0.004
y2[1] (numeric) = 1.26250078405 1.53089554792
y2[1] (closed_form) = 1.58958721874 1.32760656979
absolute error = 0.3851
relative error = 18.59 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.58958721874 1.32760656979
y1[1] (closed_form) = 1.58958721874 1.32760656979
absolute error = 5e-31
relative error = 2.414e-29 %
Correct digits = 31
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) = 34.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23498.0MB, alloc=44.3MB, time=288.64
x[1] = 0.3478 1.149
h = 0.003 0.006
y2[1] (numeric) = 1.26390217111 1.53776637361
y2[1] (closed_form) = 1.59167977579 1.33407599991
absolute error = 0.3859
relative error = 18.58 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.59167977579 1.33407599991
y1[1] (closed_form) = 1.59167977579 1.33407599991
absolute error = 5.099e-31
relative error = 2.455e-29 %
Correct digits = 31
memory used=23544.9MB, alloc=44.3MB, time=289.22
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) = 34.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23591.4MB, alloc=44.3MB, time=289.78
x[1] = 0.3508 1.155
h = 0.0001 0.005
y2[1] (numeric) = 1.26531427663 1.54465516838
y2[1] (closed_form) = 1.59950993207 1.3424247047
absolute error = 0.3906
relative error = 18.71 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.59950993207 1.3424247047
y1[1] (closed_form) = 1.59950993207 1.3424247047
absolute error = 5e-31
relative error = 2.394e-29 %
Correct digits = 31
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) = 34.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23638.0MB, alloc=44.3MB, time=290.36
memory used=23685.0MB, alloc=44.3MB, time=290.93
x[1] = 0.3509 1.16
h = 0.0001 0.003
y2[1] (numeric) = 1.26673718134 1.5515619795
y2[1] (closed_form) = 1.60213813922 1.35058356117
absolute error = 0.391
relative error = 18.66 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.60213813922 1.35058356117
y1[1] (closed_form) = 1.60213813922 1.35058356117
absolute error = 5e-31
relative error = 2.386e-29 %
Correct digits = 31
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) = 34.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23731.6MB, alloc=44.3MB, time=291.50
memory used=23779.1MB, alloc=44.3MB, time=292.10
x[1] = 0.351 1.163
h = 0.001 0.001
y2[1] (numeric) = 1.26817096724 1.55848685378
y2[1] (closed_form) = 1.60378888895 1.3554749218
absolute error = 0.3922
relative error = 18.68 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.60378888895 1.3554749218
y1[1] (closed_form) = 1.60378888895 1.3554749218
absolute error = 5e-31
relative error = 2.381e-29 %
Correct digits = 31
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) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23825.8MB, alloc=44.3MB, time=292.67
x[1] = 0.352 1.164
h = 0.001 0.003
y2[1] (numeric) = 1.26961571664 1.56542983834
y2[1] (closed_form) = 1.60593553428 1.35662695953
absolute error = 0.3959
relative error = 18.83 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.60593553428 1.35662695953
y1[1] (closed_form) = 1.60593553428 1.35662695953
absolute error = 5e-31
relative error = 2.378e-29 %
Correct digits = 31
memory used=23872.6MB, alloc=44.3MB, time=293.25
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) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23919.3MB, alloc=44.3MB, time=293.82
x[1] = 0.353 1.167
h = 0.0001 0.004
y2[1] (numeric) = 1.27107151192 1.57239098038
y2[1] (closed_form) = 1.60908660719 1.36108143761
absolute error = 0.3986
relative error = 18.91 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.60908660719 1.36108143761
y1[1] (closed_form) = 1.60908660719 1.36108143761
absolute error = 5e-31
relative error = 2.372e-29 %
Correct digits = 31
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) = 34.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23965.7MB, alloc=44.3MB, time=294.39
memory used=24012.5MB, alloc=44.3MB, time=294.96
x[1] = 0.3531 1.171
h = 0.003 0.006
y2[1] (numeric) = 1.27253843551 1.57937032711
y2[1] (closed_form) = 1.6112632102 1.3676546908
absolute error = 0.3994
relative error = 18.9 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.6112632102 1.3676546908
y1[1] (closed_form) = 1.6112632102 1.3676546908
absolute error = 6e-31
relative error = 2.839e-29 %
Correct digits = 31
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) = 34.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24058.9MB, alloc=44.3MB, time=295.54
memory used=24105.9MB, alloc=44.3MB, time=296.11
x[1] = 0.3561 1.177
h = 0.0001 0.005
y2[1] (numeric) = 1.27401657012 1.58636792581
y2[1] (closed_form) = 1.61929617267 1.37610150738
absolute error = 0.4043
relative error = 19.02 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.61929617267 1.37610150738
y1[1] (closed_form) = 1.61929617267 1.37610150738
absolute error = 6e-31
relative error = 2.823e-29 %
Correct digits = 31
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) = 34.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24152.4MB, alloc=44.3MB, time=296.68
memory used=24199.3MB, alloc=44.3MB, time=297.26
x[1] = 0.3562 1.182
h = 0.0001 0.003
y2[1] (numeric) = 1.27550599962 1.59338382302
y2[1] (closed_form) = 1.62203035999 1.38439208101
absolute error = 0.4047
relative error = 18.98 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.62203035999 1.38439208101
y1[1] (closed_form) = 1.62203035999 1.38439208101
absolute error = 6.083e-31
relative error = 2.852e-29 %
Correct digits = 31
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) = 34.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24246.2MB, alloc=44.3MB, time=297.84
x[1] = 0.3563 1.185
h = 0.001 0.001
y2[1] (numeric) = 1.27700680916 1.60041806481
y2[1] (closed_form) = 1.62374603009 1.38936203674
absolute error = 0.4059
relative error = 18.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.62374603009 1.38936203674
y1[1] (closed_form) = 1.62374603009 1.38936203674
absolute error = 6.083e-31
relative error = 2.846e-29 %
Correct digits = 31
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) = 34.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24292.8MB, alloc=44.3MB, time=298.42
memory used=24339.8MB, alloc=44.3MB, time=299.00
x[1] = 0.3573 1.186
h = 0.0001 0.004
y2[1] (numeric) = 1.27851908423 1.60747069755
y2[1] (closed_form) = 1.62594042431 1.39052021872
absolute error = 0.4096
relative error = 19.14 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.62594042431 1.39052021872
y1[1] (closed_form) = 1.62594042431 1.39052021872
absolute error = 6.083e-31
relative error = 2.843e-29 %
Correct digits = 31
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) = 34.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24386.4MB, alloc=44.3MB, time=299.56
memory used=24433.3MB, alloc=44.3MB, time=300.14
x[1] = 0.3574 1.19
h = 0.003 0.006
y2[1] (numeric) = 1.28004291038 1.61454176774
y2[1] (closed_form) = 1.62819011401 1.3971858739
absolute error = 0.4104
relative error = 19.13 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.62819011401 1.3971858739
y1[1] (closed_form) = 1.62819011401 1.3971858739
absolute error = 6.083e-31
relative error = 2.835e-29 %
Correct digits = 31
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) = 34.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24479.7MB, alloc=44.3MB, time=300.70
memory used=24526.7MB, alloc=44.3MB, time=301.28
x[1] = 0.3604 1.196
h = 0.0001 0.005
y2[1] (numeric) = 1.28157837334 1.62163132194
y2[1] (closed_form) = 1.63640095039 1.40572123301
absolute error = 0.4154
relative error = 19.25 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.63640095039 1.40572123301
y1[1] (closed_form) = 1.63640095039 1.40572123301
absolute error = 6.083e-31
relative error = 2.820e-29 %
Correct digits = 31
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) = 34.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24573.2MB, alloc=44.3MB, time=301.85
x[1] = 0.3605 1.201
h = 0.0001 0.003
y2[1] (numeric) = 1.28312556004 1.62873940596
y2[1] (closed_form) = 1.6392272854 1.41412901341
absolute error = 0.4158
relative error = 19.21 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.6392272854 1.41412901341
y1[1] (closed_form) = 1.6392272854 1.41412901341
absolute error = 6.083e-31
relative error = 2.810e-29 %
Correct digits = 31
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) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24620.0MB, alloc=44.3MB, time=302.42
memory used=24667.4MB, alloc=44.3MB, time=303.02
x[1] = 0.3606 1.204
h = 0.001 0.001
y2[1] (numeric) = 1.28468455872 1.63586606512
y2[1] (closed_form) = 1.64099942297 1.41916891938
absolute error = 0.417
relative error = 19.22 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.64099942297 1.41916891938
y1[1] (closed_form) = 1.64099942297 1.41916891938
absolute error = 6.083e-31
relative error = 2.804e-29 %
Correct digits = 31
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) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24714.2MB, alloc=44.3MB, time=303.60
memory used=24761.1MB, alloc=44.3MB, time=304.17
x[1] = 0.3616 1.205
h = 0.001 0.003
y2[1] (numeric) = 1.28625545797 1.64301134507
y2[1] (closed_form) = 1.64323586099 1.42033299292
absolute error = 0.4207
relative error = 19.37 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.64323586099 1.42033299292
y1[1] (closed_form) = 1.64323586099 1.42033299292
absolute error = 6.083e-31
relative error = 2.801e-29 %
Correct digits = 31
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) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24807.7MB, alloc=44.3MB, time=304.74
memory used=24854.7MB, alloc=44.3MB, time=305.32
x[1] = 0.3626 1.208
h = 0.0001 0.004
y2[1] (numeric) = 1.28783834641 1.65017529154
y2[1] (closed_form) = 1.6465549888 1.42490146738
absolute error = 0.4236
relative error = 19.45 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.6465549888 1.42490146738
y1[1] (closed_form) = 1.6465549888 1.42490146738
absolute error = 5.099e-31
relative error = 2.342e-29 %
Correct digits = 31
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) = 34.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24901.0MB, alloc=44.3MB, time=305.88
x[1] = 0.3627 1.212
h = 0.003 0.006
y2[1] (numeric) = 1.28943331277 1.65735795028
y2[1] (closed_form) = 1.64889344487 1.43167563134
absolute error = 0.4244
relative error = 19.44 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.64889344487 1.43167563134
y1[1] (closed_form) = 1.64889344487 1.43167563134
absolute error = 5.099e-31
relative error = 2.335e-29 %
Correct digits = 31
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) = 34.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24947.7MB, alloc=44.3MB, time=306.45
memory used=24994.5MB, alloc=44.3MB, time=307.03
x[1] = 0.3657 1.218
h = 0.0001 0.005
y2[1] (numeric) = 1.29104044603 1.66455936709
y2[1] (closed_form) = 1.6573176391 1.44031284887
absolute error = 0.4295
relative error = 19.56 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.6573176391 1.44031284887
y1[1] (closed_form) = 1.6573176391 1.44031284887
absolute error = 5.099e-31
relative error = 2.322e-29 %
Correct digits = 31
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) = 34.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25041.0MB, alloc=44.3MB, time=307.59
memory used=25088.0MB, alloc=44.3MB, time=308.17
x[1] = 0.3658 1.223
h = 0.0001 0.003
y2[1] (numeric) = 1.2926598364 1.67177958701
y2[1] (closed_form) = 1.66025589862 1.44885826136
absolute error = 0.4299
relative error = 19.51 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.66025589862 1.44885826136
y1[1] (closed_form) = 1.66025589862 1.44885826136
absolute error = 5.385e-31
relative error = 2.444e-29 %
Correct digits = 31
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) = 34.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25134.7MB, alloc=44.3MB, time=308.74
memory used=25182.0MB, alloc=44.3MB, time=309.34
x[1] = 0.3659 1.226
h = 0.001 0.001
y2[1] (numeric) = 1.29429157544 1.67901865456
y2[1] (closed_form) = 1.66209658567 1.45398027503
absolute error = 0.4312
relative error = 19.53 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.66209658567 1.45398027503
y1[1] (closed_form) = 1.66209658567 1.45398027503
absolute error = 5.385e-31
relative error = 2.439e-29 %
Correct digits = 31
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) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25228.4MB, alloc=44.3MB, time=309.91
x[1] = 0.3669 1.227
h = 0.001 0.003
y2[1] (numeric) = 1.29593575505 1.68627661459
y2[1] (closed_form) = 1.66438315582 1.45515053172
absolute error = 0.4349
relative error = 19.67 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.66438315582 1.45515053172
y1[1] (closed_form) = 1.66438315582 1.45515053172
absolute error = 5.099e-31
relative error = 2.306e-29 %
Correct digits = 31
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) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25275.0MB, alloc=44.3MB, time=310.48
memory used=25321.9MB, alloc=44.3MB, time=311.05
x[1] = 0.3679 1.23
h = 0.0001 0.004
y2[1] (numeric) = 1.29759246719 1.69355351206
y2[1] (closed_form) = 1.66779664471 1.459781573
absolute error = 0.4378
relative error = 19.75 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.66779664471 1.459781573
y1[1] (closed_form) = 1.66779664471 1.459781573
absolute error = 5.099e-31
relative error = 2.301e-29 %
Correct digits = 31
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) = 34.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25368.3MB, alloc=44.3MB, time=311.62
memory used=25415.2MB, alloc=44.3MB, time=312.19
x[1] = 0.368 1.234
h = 0.003 0.006
y2[1] (numeric) = 1.29926180392 1.70084939192
y2[1] (closed_form) = 1.67022651316 1.46666678888
absolute error = 0.4387
relative error = 19.74 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.67022651316 1.46666678888
y1[1] (closed_form) = 1.67022651316 1.46666678888
absolute error = 5.385e-31
relative error = 2.423e-29 %
Correct digits = 31
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) = 34.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25461.6MB, alloc=44.3MB, time=312.76
memory used=25508.5MB, alloc=44.3MB, time=313.34
x[1] = 0.371 1.24
h = 0.0001 0.005
y2[1] (numeric) = 1.30094385756 1.70816429919
y2[1] (closed_form) = 1.67886992039 1.47540783806
absolute error = 0.4439
relative error = 19.86 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.67886992039 1.47540783806
y1[1] (closed_form) = 1.67886992039 1.47540783806
absolute error = 4.472e-31
relative error = 2.001e-29 %
Correct digits = 31
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) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25555.0MB, alloc=44.3MB, time=313.90
memory used=25602.1MB, alloc=44.3MB, time=314.48
x[1] = 0.3711 1.245
h = 0.0001 0.003
y2[1] (numeric) = 1.30263872167 1.71549827811
y2[1] (closed_form) = 1.68192343697 1.48409409343
absolute error = 0.4443
relative error = 19.81 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.68192343697 1.48409409343
y1[1] (closed_form) = 1.68192343697 1.48409409343
absolute error = 4.472e-31
relative error = 1.994e-29 %
Correct digits = 31
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) = 34.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25649.1MB, alloc=44.3MB, time=315.07
x[1] = 0.3712 1.248
h = 0.001 0.001
y2[1] (numeric) = 1.30434649121 1.72285137236
y2[1] (closed_form) = 1.68383470725 1.48930012076
absolute error = 0.4456
relative error = 19.82 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.68383470725 1.48930012076
y1[1] (closed_form) = 1.68383470725 1.48930012076
absolute error = 4.472e-31
relative error = 1.989e-29 %
Correct digits = 31
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) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25696.0MB, alloc=44.3MB, time=315.65
memory used=25742.9MB, alloc=44.3MB, time=316.23
x[1] = 0.3722 1.249
h = 0.001 0.003
y2[1] (numeric) = 1.30606726151 1.73022362598
y2[1] (closed_form) = 1.68617272495 1.49047656089
absolute error = 0.4494
relative error = 19.97 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.68617272495 1.49047656089
y1[1] (closed_form) = 1.68617272495 1.49047656089
absolute error = 4.472e-31
relative error = 1.987e-29 %
Correct digits = 31
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) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25789.4MB, alloc=44.3MB, time=316.80
memory used=25836.4MB, alloc=44.3MB, time=317.38
x[1] = 0.3732 1.252
h = 0.0001 0.004
y2[1] (numeric) = 1.30780112792 1.73761508309
y2[1] (closed_form) = 1.68968321127 1.4951714843
absolute error = 0.4523
relative error = 20.05 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.68968321127 1.4951714843
y1[1] (closed_form) = 1.68968321127 1.4951714843
absolute error = 4.472e-31
relative error = 1.982e-29 %
Correct digits = 31
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) = 34.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25882.9MB, alloc=44.3MB, time=317.94
memory used=25929.8MB, alloc=44.3MB, time=318.52
x[1] = 0.3733 1.256
h = 0.003 0.006
y2[1] (numeric) = 1.30954818592 1.74502578785
y2[1] (closed_form) = 1.69220720568 1.50217032453
absolute error = 0.4532
relative error = 20.03 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.69220720568 1.50217032453
y1[1] (closed_form) = 1.69220720568 1.50217032453
absolute error = 4.472e-31
relative error = 1.976e-29 %
Correct digits = 31
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) = 34.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25976.3MB, alloc=44.3MB, time=319.09
x[1] = 0.3763 1.262
h = 0.0001 0.005
y2[1] (numeric) = 1.31130853124 1.75245578446
y2[1] (closed_form) = 1.7010758052 1.51101717482
absolute error = 0.4585
relative error = 20.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.7010758052 1.51101717482
y1[1] (closed_form) = 1.7010758052 1.51101717482
absolute error = 4.472e-31
relative error = 1.966e-29 %
Correct digits = 31
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) = 34.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26022.8MB, alloc=44.3MB, time=319.66
memory used=26069.8MB, alloc=44.3MB, time=320.24
x[1] = 0.3764 1.267
h = 0.0001 0.003
y2[1] (numeric) = 1.31308226091 1.75990511629
y2[1] (closed_form) = 1.7042479968 1.51984752119
absolute error = 0.459
relative error = 20.1 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.7042479968 1.51984752119
y1[1] (closed_form) = 1.7042479968 1.51984752119
absolute error = 4.472e-31
relative error = 1.958e-29 %
Correct digits = 31
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) = 34.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26116.4MB, alloc=44.3MB, time=320.81
memory used=26163.6MB, alloc=44.3MB, time=321.40
x[1] = 0.3765 1.27
h = 0.001 0.001
y2[1] (numeric) = 1.31486947336 1.76737382619
y2[1] (closed_form) = 1.70623193585 1.52513948999
absolute error = 0.4603
relative error = 20.11 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.70623193585 1.52513948999
y1[1] (closed_form) = 1.70623193585 1.52513948999
absolute error = 3.162e-31
relative error = 1.382e-29 %
Correct digits = 31
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) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26210.1MB, alloc=44.3MB, time=321.97
memory used=26257.1MB, alloc=44.3MB, time=322.55
x[1] = 0.3775 1.271
h = 0.001 0.003
y2[1] (numeric) = 1.3166702674 1.77486195733
y2[1] (closed_form) = 1.70862274142 1.52632210466
absolute error = 0.4641
relative error = 20.26 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.70862274142 1.52632210466
y1[1] (closed_form) = 1.70862274142 1.52632210466
absolute error = 4.123e-31
relative error = 1.800e-29 %
Correct digits = 31
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) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26303.5MB, alloc=44.3MB, time=323.12
x[1] = 0.3785 1.274
h = 0.0001 0.004
y2[1] (numeric) = 1.3184847419 1.78236955301
y2[1] (closed_form) = 1.7122329206 1.53108223201
absolute error = 0.4671
relative error = 20.34 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.7122329206 1.53108223201
y1[1] (closed_form) = 1.7122329206 1.53108223201
absolute error = 3.162e-31
relative error = 1.377e-29 %
Correct digits = 31
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) = 34.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26349.9MB, alloc=44.3MB, time=323.68
memory used=26396.8MB, alloc=44.3MB, time=324.26
x[1] = 0.3786 1.278
h = 0.003 0.006
y2[1] (numeric) = 1.32031299582 1.7898966565
y2[1] (closed_form) = 1.71485382398 1.53819729889
absolute error = 0.468
relative error = 20.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.71485382398 1.53819729889
y1[1] (closed_form) = 1.71485382398 1.53819729889
absolute error = 4.472e-31
relative error = 1.941e-29 %
Correct digits = 31
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) = 34.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26443.4MB, alloc=44.3MB, time=324.83
memory used=26490.2MB, alloc=44.3MB, time=325.40
x[1] = 0.3816 1.284
h = 0.0001 0.005
y2[1] (numeric) = 1.32215512841 1.79744331117
y2[1] (closed_form) = 1.72395372242 1.54715191543
absolute error = 0.4734
relative error = 20.44 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.72395372242 1.54715191543
y1[1] (closed_form) = 1.72395372242 1.54715191543
absolute error = 4.123e-31
relative error = 1.780e-29 %
Correct digits = 31
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) = 34.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26536.7MB, alloc=44.3MB, time=325.97
memory used=26583.8MB, alloc=44.3MB, time=326.56
x[1] = 0.3817 1.289
h = 0.0001 0.003
y2[1] (numeric) = 1.32401124022 1.80500955952
y2[1] (closed_form) = 1.72724809471 1.55612963896
absolute error = 0.4739
relative error = 20.38 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.72724809471 1.55612963896
y1[1] (closed_form) = 1.72724809471 1.55612963896
absolute error = 4.472e-31
relative error = 1.924e-29 %
Correct digits = 31
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) = 34.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26630.5MB, alloc=44.3MB, time=327.13
x[1] = 0.3818 1.292
h = 0.001 0.001
y2[1] (numeric) = 1.32588143325 1.8125954435
y2[1] (closed_form) = 1.72930684123 1.56150949926
absolute error = 0.4752
relative error = 20.39 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.72930684123 1.56150949926
y1[1] (closed_form) = 1.72930684123 1.56150949926
absolute error = 4.472e-31
relative error = 1.919e-29 %
Correct digits = 31
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) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26677.5MB, alloc=44.3MB, time=327.72
memory used=26724.5MB, alloc=44.3MB, time=328.29
x[1] = 0.3828 1.293
h = 0.0001 0.004
y2[1] (numeric) = 1.3277658099 1.8202010054
y2[1] (closed_form) = 1.7317518005 1.56269827007
absolute error = 0.4791
relative error = 20.54 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.7317518005 1.56269827007
y1[1] (closed_form) = 1.7317518005 1.56269827007
absolute error = 4.472e-31
relative error = 1.917e-29 %
Correct digits = 31
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) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26770.9MB, alloc=44.3MB, time=328.86
memory used=26817.9MB, alloc=44.3MB, time=329.44
x[1] = 0.3829 1.297
h = 0.003 0.006
y2[1] (numeric) = 1.32966447263 1.82782628765
y2[1] (closed_form) = 1.73445697558 1.56991668882
absolute error = 0.48
relative error = 20.52 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.73445697558 1.56991668882
y1[1] (closed_form) = 1.73445697558 1.56991668882
absolute error = 4.472e-31
relative error = 1.912e-29 %
Correct digits = 31
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) = 35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26864.5MB, alloc=44.3MB, time=330.00
memory used=26911.4MB, alloc=44.3MB, time=330.58
x[1] = 0.3859 1.303
h = 0.0001 0.005
y2[1] (numeric) = 1.33157752409 1.83547133273
y2[1] (closed_form) = 1.7437596426 1.57896849362
absolute error = 0.4855
relative error = 20.64 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.7437596426 1.57896849362
y1[1] (closed_form) = 1.7437596426 1.57896849362
absolute error = 4.472e-31
relative error = 1.901e-29 %
Correct digits = 31
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) = 35.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26957.9MB, alloc=44.3MB, time=331.15
x[1] = 0.386 1.308
h = 0.0001 0.003
y2[1] (numeric) = 1.3335050683 1.84313618229
y2[1] (closed_form) = 1.74716025038 1.58807724939
absolute error = 0.486
relative error = 20.58 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.74716025038 1.58807724939
y1[1] (closed_form) = 1.74716025038 1.58807724939
absolute error = 4.472e-31
relative error = 1.894e-29 %
Correct digits = 31
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) = 35.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27004.8MB, alloc=44.3MB, time=331.72
memory used=27052.0MB, alloc=44.3MB, time=332.31
x[1] = 0.3861 1.311
h = 0.001 0.001
y2[1] (numeric) = 1.33544721074 1.85082087737
y2[1] (closed_form) = 1.74928406394 1.59353526936
absolute error = 0.4873
relative error = 20.59 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.74928406394 1.59353526936
y1[1] (closed_form) = 1.74928406394 1.59353526936
absolute error = 4.472e-31
relative error = 1.890e-29 %
Correct digits = 31
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) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27098.7MB, alloc=44.3MB, time=332.90
memory used=27145.6MB, alloc=44.3MB, time=333.47
x[1] = 0.3871 1.312
h = 0.001 0.003
y2[1] (numeric) = 1.33740405728 1.85852545938
y2[1] (closed_form) = 1.75177667772 1.59472998465
absolute error = 0.4912
relative error = 20.74 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.75177667772 1.59472998465
y1[1] (closed_form) = 1.75177667772 1.59472998465
absolute error = 4.472e-31
relative error = 1.888e-29 %
Correct digits = 31
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) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27192.2MB, alloc=44.3MB, time=334.04
memory used=27239.1MB, alloc=44.3MB, time=334.62
x[1] = 0.3881 1.315
h = 0.0001 0.004
y2[1] (numeric) = 1.33937571386 1.86624996983
y2[1] (closed_form) = 1.75557893084 1.59961624775
absolute error = 0.4943
relative error = 20.81 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.75557893084 1.59961624775
y1[1] (closed_form) = 1.75557893084 1.59961624775
absolute error = 4.243e-31
relative error = 1.786e-29 %
Correct digits = 31
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) = 35.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27285.6MB, alloc=44.3MB, time=335.18
x[1] = 0.3882 1.319
h = 0.003 0.006
y2[1] (numeric) = 1.34136228652 1.87399445025
y2[1] (closed_form) = 1.75838635273 1.60695585189
absolute error = 0.4952
relative error = 20.79 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.75838635273 1.60695585189
y1[1] (closed_form) = 1.75838635273 1.60695585189
absolute error = 3.606e-31
relative error = 1.514e-29 %
Correct digits = 31
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) = 35.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27332.2MB, alloc=44.3MB, time=335.75
memory used=27379.0MB, alloc=44.3MB, time=336.32
x[1] = 0.3912 1.325
h = 0.0001 0.005
y2[1] (numeric) = 1.34336388157 1.88175894223
y2[1] (closed_form) = 1.76793200853 1.61611914291
absolute error = 0.5008
relative error = 20.91 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.76793200853 1.61611914291
y1[1] (closed_form) = 1.76793200853 1.61611914291
absolute error = 4.243e-31
relative error = 1.771e-29 %
Correct digits = 31
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) = 35.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27425.3MB, alloc=44.3MB, time=336.89
memory used=27472.3MB, alloc=44.3MB, time=337.47
x[1] = 0.3913 1.33
h = 0.0001 0.003
y2[1] (numeric) = 1.34538060673 1.88954348646
y2[1] (closed_form) = 1.77146152156 1.62538153844
absolute error = 0.5013
relative error = 20.85 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.77146152156 1.62538153844
y1[1] (closed_form) = 1.77146152156 1.62538153844
absolute error = 4.243e-31
relative error = 1.765e-29 %
Correct digits = 31
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) = 35.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27518.9MB, alloc=44.3MB, time=338.04
memory used=27566.3MB, alloc=44.3MB, time=338.63
x[1] = 0.3914 1.333
h = 0.001 0.001
y2[1] (numeric) = 1.34741257122 1.89734812302
y2[1] (closed_form) = 1.77366424479 1.63093116603
absolute error = 0.5027
relative error = 20.86 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.77366424479 1.63093116603
y1[1] (closed_form) = 1.77366424479 1.63093116603
absolute error = 4.243e-31
relative error = 1.761e-29 %
Correct digits = 31
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) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27612.8MB, alloc=44.3MB, time=339.20
x[1] = 0.3924 1.334
h = 0.001 0.003
y2[1] (numeric) = 1.34945988464 1.90517289239
y2[1] (closed_form) = 1.77621362428 1.63213199384
absolute error = 0.5066
relative error = 21 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.77621362428 1.63213199384
y1[1] (closed_form) = 1.77621362428 1.63213199384
absolute error = 4.243e-31
relative error = 1.759e-29 %
Correct digits = 31
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) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27659.7MB, alloc=44.3MB, time=339.78
memory used=27706.4MB, alloc=44.3MB, time=340.35
x[1] = 0.3934 1.337
h = 0.0001 0.004
y2[1] (numeric) = 1.35152265668 1.91301783513
y2[1] (closed_form) = 1.78012360568 1.63708731254
absolute error = 0.5097
relative error = 21.08 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.78012360568 1.63708731254
y1[1] (closed_form) = 1.78012360568 1.63708731254
absolute error = 4.243e-31
relative error = 1.754e-29 %
Correct digits = 31
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) = 35.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27752.9MB, alloc=44.3MB, time=340.91
memory used=27799.8MB, alloc=44.3MB, time=341.49
x[1] = 0.3935 1.341
h = 0.003 0.006
y2[1] (numeric) = 1.35360099713 1.9208829918
y2[1] (closed_form) = 1.78303626608 1.64455079361
absolute error = 0.5107
relative error = 21.05 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.78303626608 1.64455079361
y1[1] (closed_form) = 1.78303626608 1.64455079361
absolute error = 4.243e-31
relative error = 1.749e-29 %
Correct digits = 31
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) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27846.3MB, alloc=44.3MB, time=342.06
memory used=27893.4MB, alloc=44.3MB, time=342.63
x[1] = 0.3965 1.347
h = 0.0001 0.005
y2[1] (numeric) = 1.35569501606 1.92876840306
y2[1] (closed_form) = 1.79283139978 1.6538275224
absolute error = 0.5164
relative error = 21.17 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.79283139978 1.6538275224
y1[1] (closed_form) = 1.79283139978 1.6538275224
absolute error = 4.243e-31
relative error = 1.739e-29 %
Correct digits = 31
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) = 35.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27939.8MB, alloc=44.3MB, time=343.20
memory used=27986.8MB, alloc=44.3MB, time=343.78
x[1] = 0.3966 1.352
h = 0.0001 0.003
y2[1] (numeric) = 1.35780482498 1.93667410863
y2[1] (closed_form) = 1.79649358741 1.66324695748
absolute error = 0.5169
relative error = 21.11 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.79649358741 1.66324695748
y1[1] (closed_form) = 1.79649358741 1.66324695748
absolute error = 4.243e-31
relative error = 1.733e-29 %
Correct digits = 31
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) = 35.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28033.6MB, alloc=44.3MB, time=344.36
x[1] = 0.3967 1.355
h = 0.001 0.001
y2[1] (numeric) = 1.35993053692 1.94460014758
y2[1] (closed_form) = 1.79877751885 1.66889020918
absolute error = 0.5183
relative error = 21.12 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.79877751885 1.66889020918
y1[1] (closed_form) = 1.79877751885 1.66889020918
absolute error = 4.243e-31
relative error = 1.729e-29 %
Correct digits = 31
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) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28080.4MB, alloc=44.3MB, time=344.93
memory used=28127.3MB, alloc=44.3MB, time=345.51
x[1] = 0.3977 1.356
h = 0.001 0.003
y2[1] (numeric) = 1.36207226533 1.95254655941
y2[1] (closed_form) = 1.80138510642 1.67009710244
absolute error = 0.5223
relative error = 21.26 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.80138510642 1.67009710244
y1[1] (closed_form) = 1.80138510642 1.67009710244
absolute error = 4.243e-31
relative error = 1.727e-29 %
Correct digits = 31
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) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28173.7MB, alloc=44.3MB, time=346.08
memory used=28220.8MB, alloc=44.3MB, time=346.66
x[1] = 0.3987 1.359
h = 0.0001 0.004
y2[1] (numeric) = 1.36423012373 1.96051338371
y2[1] (closed_form) = 1.80540575442 1.67512282409
absolute error = 0.5254
relative error = 21.33 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.80540575442 1.67512282409
y1[1] (closed_form) = 1.80540575442 1.67512282409
absolute error = 4.243e-31
relative error = 1.723e-29 %
Correct digits = 31
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) = 35.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28267.1MB, alloc=44.3MB, time=347.23
memory used=28314.2MB, alloc=44.3MB, time=347.81
x[1] = 0.3988 1.363
h = 0.003 0.006
y2[1] (numeric) = 1.36640422575 1.96850066004
y2[1] (closed_form) = 1.8084267219 1.68271290559
absolute error = 0.5264
relative error = 21.31 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.8084267219 1.68271290559
y1[1] (closed_form) = 1.8084267219 1.68271290559
absolute error = 3.606e-31
relative error = 1.460e-29 %
Correct digits = 31
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) = 35.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28360.7MB, alloc=44.3MB, time=348.37
x[1] = 0.4018 1.369
h = 0.0001 0.005
y2[1] (numeric) = 1.36859468531 1.97650842808
y2[1] (closed_form) = 1.81847796281 1.69210501722
absolute error = 0.5322
relative error = 21.43 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.81847796281 1.69210501722
y1[1] (closed_form) = 1.81847796281 1.69210501722
absolute error = 4.243e-31
relative error = 1.708e-29 %
Correct digits = 31
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) = 35.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28407.1MB, alloc=44.3MB, time=348.94
memory used=28454.1MB, alloc=44.3MB, time=349.51
x[1] = 0.4019 1.374
h = 0.0001 0.003
y2[1] (numeric) = 1.37080161779 1.98453672653
y2[1] (closed_form) = 1.8222766915 1.70168493229
absolute error = 0.5328
relative error = 21.37 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.8222766915 1.70168493229
y1[1] (closed_form) = 1.8222766915 1.70168493229
absolute error = 3.606e-31
relative error = 1.446e-29 %
Correct digits = 31
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) = 35.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28500.6MB, alloc=44.3MB, time=350.09
memory used=28548.1MB, alloc=44.3MB, time=350.68
x[1] = 0.402 1.377
h = 0.001 0.001
y2[1] (numeric) = 1.37302514013 1.99258559346
y2[1] (closed_form) = 1.82464418855 1.70742384834
absolute error = 0.5341
relative error = 21.37 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.82464418855 1.70742384834
y1[1] (closed_form) = 1.82464418855 1.70742384834
absolute error = 3.606e-31
relative error = 1.443e-29 %
Correct digits = 31
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) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28594.7MB, alloc=44.3MB, time=351.26
memory used=28641.6MB, alloc=44.3MB, time=351.83
x[1] = 0.403 1.378
h = 0.001 0.003
y2[1] (numeric) = 1.37526536973 2.0006550673
y2[1] (closed_form) = 1.82731145453 1.70863674915
absolute error = 0.5382
relative error = 21.51 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.82731145453 1.70863674915
y1[1] (closed_form) = 1.82731145453 1.70863674915
absolute error = 3.606e-31
relative error = 1.441e-29 %
Correct digits = 31
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) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28688.1MB, alloc=44.3MB, time=352.41
x[1] = 0.404 1.381
h = 0.0001 0.004
y2[1] (numeric) = 1.37752242402 2.00874518664
y2[1] (closed_form) = 1.83144577433 1.71373422742
absolute error = 0.5414
relative error = 21.58 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.83144577433 1.71373422742
y1[1] (closed_form) = 1.83144577433 1.71373422742
absolute error = 3.606e-31
relative error = 1.438e-29 %
Correct digits = 31
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) = 35.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28734.6MB, alloc=44.3MB, time=352.97
memory used=28781.4MB, alloc=44.3MB, time=353.54
x[1] = 0.4041 1.385
h = 0.003 0.006
y2[1] (numeric) = 1.37979642056 2.01685599002
y2[1] (closed_form) = 1.83457819635 1.72145366529
absolute error = 0.5423
relative error = 21.56 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.83457819635 1.72145366529
y1[1] (closed_form) = 1.83457819635 1.72145366529
absolute error = 3.606e-31
relative error = 1.433e-29 %
Correct digits = 31
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) = 35.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28827.8MB, alloc=44.3MB, time=354.11
memory used=28874.8MB, alloc=44.3MB, time=354.69
x[1] = 0.4071 1.391
h = 0.0001 0.005
y2[1] (numeric) = 1.38208747722 2.02498751609
y2[1] (closed_form) = 1.84489231748 1.73096309771
absolute error = 0.5483
relative error = 21.67 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.84489231748 1.73096309771
y1[1] (closed_form) = 1.84489231748 1.73096309771
absolute error = 3.606e-31
relative error = 1.425e-29 %
Correct digits = 31
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) = 35.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28921.3MB, alloc=44.3MB, time=355.26
memory used=28968.4MB, alloc=44.3MB, time=355.84
x[1] = 0.4072 1.396
h = 0.0001 0.003
y2[1] (numeric) = 1.38439571335 2.03313980251
y2[1] (closed_form) = 1.84883155335 1.74070697454
absolute error = 0.5488
relative error = 21.61 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.84883155335 1.74070697454
y1[1] (closed_form) = 1.84883155335 1.74070697454
absolute error = 3.606e-31
relative error = 1.420e-29 %
Correct digits = 31
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) = 35.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29015.1MB, alloc=44.3MB, time=356.42
x[1] = 0.4073 1.399
h = 0.001 0.001
y2[1] (numeric) = 1.3867212499 2.04131288626
y2[1] (closed_form) = 1.85128503383 1.7465436193
absolute error = 0.5502
relative error = 21.62 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.85128503383 1.7465436193
y1[1] (closed_form) = 1.85128503383 1.7465436193
absolute error = 3.606e-31
relative error = 1.417e-29 %
Correct digits = 31
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) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29061.9MB, alloc=44.3MB, time=357.00
memory used=29108.8MB, alloc=44.3MB, time=357.57
x[1] = 0.4083 1.4
h = 0.003 0.006
y2[1] (numeric) = 1.38906420827 2.04950680473
y2[1] (closed_form) = 1.85401347716 1.74776245861
absolute error = 0.5543
relative error = 21.75 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.85401347716 1.74776245861
y1[1] (closed_form) = 1.85401347716 1.74776245861
absolute error = 3.606e-31
relative error = 1.415e-29 %
Correct digits = 31
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) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29155.4MB, alloc=44.3MB, time=358.13
memory used=29202.5MB, alloc=44.3MB, time=358.71
x[1] = 0.4113 1.406
h = 0.0001 0.005
y2[1] (numeric) = 1.39142471005 2.05772159531
y2[1] (closed_form) = 1.86451544948 1.75734688534
absolute error = 0.5604
relative error = 21.87 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.86451544948 1.75734688534
y1[1] (closed_form) = 1.86451544948 1.75734688534
absolute error = 5.000e-31
relative error = 1.951e-29 %
Correct digits = 31
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) = 35.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29248.8MB, alloc=44.3MB, time=359.28
memory used=29295.7MB, alloc=44.3MB, time=359.86
x[1] = 0.4114 1.411
h = 0.0001 0.003
y2[1] (numeric) = 1.39380287819 2.06595729421
y2[1] (closed_form) = 1.86855792855 1.76720192988
absolute error = 0.5609
relative error = 21.81 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.86855792855 1.76720192988
y1[1] (closed_form) = 1.86855792855 1.76720192988
absolute error = 5.000e-31
relative error = 1.944e-29 %
Correct digits = 31
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) = 35.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29342.5MB, alloc=44.3MB, time=360.43
x[1] = 0.4115 1.414
h = 0.001 0.001
y2[1] (numeric) = 1.39619883728 2.07421393693
y2[1] (closed_form) = 1.87107451533 1.77310477112
absolute error = 0.5623
relative error = 21.81 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.87107451533 1.77310477112
y1[1] (closed_form) = 1.87107451533 1.77310477112
absolute error = 4.243e-31
relative error = 1.646e-29 %
Correct digits = 31
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) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29389.6MB, alloc=44.3MB, time=361.01
memory used=29436.5MB, alloc=44.3MB, time=361.64
x[1] = 0.4125 1.415
h = 0.001 0.003
y2[1] (numeric) = 1.39861271235 2.08249155936
y2[1] (closed_form) = 1.87384607382 1.77432606248
absolute error = 0.5664
relative error = 21.95 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.87384607382 1.77432606248
y1[1] (closed_form) = 1.87384607382 1.77432606248
absolute error = 4.243e-31
relative error = 1.644e-29 %
Correct digits = 31
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) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29482.8MB, alloc=44.3MB, time=362.20
memory used=29529.8MB, alloc=44.3MB, time=362.78
x[1] = 0.4135 1.418
h = 0.0001 0.004
y2[1] (numeric) = 1.4010446285 2.09079019752
y2[1] (closed_form) = 1.87818114954 1.77954471017
absolute error = 0.5697
relative error = 22.02 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.87818114954 1.77954471017
y1[1] (closed_form) = 1.87818114954 1.77954471017
absolute error = 4.243e-31
relative error = 1.640e-29 %
Correct digits = 31
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) = 35.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29576.2MB, alloc=44.3MB, time=363.34
memory used=29623.1MB, alloc=44.3MB, time=363.92
x[1] = 0.4136 1.422
h = 0.003 0.006
y2[1] (numeric) = 1.40349471094 2.09910988744
y2[1] (closed_form) = 1.88151247317 1.78748584172
absolute error = 0.5706
relative error = 21.99 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.88151247317 1.78748584172
y1[1] (closed_form) = 1.88151247317 1.78748584172
absolute error = 4.243e-31
relative error = 1.635e-29 %
Correct digits = 31
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) = 35.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29669.6MB, alloc=44.3MB, time=364.49
x[1] = 0.4166 1.428
h = 0.0001 0.005
y2[1] (numeric) = 1.40596308522 2.10745066521
y2[1] (closed_form) = 1.8922891419 1.79719066332
absolute error = 0.5769
relative error = 22.1 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.8922891419 1.79719066332
y1[1] (closed_form) = 1.8922891419 1.79719066332
absolute error = 4.243e-31
relative error = 1.626e-29 %
Correct digits = 31
memory used=29716.6MB, alloc=44.3MB, time=365.07
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) = 35.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29763.3MB, alloc=44.3MB, time=365.64
x[1] = 0.4167 1.433
h = 0.0001 0.003
y2[1] (numeric) = 1.40844987842 2.11581256589
y2[1] (closed_form) = 1.89647914599 1.8072155364
absolute error = 0.5774
relative error = 22.04 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.89647914599 1.8072155364
y1[1] (closed_form) = 1.89647914599 1.8072155364
absolute error = 5.000e-31
relative error = 1.909e-29 %
Correct digits = 31
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) = 35.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29809.8MB, alloc=44.3MB, time=366.21
memory used=29857.1MB, alloc=44.3MB, time=366.81
x[1] = 0.4168 1.436
h = 0.001 0.001
y2[1] (numeric) = 1.41095521928 2.12419562382
y2[1] (closed_form) = 1.89908599201 1.81321958215
absolute error = 0.5788
relative error = 22.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.89908599201 1.81321958215
y1[1] (closed_form) = 1.89908599201 1.81321958215
absolute error = 5.000e-31
relative error = 1.904e-29 %
Correct digits = 31
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) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29903.8MB, alloc=44.3MB, time=367.39
memory used=29950.8MB, alloc=44.3MB, time=367.98
x[1] = 0.4178 1.437
h = 0.001 0.003
y2[1] (numeric) = 1.41347923701 2.13259987377
y2[1] (closed_form) = 1.90192132225 1.81444662962
absolute error = 0.5829
relative error = 22.18 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.90192132225 1.81444662962
y1[1] (closed_form) = 1.90192132225 1.81444662962
absolute error = 4.243e-31
relative error = 1.614e-29 %
Correct digits = 31
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) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29997.3MB, alloc=44.3MB, time=368.55
x[1] = 0.4188 1.44
h = 0.0001 0.004
y2[1] (numeric) = 1.41602206091 2.14102535064
y2[1] (closed_form) = 1.90637852656 1.8197406215
absolute error = 0.5862
relative error = 22.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.90637852656 1.8197406215
y1[1] (closed_form) = 1.90637852656 1.8197406215
absolute error = 4.243e-31
relative error = 1.610e-29 %
Correct digits = 31
memory used=30044.4MB, alloc=44.3MB, time=369.15
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) = 35.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30090.8MB, alloc=44.3MB, time=369.73
x[1] = 0.4189 1.444
h = 0.003 0.006
y2[1] (numeric) = 1.41858382037 2.1494720893
y2[1] (closed_form) = 1.90983024418 1.82781859604
absolute error = 0.5872
relative error = 22.21 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.90983024418 1.82781859604
y1[1] (closed_form) = 1.90983024418 1.82781859604
absolute error = 5.000e-31
relative error = 1.891e-29 %
Correct digits = 31
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) = 35.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30137.2MB, alloc=44.3MB, time=370.32
memory used=30184.3MB, alloc=44.3MB, time=370.92
x[1] = 0.4219 1.45
h = 0.0001 0.005
y2[1] (numeric) = 1.42116464512 2.15794012471
y2[1] (closed_form) = 1.92088878598 1.83764572385
absolute error = 0.5936
relative error = 22.33 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.92088878598 1.83764572385
y1[1] (closed_form) = 1.92088878598 1.83764572385
absolute error = 5.000e-31
relative error = 1.881e-29 %
Correct digits = 31
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) = 35.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30230.7MB, alloc=44.3MB, time=371.51
memory used=30277.8MB, alloc=44.3MB, time=372.11
x[1] = 0.422 1.455
h = 0.0001 0.003
y2[1] (numeric) = 1.42376466648 2.16642949076
y2[1] (closed_form) = 1.92523056339 1.84784401885
absolute error = 0.5941
relative error = 22.26 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.92523056339 1.84784401885
y1[1] (closed_form) = 1.92523056339 1.84784401885
absolute error = 5.000e-31
relative error = 1.874e-29 %
Correct digits = 31
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) = 35.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30324.5MB, alloc=44.3MB, time=372.72
memory used=30371.9MB, alloc=44.3MB, time=373.33
x[1] = 0.4221 1.458
h = 0.001 0.001
y2[1] (numeric) = 1.42638401744 2.17494022062
y2[1] (closed_form) = 1.92793025742 1.85395139853
absolute error = 0.5955
relative error = 22.26 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.92793025742 1.85395139853
y1[1] (closed_form) = 1.92793025742 1.85395139853
absolute error = 5.000e-31
relative error = 1.869e-29 %
Correct digits = 31
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) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30418.4MB, alloc=44.3MB, time=373.92
x[1] = 0.4231 1.459
h = 0.001 0.003
y2[1] (numeric) = 1.42902283152 2.18347234788
y2[1] (closed_form) = 1.93083093826 1.85518410029
absolute error = 0.5997
relative error = 22.39 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.93083093826 1.85518410029
y1[1] (closed_form) = 1.93083093826 1.85518410029
absolute error = 5.000e-31
relative error = 1.867e-29 %
Correct digits = 31
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) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30464.9MB, alloc=44.3MB, time=374.51
memory used=30512.1MB, alloc=44.3MB, time=375.12
x[1] = 0.4241 1.462
h = 0.0001 0.004
y2[1] (numeric) = 1.43168124227 2.19202590623
y2[1] (closed_form) = 1.93541353796 1.86055481053
absolute error = 0.603
relative error = 22.46 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.93541353796 1.86055481053
y1[1] (closed_form) = 1.93541353796 1.86055481053
absolute error = 5.000e-31
relative error = 1.862e-29 %
Correct digits = 31
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) = 35.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30558.7MB, alloc=44.3MB, time=375.71
memory used=30605.6MB, alloc=44.3MB, time=376.31
x[1] = 0.4242 1.466
h = 0.003 0.006
y2[1] (numeric) = 1.43435938337 2.20060092939
y2[1] (closed_form) = 1.93898910722 1.86877250597
absolute error = 0.604
relative error = 22.43 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.93898910722 1.86877250597
y1[1] (closed_form) = 1.93898910722 1.86877250597
absolute error = 5.831e-31
relative error = 2.165e-29 %
Correct digits = 31
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) = 35.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30652.1MB, alloc=44.3MB, time=376.92
memory used=30699.1MB, alloc=44.3MB, time=377.52
x[1] = 0.4272 1.472
h = 0.0001 0.005
y2[1] (numeric) = 1.43705738885 2.20919745113
y2[1] (closed_form) = 1.95033685578 1.87872384136
absolute error = 0.6105
relative error = 22.54 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.95033685578 1.87872384136
y1[1] (closed_form) = 1.95033685578 1.87872384136
absolute error = 4.472e-31
relative error = 1.651e-29 %
Correct digits = 31
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) = 35.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30745.6MB, alloc=44.3MB, time=378.11
x[1] = 0.4273 1.477
h = 0.0001 0.003
y2[1] (numeric) = 1.43977539434 2.21781550414
y2[1] (closed_form) = 1.95483476446 1.88909919533
absolute error = 0.611
relative error = 22.48 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.95483476446 1.88909919533
y1[1] (closed_form) = 1.95483476446 1.88909919533
absolute error = 5.385e-31
relative error = 1.981e-29 %
Correct digits = 31
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) = 35.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30792.1MB, alloc=44.3MB, time=378.70
memory used=30839.6MB, alloc=44.3MB, time=379.32
x[1] = 0.4274 1.48
h = 0.001 0.001
y2[1] (numeric) = 1.44251353722 2.22645512034
y2[1] (closed_form) = 1.95762996169 1.89531206382
absolute error = 0.6124
relative error = 22.47 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.95762996169 1.89531206382
y1[1] (closed_form) = 1.95762996169 1.89531206382
absolute error = 4.472e-31
relative error = 1.641e-29 %
Correct digits = 31
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) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30886.3MB, alloc=44.3MB, time=379.92
memory used=30933.4MB, alloc=44.3MB, time=380.51
x[1] = 0.4284 1.481
h = 0.0001 0.004
y2[1] (numeric) = 1.44527195536 2.2351163321
y2[1] (closed_form) = 1.96059760312 1.8965503054
absolute error = 0.6166
relative error = 22.6 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.96059760312 1.8965503054
y1[1] (closed_form) = 1.96059760312 1.8965503054
absolute error = 4.472e-31
relative error = 1.639e-29 %
Correct digits = 31
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) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30979.8MB, alloc=44.3MB, time=381.09
memory used=31026.8MB, alloc=44.3MB, time=381.68
x[1] = 0.4285 1.485
h = 0.003 0.006
y2[1] (numeric) = 1.44805078671 2.24379917192
y2[1] (closed_form) = 1.96428090481 1.90489213211
absolute error = 0.6175
relative error = 22.57 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.96428090481 1.90489213211
y1[1] (closed_form) = 1.96428090481 1.90489213211
absolute error = 5.000e-31
relative error = 1.827e-29 %
Correct digits = 31
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) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31073.3MB, alloc=44.3MB, time=382.25
x[1] = 0.4315 1.491
h = 0.0001 0.005
y2[1] (numeric) = 1.45085016949 2.25250367239
y2[1] (closed_form) = 1.97588207807 1.91495546245
absolute error = 0.6242
relative error = 22.68 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.97588207807 1.91495546245
y1[1] (closed_form) = 1.97588207807 1.91495546245
absolute error = 5.000e-31
relative error = 1.817e-29 %
Correct digits = 31
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) = 35.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31120.0MB, alloc=44.3MB, time=382.83
memory used=31167.1MB, alloc=44.3MB, time=383.42
x[1] = 0.4316 1.496
h = 0.0001 0.003
y2[1] (numeric) = 1.45367024354 2.26122986498
y2[1] (closed_form) = 1.98051578594 1.92548810173
absolute error = 0.6247
relative error = 22.62 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.98051578594 1.92548810173
y1[1] (closed_form) = 1.98051578594 1.92548810173
absolute error = 5.000e-31
relative error = 1.810e-29 %
Correct digits = 31
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) = 35.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31213.7MB, alloc=44.3MB, time=384.01
memory used=31261.0MB, alloc=44.3MB, time=384.61
x[1] = 0.4317 1.499
h = 0.001 0.001
y2[1] (numeric) = 1.45651115048 2.26997778039
y2[1] (closed_form) = 1.98339407536 1.93179469868
absolute error = 0.6261
relative error = 22.61 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.98339407536 1.93179469868
y1[1] (closed_form) = 1.98339407536 1.93179469868
absolute error = 5.000e-31
relative error = 1.806e-29 %
Correct digits = 31
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) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31307.7MB, alloc=44.3MB, time=385.20
memory used=31354.5MB, alloc=44.3MB, time=385.80
x[1] = 0.4327 1.5
h = 0.001 0.003
y2[1] (numeric) = 1.45937303243 2.27874744976
y2[1] (closed_form) = 1.98642060384 1.93303843142
absolute error = 0.6303
relative error = 22.74 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.98642060384 1.93303843142
y1[1] (closed_form) = 1.98642060384 1.93303843142
absolute error = 5.000e-31
relative error = 1.804e-29 %
Correct digits = 31
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) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31401.1MB, alloc=44.3MB, time=386.37
x[1] = 0.4337 1.503
h = 0.0001 0.004
y2[1] (numeric) = 1.46225603162 2.28753890433
y2[1] (closed_form) = 1.99124453546 1.93855716263
absolute error = 0.6337
relative error = 22.8 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.99124453546 1.93855716263
y1[1] (closed_form) = 1.99124453546 1.93855716263
absolute error = 5.000e-31
relative error = 1.799e-29 %
Correct digits = 31
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) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31447.9MB, alloc=44.3MB, time=386.94
memory used=31494.8MB, alloc=44.3MB, time=387.52
x[1] = 0.4338 1.507
h = 0.003 0.006
y2[1] (numeric) = 1.46516029035 2.29635217538
y2[1] (closed_form) = 1.99505832615 1.94704420219
absolute error = 0.6347
relative error = 22.77 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.99505832615 1.94704420219
y1[1] (closed_form) = 1.99505832615 1.94704420219
absolute error = 5.000e-31
relative error = 1.794e-29 %
Correct digits = 31
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) = 36.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31541.1MB, alloc=44.3MB, time=388.08
memory used=31588.2MB, alloc=44.3MB, time=388.67
x[1] = 0.4368 1.513
h = 0.0001 0.005
y2[1] (numeric) = 1.46808595132 2.30518729422
y2[1] (closed_form) = 2.00696276114 1.95723534058
absolute error = 0.6415
relative error = 22.88 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.00696276114 1.95723534058
y1[1] (closed_form) = 2.00696276114 1.95723534058
absolute error = 4.472e-31
relative error = 1.595e-29 %
Correct digits = 31
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) = 36.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31634.7MB, alloc=44.3MB, time=389.24
memory used=31681.7MB, alloc=44.3MB, time=389.82
x[1] = 0.4369 1.518
h = 0.0001 0.003
y2[1] (numeric) = 1.47103315888 2.31404429105
y2[1] (closed_form) = 2.01176096637 1.96795198011
absolute error = 0.642
relative error = 22.81 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.01176096637 1.96795198011
y1[1] (closed_form) = 2.01176096637 1.96795198011
absolute error = 4.472e-31
relative error = 1.589e-29 %
Correct digits = 31
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) = 36.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31728.5MB, alloc=44.3MB, time=390.41
x[1] = 0.437 1.521
h = 0.001 0.001
y2[1] (numeric) = 1.47400205921 2.32292319522
y2[1] (closed_form) = 2.014739856 1.97436817816
absolute error = 0.6433
relative error = 22.81 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.014739856 1.97436817816
y1[1] (closed_form) = 2.014739856 1.97436817816
absolute error = 5.000e-31
relative error = 1.773e-29 %
Correct digits = 31
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) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31775.7MB, alloc=44.3MB, time=391.01
memory used=31822.5MB, alloc=44.3MB, time=391.60
x[1] = 0.438 1.522
h = 0.001 0.003
y2[1] (numeric) = 1.476992799 2.33182403657
y2[1] (closed_form) = 2.01783642784 1.97561722263
absolute error = 0.6476
relative error = 22.93 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.01783642784 1.97561722263
y1[1] (closed_form) = 2.01783642784 1.97561722263
absolute error = 5.000e-31
relative error = 1.771e-29 %
Correct digits = 31
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) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31868.9MB, alloc=44.3MB, time=392.17
memory used=31916.0MB, alloc=44.3MB, time=392.76
x[1] = 0.439 1.525
h = 0.0001 0.004
y2[1] (numeric) = 1.48000552503 2.34074684504
y2[1] (closed_form) = 2.02279550466 1.98121667646
absolute error = 0.6511
relative error = 22.99 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.02279550466 1.98121667646
y1[1] (closed_form) = 2.02279550466 1.98121667646
absolute error = 5.000e-31
relative error = 1.766e-29 %
Correct digits = 31
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) = 36.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31962.5MB, alloc=44.3MB, time=393.33
memory used=32009.5MB, alloc=44.3MB, time=393.92
x[1] = 0.4391 1.529
h = 0.003 0.006
y2[1] (numeric) = 1.48304038419 2.34969165057
y2[1] (closed_form) = 2.02674350247 1.98985190887
absolute error = 0.652
relative error = 22.96 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.02674350247 1.98985190887
y1[1] (closed_form) = 2.02674350247 1.98985190887
absolute error = 4.243e-31
relative error = 1.494e-29 %
Correct digits = 31
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) = 36.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32056.0MB, alloc=44.3MB, time=394.50
x[1] = 0.4421 1.535
h = 0.0001 0.005
y2[1] (numeric) = 1.48609752376 2.35865848319
y2[1] (closed_form) = 2.03895900344 2.00017272536
absolute error = 0.6589
relative error = 23.07 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.03895900344 2.00017272536
y1[1] (closed_form) = 2.03895900344 2.00017272536
absolute error = 4.243e-31
relative error = 1.485e-29 %
Correct digits = 31
memory used=32102.9MB, alloc=44.3MB, time=395.08
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) = 36.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32149.5MB, alloc=44.3MB, time=395.66
x[1] = 0.4422 1.54
h = 0.0001 0.003
y2[1] (numeric) = 1.48917709271 2.36764737173
y2[1] (closed_form) = 2.04392639296 2.01107713205
absolute error = 0.6595
relative error = 23 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.04392639296 2.01107713205
y1[1] (closed_form) = 2.04392639296 2.01107713205
absolute error = 4.243e-31
relative error = 1.480e-29 %
Correct digits = 31
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) = 36.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32195.9MB, alloc=44.3MB, time=396.24
memory used=32243.4MB, alloc=44.3MB, time=396.84
x[1] = 0.4423 1.543
h = 0.001 0.001
y2[1] (numeric) = 1.49227924187 2.37665834419
y2[1] (closed_form) = 2.04700873732 2.01760516178
absolute error = 0.6608
relative error = 22.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.04700873732 2.01760516178
y1[1] (closed_form) = 2.04700873732 2.01760516178
absolute error = 4.243e-31
relative error = 1.476e-29 %
Correct digits = 31
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) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32290.1MB, alloc=44.3MB, time=397.43
memory used=32337.2MB, alloc=44.3MB, time=398.01
x[1] = 0.4433 1.544
h = 0.001 0.003
y2[1] (numeric) = 1.49540412261 2.38569142904
y2[1] (closed_form) = 2.05017705561 2.01885936525
absolute error = 0.6651
relative error = 23.11 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.05017705561 2.01885936525
y1[1] (closed_form) = 2.05017705561 2.01885936525
absolute error = 4.243e-31
relative error = 1.475e-29 %
Correct digits = 31
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) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32383.7MB, alloc=44.3MB, time=398.59
x[1] = 0.4443 1.547
h = 0.0001 0.004
y2[1] (numeric) = 1.49855188638 2.39474665485
y2[1] (closed_form) = 2.05527484447 2.02454093809
absolute error = 0.6686
relative error = 23.17 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.05527484447 2.02454093809
y1[1] (closed_form) = 2.05527484447 2.02454093809
absolute error = 5.657e-31
relative error = 1.961e-29 %
Correct digits = 31
memory used=32430.8MB, alloc=44.3MB, time=399.18
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) = 36.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32477.3MB, alloc=44.3MB, time=399.75
x[1] = 0.4444 1.551
h = 0.003 0.006
y2[1] (numeric) = 1.50172268475 2.40382405021
y2[1] (closed_form) = 2.05936086328 2.0333273796
absolute error = 0.6695
relative error = 23.13 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.05936086328 2.0333273796
y1[1] (closed_form) = 2.05936086328 2.0333273796
absolute error = 5.000e-31
relative error = 1.728e-29 %
Correct digits = 31
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) = 36.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32523.7MB, alloc=44.3MB, time=400.33
memory used=32570.6MB, alloc=44.3MB, time=400.91
x[1] = 0.4474 1.557
h = 0.0001 0.005
y2[1] (numeric) = 1.50491666968 2.41292364378
y2[1] (closed_form) = 2.07189540655 2.0437797308
absolute error = 0.6766
relative error = 23.25 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.07189540655 2.0437797308
y1[1] (closed_form) = 2.07189540655 2.0437797308
absolute error = 5.000e-31
relative error = 1.718e-29 %
Correct digits = 31
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) = 36.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32617.1MB, alloc=44.3MB, time=401.48
memory used=32664.1MB, alloc=44.3MB, time=402.06
x[1] = 0.4475 1.562
h = 0.0001 0.003
y2[1] (numeric) = 1.50813399487 2.42204546301
y2[1] (closed_form) = 2.0770367882 2.05487571776
absolute error = 0.6771
relative error = 23.17 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.0770367882 2.05487571776
y1[1] (closed_form) = 2.0770367882 2.05487571776
absolute error = 4.243e-31
relative error = 1.452e-29 %
Correct digits = 31
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) = 36.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32710.8MB, alloc=44.3MB, time=402.64
memory used=32758.2MB, alloc=44.3MB, time=403.25
x[1] = 0.4476 1.565
h = 0.001 0.001
y2[1] (numeric) = 1.51137481591 2.43118953446
y2[1] (closed_form) = 2.08022551506 2.06151783657
absolute error = 0.6784
relative error = 23.16 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.08022551506 2.06151783657
y1[1] (closed_form) = 2.08022551506 2.06151783657
absolute error = 4.243e-31
relative error = 1.449e-29 %
Correct digits = 31
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) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32804.6MB, alloc=44.3MB, time=403.82
x[1] = 0.4486 1.566
h = 0.001 0.003
y2[1] (numeric) = 1.51463928895 2.44035588519
y2[1] (closed_form) = 2.08346731681 2.06277703198
absolute error = 0.6827
relative error = 23.29 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.08346731681 2.06277703198
y1[1] (closed_form) = 2.08346731681 2.06277703198
absolute error = 4.243e-31
relative error = 1.447e-29 %
Correct digits = 31
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) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32851.0MB, alloc=44.3MB, time=404.40
memory used=32898.0MB, alloc=44.3MB, time=404.99
x[1] = 0.4496 1.569
h = 0.0001 0.004
y2[1] (numeric) = 1.51792757022 2.44954454237
y2[1] (closed_form) = 2.08870746695 2.06854212527
absolute error = 0.6863
relative error = 23.34 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.08870746695 2.06854212527
y1[1] (closed_form) = 2.08870746695 2.06854212527
absolute error = 3.606e-31
relative error = 1.227e-29 %
Correct digits = 31
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) = 36.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32944.5MB, alloc=44.3MB, time=405.56
memory used=32991.4MB, alloc=44.3MB, time=406.14
x[1] = 0.4497 1.573
h = 0.003 0.006
y2[1] (numeric) = 1.52123981608 2.45875553316
y2[1] (closed_form) = 2.09293541882 2.07748282889
absolute error = 0.6872
relative error = 23.3 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.09293541882 2.07748282889
y1[1] (closed_form) = 2.09293541882 2.07748282889
absolute error = 3.606e-31
relative error = 1.223e-29 %
Correct digits = 31
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) = 36.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33037.9MB, alloc=44.3MB, time=406.72
memory used=33084.9MB, alloc=44.3MB, time=407.31
x[1] = 0.4527 1.579
h = 0.0001 0.005
y2[1] (numeric) = 1.52457618328 2.46798888482
y2[1] (closed_form) = 2.10579715686 2.08806855701
absolute error = 0.6944
relative error = 23.41 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.10579715686 2.08806855701
y1[1] (closed_form) = 2.10579715686 2.08806855701
absolute error = 5.000e-31
relative error = 1.686e-29 %
Correct digits = 31
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) = 36.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33131.5MB, alloc=44.3MB, time=407.89
x[1] = 0.4528 1.584
h = 0.0001 0.003
y2[1] (numeric) = 1.52793683035 2.47724462335
y2[1] (closed_form) = 2.11111746249 2.09935998408
absolute error = 0.6949
relative error = 23.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.11111746249 2.09935998408
y1[1] (closed_form) = 2.11111746249 2.09935998408
absolute error = 5.000e-31
relative error = 1.679e-29 %
Correct digits = 31
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) = 36.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33178.2MB, alloc=44.3MB, time=408.47
memory used=33225.6MB, alloc=44.3MB, time=409.08
x[1] = 0.4529 1.587
h = 0.001 0.001
y2[1] (numeric) = 1.53132191774 2.48652277384
y2[1] (closed_form) = 2.11441557471 2.1061184766
absolute error = 0.6962
relative error = 23.33 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.11441557471 2.1061184766
y1[1] (closed_form) = 2.11441557471 2.1061184766
absolute error = 5.000e-31
relative error = 1.675e-29 %
Correct digits = 31
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) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33272.4MB, alloc=44.3MB, time=409.66
memory used=33319.4MB, alloc=44.3MB, time=410.25
x[1] = 0.4539 1.588
h = 0.0001 0.004
y2[1] (numeric) = 1.5347316065 2.49582336186
y2[1] (closed_form) = 2.1177326316 2.10738248198
absolute error = 0.7006
relative error = 23.45 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.1177326316 2.10738248198
y1[1] (closed_form) = 2.1177326316 2.10738248198
absolute error = 4.243e-31
relative error = 1.420e-29 %
Correct digits = 31
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) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33366.0MB, alloc=44.3MB, time=410.83
memory used=33412.8MB, alloc=44.3MB, time=411.42
x[1] = 0.454 1.592
h = 0.003 0.006
y2[1] (numeric) = 1.53816605776 2.50514641315
y2[1] (closed_form) = 2.12208407645 2.11646019845
absolute error = 0.7015
relative error = 23.4 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.12208407645 2.11646019845
y1[1] (closed_form) = 2.12208407645 2.11646019845
absolute error = 5.000e-31
relative error = 1.668e-29 %
Correct digits = 31
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) = 36.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33459.4MB, alloc=44.3MB, time=412.00
x[1] = 0.457 1.598
h = 0.0001 0.005
y2[1] (numeric) = 1.54162543293 2.51449195354
y2[1] (closed_form) = 2.13523250029 2.12716622938
absolute error = 0.7088
relative error = 23.52 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.13523250029 2.12716622938
y1[1] (closed_form) = 2.13523250029 2.12716622938
absolute error = 5.000e-31
relative error = 1.659e-29 %
Correct digits = 31
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) = 36.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33506.0MB, alloc=44.3MB, time=412.58
memory used=33552.9MB, alloc=44.3MB, time=413.17
x[1] = 0.4571 1.603
h = 0.0001 0.003
y2[1] (numeric) = 1.54510989525 2.52386000757
y2[1] (closed_form) = 2.14070847248 2.13863122546
absolute error = 0.7093
relative error = 23.44 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.14070847248 2.13863122546
y1[1] (closed_form) = 2.14070847248 2.13863122546
absolute error = 4.243e-31
relative error = 1.402e-29 %
Correct digits = 31
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) = 36.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33599.5MB, alloc=44.3MB, time=413.75
memory used=33646.8MB, alloc=44.3MB, time=414.36
x[1] = 0.4572 1.606
h = 0.001 0.001
y2[1] (numeric) = 1.54861960992 2.53325059887
y2[1] (closed_form) = 2.14410177957 2.14549309219
absolute error = 0.7106
relative error = 23.43 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.14410177957 2.14549309219
y1[1] (closed_form) = 2.14410177957 2.14549309219
absolute error = 4.243e-31
relative error = 1.399e-29 %
Correct digits = 31
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) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33693.5MB, alloc=44.3MB, time=414.95
memory used=33740.4MB, alloc=44.3MB, time=415.54
x[1] = 0.4582 1.607
h = 0.001 0.003
y2[1] (numeric) = 1.55215474272 2.54266375154
y2[1] (closed_form) = 2.14748500526 2.14676200624
absolute error = 0.715
relative error = 23.55 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.14748500526 2.14676200624
y1[1] (closed_form) = 2.14748500526 2.14676200624
absolute error = 3.606e-31
relative error = 1.187e-29 %
Correct digits = 31
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) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33786.9MB, alloc=44.3MB, time=416.12
x[1] = 0.4592 1.61
h = 0.0001 0.004
y2[1] (numeric) = 1.55571545952 2.55209948985
y2[1] (closed_form) = 2.15299902511 2.15268806063
absolute error = 0.7185
relative error = 23.6 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.15299902511 2.15268806063
y1[1] (closed_form) = 2.15299902511 2.15268806063
absolute error = 3.606e-31
relative error = 1.184e-29 %
Correct digits = 31
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) = 36.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33833.6MB, alloc=44.3MB, time=416.70
memory used=33880.3MB, alloc=44.3MB, time=417.29
x[1] = 0.4593 1.614
h = 0.003 0.006
y2[1] (numeric) = 1.55930192633 2.56155783802
y2[1] (closed_form) = 2.15749991496 2.16192586907
absolute error = 0.7194
relative error = 23.55 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.15749991496 2.16192586907
y1[1] (closed_form) = 2.15749991496 2.16192586907
absolute error = 5.000e-31
relative error = 1.637e-29 %
Correct digits = 31
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) = 36.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33926.8MB, alloc=44.3MB, time=417.86
memory used=33973.9MB, alloc=44.3MB, time=418.45
x[1] = 0.4623 1.62
h = 0.0001 0.005
y2[1] (numeric) = 1.56291430956 2.57103882038
y2[1] (closed_form) = 2.17099116495 2.17276876495
absolute error = 0.7269
relative error = 23.67 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.17099116495 2.17276876495
y1[1] (closed_form) = 2.17099116495 2.17276876495
absolute error = 5.000e-31
relative error = 1.628e-29 %
Correct digits = 31
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) = 36.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34020.5MB, alloc=44.3MB, time=419.04
memory used=34067.6MB, alloc=44.3MB, time=419.62
x[1] = 0.4624 1.625
h = 0.0001 0.003
y2[1] (numeric) = 1.56655277746 2.58054245994
y2[1] (closed_form) = 2.17665553172 2.18443657237
absolute error = 0.7274
relative error = 23.59 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.17665553172 2.18443657237
y1[1] (closed_form) = 2.17665553172 2.18443657237
absolute error = 5.000e-31
relative error = 1.621e-29 %
Correct digits = 31
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) = 36.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34114.3MB, alloc=44.3MB, time=420.21
x[1] = 0.4625 1.628
h = 0.001 0.001
y2[1] (numeric) = 1.57021750033 2.59006877871
y2[1] (closed_form) = 2.18016399027 2.19141917551
absolute error = 0.7287
relative error = 23.57 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.18016399027 2.19141917551
y1[1] (closed_form) = 2.18016399027 2.19141917551
absolute error = 5.000e-31
relative error = 1.618e-29 %
Correct digits = 31
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) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34161.5MB, alloc=44.3MB, time=420.80
memory used=34208.3MB, alloc=44.3MB, time=421.39
x[1] = 0.4635 1.629
h = 0.001 0.003
y2[1] (numeric) = 1.57390864904 2.59961779926
y2[1] (closed_form) = 2.18362586529 2.19269254182
absolute error = 0.733
relative error = 23.69 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.18362586529 2.19269254182
y1[1] (closed_form) = 2.18362586529 2.19269254182
absolute error = 5.000e-31
relative error = 1.616e-29 %
Correct digits = 31
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) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34254.8MB, alloc=44.3MB, time=421.96
memory used=34301.9MB, alloc=44.3MB, time=422.55
x[1] = 0.4645 1.632
h = 0.0001 0.004
y2[1] (numeric) = 1.57762639455 2.60918954427
y2[1] (closed_form) = 2.18929314216 2.19870619901
absolute error = 0.7366
relative error = 23.74 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.18929314216 2.19870619901
y1[1] (closed_form) = 2.18929314216 2.19870619901
absolute error = 5.831e-31
relative error = 1.879e-29 %
Correct digits = 31
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) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34348.4MB, alloc=44.3MB, time=423.13
memory used=34395.2MB, alloc=44.3MB, time=423.71
x[1] = 0.4646 1.636
h = 0.003 0.006
y2[1] (numeric) = 1.58137090797 2.61878403639
y2[1] (closed_form) = 2.19394768349 2.20810726147
absolute error = 0.7375
relative error = 23.69 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.19394768349 2.20810726147
y1[1] (closed_form) = 2.19394768349 2.20810726147
absolute error = 5.831e-31
relative error = 1.873e-29 %
Correct digits = 31
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) = 36.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34441.6MB, alloc=44.3MB, time=424.29
memory used=34488.6MB, alloc=44.3MB, time=424.88
x[1] = 0.4676 1.642
h = 0.0001 0.005
y2[1] (numeric) = 1.58514236083 2.6284012984
y2[1] (closed_form) = 2.20779043935 2.21908881943
absolute error = 0.7451
relative error = 23.8 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.20779043935 2.21908881943
y1[1] (closed_form) = 2.20779043935 2.21908881943
absolute error = 5.831e-31
relative error = 1.863e-29 %
Correct digits = 31
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) = 36.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34535.3MB, alloc=44.3MB, time=425.46
x[1] = 0.4677 1.647
h = 0.0001 0.003
y2[1] (numeric) = 1.58894092652 2.63804135168
y2[1] (closed_form) = 2.21364850434 2.23096343677
absolute error = 0.7456
relative error = 23.72 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.21364850434 2.23096343677
y1[1] (closed_form) = 2.21364850434 2.23096343677
absolute error = 5.831e-31
relative error = 1.855e-29 %
Correct digits = 31
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) = 36.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34581.9MB, alloc=44.3MB, time=426.04
memory used=34629.5MB, alloc=44.3MB, time=426.65
x[1] = 0.4678 1.65
h = 0.001 0.001
y2[1] (numeric) = 1.59276678052 2.64770421662
y2[1] (closed_form) = 2.21727534242 2.23806914163
absolute error = 0.7469
relative error = 23.71 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.21727534242 2.23806914163
y1[1] (closed_form) = 2.21727534242 2.23806914163
absolute error = 6.403e-31
relative error = 2.032e-29 %
Correct digits = 31
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) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34676.3MB, alloc=44.3MB, time=427.24
memory used=34723.2MB, alloc=44.3MB, time=427.84
x[1] = 0.4688 1.651
h = 0.001 0.003
y2[1] (numeric) = 1.59662009892 2.65738991416
y2[1] (closed_form) = 2.22081774208 2.23934673338
absolute error = 0.7513
relative error = 23.82 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.22081774208 2.23934673338
y1[1] (closed_form) = 2.22081774208 2.23934673338
absolute error = 6.403e-31
relative error = 2.030e-29 %
Correct digits = 31
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) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34769.6MB, alloc=44.3MB, time=428.41
memory used=34816.6MB, alloc=44.3MB, time=429.00
x[1] = 0.4698 1.654
h = 0.0001 0.004
y2[1] (numeric) = 1.60050105789 2.66709846533
y2[1] (closed_form) = 2.2266422623 2.24544941343
absolute error = 0.7549
relative error = 23.87 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.2266422623 2.24544941343
y1[1] (closed_form) = 2.2266422623 2.24544941343
absolute error = 6.403e-31
relative error = 2.025e-29 %
Correct digits = 31
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) = 36.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34863.1MB, alloc=44.3MB, time=429.58
x[1] = 0.4699 1.658
h = 0.003 0.006
y2[1] (numeric) = 1.60440983374 2.6768298912
y2[1] (closed_form) = 2.23145476971 2.25501693053
absolute error = 0.7557
relative error = 23.82 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.23145476971 2.25501693053
y1[1] (closed_form) = 2.23145476971 2.25501693053
absolute error = 6.403e-31
relative error = 2.018e-29 %
Correct digits = 31
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) = 36.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34909.6MB, alloc=44.3MB, time=430.16
memory used=34956.6MB, alloc=44.3MB, time=430.73
x[1] = 0.4729 1.664
h = 0.0001 0.005
y2[1] (numeric) = 1.60834660323 2.68658421287
y2[1] (closed_form) = 2.24565790377 2.26613892894
absolute error = 0.7635
relative error = 23.93 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.24565790377 2.26613892894
y1[1] (closed_form) = 2.24565790377 2.26613892894
absolute error = 5.657e-31
relative error = 1.773e-29 %
Correct digits = 31
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) = 37.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35003.1MB, alloc=44.3MB, time=431.30
memory used=35050.1MB, alloc=44.3MB, time=431.89
x[1] = 0.473 1.669
h = 0.0001 0.003
y2[1] (numeric) = 1.61231154503 2.69636145009
y2[1] (closed_form) = 2.25171510718 2.27822440391
absolute error = 0.764
relative error = 23.85 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.25171510718 2.27822440391
y1[1] (closed_form) = 2.25171510718 2.27822440391
absolute error = 6.403e-31
relative error = 1.999e-29 %
Correct digits = 31
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) = 37.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35096.8MB, alloc=44.3MB, time=432.48
memory used=35144.3MB, alloc=44.3MB, time=433.09
x[1] = 0.4731 1.672
h = 0.001 0.001
y2[1] (numeric) = 1.6163048399 2.70616162154
y2[1] (closed_form) = 2.25546363553 2.28545560429
absolute error = 0.7652
relative error = 23.83 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.25546363553 2.28545560429
y1[1] (closed_form) = 2.25546363553 2.28545560429
absolute error = 6.403e-31
relative error = 1.994e-29 %
Correct digits = 31
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) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35190.8MB, alloc=44.3MB, time=433.66
x[1] = 0.4741 1.673
h = 0.001 0.003
y2[1] (numeric) = 1.62032666926 2.71598474646
y2[1] (closed_form) = 2.25908847285 2.28673717781
absolute error = 0.7696
relative error = 23.94 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.25908847285 2.28673717781
y1[1] (closed_form) = 2.25908847285 2.28673717781
absolute error = 6.403e-31
relative error = 1.992e-29 %
Correct digits = 31
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) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35237.2MB, alloc=44.3MB, time=434.22
memory used=35284.3MB, alloc=44.3MB, time=434.80
x[1] = 0.4751 1.676
h = 0.0001 0.004
y2[1] (numeric) = 1.62437721461 2.72583084421
y2[1] (closed_form) = 2.26507431519 2.29293030469
absolute error = 0.7732
relative error = 23.99 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.26507431519 2.29293030469
y1[1] (closed_form) = 2.26507431519 2.29293030469
absolute error = 7.071e-31
relative error = 2.194e-29 %
Correct digits = 31
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) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35330.8MB, alloc=44.3MB, time=435.36
memory used=35377.7MB, alloc=44.3MB, time=435.94
x[1] = 0.4752 1.68
h = 0.003 0.006
y2[1] (numeric) = 1.6284566576 2.73569993416
y2[1] (closed_form) = 2.27004921414 2.30266751613
absolute error = 0.7741
relative error = 23.94 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.27004921414 2.30266751613
y1[1] (closed_form) = 2.27004921414 2.30266751613
absolute error = 5.657e-31
relative error = 1.749e-29 %
Correct digits = 31
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) = 37.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35424.3MB, alloc=44.3MB, time=436.50
memory used=35471.4MB, alloc=44.3MB, time=437.09
x[1] = 0.4782 1.686
h = 0.0001 0.005
y2[1] (numeric) = 1.63256518031 2.74559203574
y2[1] (closed_form) = 2.28462179578 2.31393171334
absolute error = 0.782
relative error = 24.05 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.28462179578 2.31393171334
y1[1] (closed_form) = 2.28462179578 2.31393171334
absolute error = 6.403e-31
relative error = 1.969e-29 %
Correct digits = 31
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) = 37.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35517.9MB, alloc=44.3MB, time=437.66
x[1] = 0.4783 1.691
h = 0.0001 0.003
y2[1] (numeric) = 1.63670296679 2.75550716696
y2[1] (closed_form) = 2.29088371777 2.32623214333
absolute error = 0.7825
relative error = 23.97 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.29088371777 2.32623214333
y1[1] (closed_form) = 2.29088371777 2.32623214333
absolute error = 5.657e-31
relative error = 1.733e-29 %
Correct digits = 31
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) = 37.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35564.7MB, alloc=44.3MB, time=438.22
memory used=35612.2MB, alloc=44.3MB, time=438.82
x[1] = 0.4784 1.694
h = 0.001 0.001
y2[1] (numeric) = 1.64087020324 2.76544534473
y2[1] (closed_form) = 2.29475733186 2.33359126187
absolute error = 0.7836
relative error = 23.94 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.29475733186 2.33359126187
y1[1] (closed_form) = 2.29475733186 2.33359126187
absolute error = 5.657e-31
relative error = 1.728e-29 %
Correct digits = 31
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) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35659.1MB, alloc=44.3MB, time=439.40
memory used=35706.3MB, alloc=44.3MB, time=439.98
x[1] = 0.4794 1.695
h = 0.0001 0.004
y2[1] (numeric) = 1.6450670765 2.77540658656
y2[1] (closed_form) = 2.29846655837 2.3348765561
absolute error = 0.788
relative error = 24.05 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.29846655837 2.3348765561
y1[1] (closed_form) = 2.29846655837 2.3348765561
absolute error = 5.657e-31
relative error = 1.727e-29 %
Correct digits = 31
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) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35752.8MB, alloc=44.3MB, time=440.54
memory used=35799.6MB, alloc=44.3MB, time=441.12
x[1] = 0.4795 1.699
h = 0.003 0.006
y2[1] (numeric) = 1.64929377353 2.78539091007
y2[1] (closed_form) = 2.30358279433 2.34476446742
absolute error = 0.7888
relative error = 24 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.30358279433 2.34476446742
y1[1] (closed_form) = 2.30358279433 2.34476446742
absolute error = 5.657e-31
relative error = 1.721e-29 %
Correct digits = 31
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) = 37.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35846.1MB, alloc=44.3MB, time=441.69
x[1] = 0.4825 1.705
h = 0.0001 0.005
y2[1] (numeric) = 1.65355048163 2.79539833301
y2[1] (closed_form) = 2.31847907848 2.35615700801
absolute error = 0.7969
relative error = 24.11 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.31847907848 2.35615700801
y1[1] (closed_form) = 2.31847907848 2.35615700801
absolute error = 5.657e-31
relative error = 1.711e-29 %
Correct digits = 31
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) = 37.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35892.8MB, alloc=44.3MB, time=442.26
memory used=35939.8MB, alloc=44.3MB, time=442.84
x[1] = 0.4826 1.71
h = 0.0001 0.003
y2[1] (numeric) = 1.65783739006 2.80542887165
y2[1] (closed_form) = 2.3249191654 2.3686483153
absolute error = 0.7974
relative error = 24.02 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.3249191654 2.3686483153
y1[1] (closed_form) = 2.3249191654 2.3686483153
absolute error = 5.657e-31
relative error = 1.704e-29 %
Correct digits = 31
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) = 37.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35986.6MB, alloc=44.3MB, time=443.41
memory used=36034.1MB, alloc=44.3MB, time=444.00
x[1] = 0.4827 1.713
h = 0.001 0.001
y2[1] (numeric) = 1.6621546903 2.81548254117
y2[1] (closed_form) = 2.32890167083 2.37612105044
absolute error = 0.7985
relative error = 24 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.32890167083 2.37612105044
y1[1] (closed_form) = 2.32890167083 2.37612105044
absolute error = 4.243e-31
relative error = 1.275e-29 %
Correct digits = 31
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) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36080.8MB, alloc=44.3MB, time=444.58
memory used=36127.7MB, alloc=44.3MB, time=445.15
x[1] = 0.4837 1.714
h = 0.001 0.003
y2[1] (numeric) = 1.66650257448 2.82555935732
y2[1] (closed_form) = 2.33268508975 2.37741036215
absolute error = 0.8029
relative error = 24.11 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.33268508975 2.37741036215
y1[1] (closed_form) = 2.33268508975 2.37741036215
absolute error = 4.243e-31
relative error = 1.274e-29 %
Correct digits = 31
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) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36174.3MB, alloc=44.3MB, time=445.72
x[1] = 0.4847 1.717
h = 0.0001 0.004
y2[1] (numeric) = 1.67088123484 2.83565933594
y2[1] (closed_form) = 2.33898117898 2.3837776324
absolute error = 0.8066
relative error = 24.15 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.33898117898 2.3837776324
y1[1] (closed_form) = 2.33898117898 2.3837776324
absolute error = 4.243e-31
relative error = 1.270e-29 %
Correct digits = 31
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) = 37.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36220.9MB, alloc=44.3MB, time=446.29
memory used=36267.8MB, alloc=44.3MB, time=446.87
x[1] = 0.4848 1.721
h = 0.003 0.006
y2[1] (numeric) = 1.67529086376 2.84578249293
y2[1] (closed_form) = 2.34426830603 2.39384142778
absolute error = 0.8073
relative error = 24.1 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.34426830603 2.39384142778
y1[1] (closed_form) = 2.34426830603 2.39384142778
absolute error = 5.657e-31
relative error = 1.688e-29 %
Correct digits = 31
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) = 37.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36314.3MB, alloc=44.3MB, time=447.44
memory used=36361.2MB, alloc=44.3MB, time=448.01
x[1] = 0.4878 1.727
h = 0.0001 0.005
y2[1] (numeric) = 1.67973165408 2.85592884421
y2[1] (closed_form) = 2.35955143354 2.40537949502
absolute error = 0.8156
relative error = 24.2 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.35955143354 2.40537949502
y1[1] (closed_form) = 2.35955143354 2.40537949502
absolute error = 5.657e-31
relative error = 1.679e-29 %
Correct digits = 31
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) = 37.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36407.7MB, alloc=44.3MB, time=448.58
memory used=36454.7MB, alloc=44.3MB, time=449.15
x[1] = 0.4879 1.732
h = 0.0001 0.003
y2[1] (numeric) = 1.68420380066 2.86609840422
y2[1] (closed_form) = 2.36620695678 2.4180935864
absolute error = 0.816
relative error = 24.12 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.36620695678 2.4180935864
y1[1] (closed_form) = 2.36620695678 2.4180935864
absolute error = 5.657e-31
relative error = 1.672e-29 %
Correct digits = 31
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) = 37.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36501.5MB, alloc=44.3MB, time=449.73
x[1] = 0.488 1.735
h = 0.001 0.001
y2[1] (numeric) = 1.68870750065 2.87629118624
y2[1] (closed_form) = 2.3703210693 2.42569886843
absolute error = 0.8171
relative error = 24.09 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.3703210693 2.42569886843
y1[1] (closed_form) = 2.3703210693 2.42569886843
absolute error = 5.657e-31
relative error = 1.668e-29 %
Correct digits = 31
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) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36548.7MB, alloc=44.3MB, time=450.31
memory used=36595.5MB, alloc=44.3MB, time=450.88
x[1] = 0.489 1.736
h = 0.001 0.003
y2[1] (numeric) = 1.69324295182 2.88650720415
y2[1] (closed_form) = 2.37419261774 2.42699139108
absolute error = 0.8215
relative error = 24.2 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.37419261774 2.42699139108
y1[1] (closed_form) = 2.37419261774 2.42699139108
absolute error = 6.403e-31
relative error = 1.886e-29 %
Correct digits = 31
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) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36642.1MB, alloc=44.3MB, time=451.45
memory used=36689.2MB, alloc=44.3MB, time=452.03
x[1] = 0.49 1.739
h = 0.0001 0.004
y2[1] (numeric) = 1.69781035209 2.89674647194
y2[1] (closed_form) = 2.3806622108 2.43345325312
absolute error = 0.8252
relative error = 24.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.3806622108 2.43345325312
y1[1] (closed_form) = 2.3806622108 2.43345325312
absolute error = 5.657e-31
relative error = 1.662e-29 %
Correct digits = 31
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) = 37.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36735.8MB, alloc=44.3MB, time=452.59
memory used=36782.6MB, alloc=44.3MB, time=453.17
x[1] = 0.4901 1.743
h = 0.003 0.006
y2[1] (numeric) = 1.7024098995 2.90700900361
y2[1] (closed_form) = 2.38612498653 2.44369628781
absolute error = 0.8259
relative error = 24.18 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.38612498653 2.44369628781
y1[1] (closed_form) = 2.38612498653 2.44369628781
absolute error = 5.000e-31
relative error = 1.464e-29 %
Correct digits = 31
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) = 37.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36829.1MB, alloc=44.3MB, time=453.73
x[1] = 0.4931 1.749
h = 0.0001 0.005
y2[1] (numeric) = 1.7070417926 2.91729481323
y2[1] (closed_form) = 2.40180461621 2.45538157787
absolute error = 0.8343
relative error = 24.29 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.40180461621 2.45538157787
y1[1] (closed_form) = 2.40180461621 2.45538157787
absolute error = 5.000e-31
relative error = 1.456e-29 %
Correct digits = 31
memory used=36876.1MB, alloc=44.3MB, time=454.30
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) = 37.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36922.8MB, alloc=44.3MB, time=454.88
x[1] = 0.4932 1.754
h = 0.0001 0.003
y2[1] (numeric) = 1.71170623196 2.92760391333
y2[1] (closed_form) = 2.40868157531 2.46832269779
absolute error = 0.8347
relative error = 24.2 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.40868157531 2.46832269779
y1[1] (closed_form) = 2.40868157531 2.46832269779
absolute error = 6.403e-31
relative error = 1.857e-29 %
Correct digits = 31
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) = 37.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36969.5MB, alloc=44.3MB, time=455.44
memory used=37017.1MB, alloc=44.3MB, time=456.04
x[1] = 0.4933 1.757
h = 0.001 0.001
y2[1] (numeric) = 1.71640342048 2.93793631522
y2[1] (closed_form) = 2.41293094433 2.47606303465
absolute error = 0.8357
relative error = 24.17 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.41293094433 2.47606303465
y1[1] (closed_form) = 2.41293094433 2.47606303465
absolute error = 6.403e-31
relative error = 1.852e-29 %
Correct digits = 31
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) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37063.9MB, alloc=44.3MB, time=456.62
memory used=37110.9MB, alloc=44.3MB, time=457.20
x[1] = 0.4943 1.758
h = 0.001 0.003
y2[1] (numeric) = 1.72113356175 2.94829203086
y2[1] (closed_form) = 2.41689268886 2.47735845462
absolute error = 0.8402
relative error = 24.27 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.41689268886 2.47735845462
y1[1] (closed_form) = 2.41689268886 2.47735845462
absolute error = 6.403e-31
relative error = 1.850e-29 %
Correct digits = 31
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) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37157.4MB, alloc=44.3MB, time=457.77
x[1] = 0.4953 1.761
h = 0.0001 0.004
y2[1] (numeric) = 1.72589685947 2.95867107228
y2[1] (closed_form) = 2.42354024241 2.48391634574
absolute error = 0.8439
relative error = 24.32 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.42354024241 2.48391634574
y1[1] (closed_form) = 2.42354024241 2.48391634574
absolute error = 6.403e-31
relative error = 1.845e-29 %
Correct digits = 31
memory used=37204.3MB, alloc=44.3MB, time=458.33
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) = 37.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37251.0MB, alloc=44.3MB, time=458.91
x[1] = 0.4954 1.765
h = 0.003 0.006
y2[1] (numeric) = 1.73069351748 2.96907345156
y2[1] (closed_form) = 2.42918354627 2.49434201576
absolute error = 0.8445
relative error = 24.26 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.42918354627 2.49434201576
y1[1] (closed_form) = 2.42918354627 2.49434201576
absolute error = 7.211e-31
relative error = 2.071e-29 %
Correct digits = 31
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) = 37.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37297.4MB, alloc=44.3MB, time=459.47
memory used=37344.4MB, alloc=44.3MB, time=460.05
x[1] = 0.4984 1.771
h = 0.0001 0.005
y2[1] (numeric) = 1.73552374013 2.97949918083
y2[1] (closed_form) = 2.44526955204 2.50617619947
absolute error = 0.8531
relative error = 24.36 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.44526955204 2.50617619947
y1[1] (closed_form) = 2.44526955204 2.50617619947
absolute error = 7.810e-31
relative error = 2.231e-29 %
Correct digits = 31
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) = 37.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37391.0MB, alloc=44.3MB, time=460.61
memory used=37438.1MB, alloc=44.3MB, time=461.19
x[1] = 0.4985 1.776
h = 0.0001 0.003
y2[1] (numeric) = 1.74038773384 2.98994827061
y2[1] (closed_form) = 2.45237410047 2.51934864425
absolute error = 0.8535
relative error = 24.27 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.45237410047 2.51934864425
y1[1] (closed_form) = 2.45237410047 2.51934864425
absolute error = 7.810e-31
relative error = 2.221e-29 %
Correct digits = 31
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) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37485.0MB, alloc=44.3MB, time=461.77
x[1] = 0.4986 1.779
h = 0.001 0.001
y2[1] (numeric) = 1.74528570742 3.00042073023
y2[1] (closed_form) = 2.45676246856 2.5272265739
absolute error = 0.8545
relative error = 24.24 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.45676246856 2.5272265739
y1[1] (closed_form) = 2.45676246856 2.5272265739
absolute error = 7.071e-31
relative error = 2.006e-29 %
Correct digits = 31
memory used=37532.5MB, alloc=44.3MB, time=462.36
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) = 37.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37579.1MB, alloc=44.3MB, time=462.93
x[1] = 0.4996 1.78
h = 0.001 0.003
y2[1] (numeric) = 1.75021787036 3.01091656959
y2[1] (closed_form) = 2.46081651754 2.52852455786
absolute error = 0.8589
relative error = 24.34 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.46081651754 2.52852455786
y1[1] (closed_form) = 2.46081651754 2.52852455786
absolute error = 7.071e-31
relative error = 2.004e-29 %
Correct digits = 31
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) = 37.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37625.6MB, alloc=44.3MB, time=463.50
memory used=37672.6MB, alloc=44.3MB, time=464.08
x[1] = 0.5006 1.783
h = 0.0001 0.004
y2[1] (numeric) = 1.75518443228 3.02143579875
y2[1] (closed_form) = 2.46764659177 2.53517991762
absolute error = 0.8626
relative error = 24.38 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.46764659177 2.53517991762
y1[1] (closed_form) = 2.46764659177 2.53517991762
absolute error = 7.211e-31
relative error = 2.038e-29 %
Correct digits = 31
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) = 38.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37719.1MB, alloc=44.3MB, time=464.64
memory used=37765.9MB, alloc=44.3MB, time=465.22
x[1] = 0.5007 1.787
h = 0.003 0.006
y2[1] (numeric) = 1.76018560294 3.03197842777
y2[1] (closed_form) = 2.47347542812 2.54579166015
absolute error = 0.8632
relative error = 24.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.47347542812 2.54579166015
y1[1] (closed_form) = 2.47347542812 2.54579166015
absolute error = 7.810e-31
relative error = 2.200e-29 %
Correct digits = 31
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) = 38.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37812.5MB, alloc=44.3MB, time=465.79
memory used=37859.6MB, alloc=44.3MB, time=466.36
x[1] = 0.5037 1.793
h = 0.0001 0.005
y2[1] (numeric) = 1.76522159263 3.04254446676
y2[1] (closed_form) = 2.48997790389 2.55777638144
absolute error = 0.8719
relative error = 24.43 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.48997790389 2.55777638144
y1[1] (closed_form) = 2.48997790389 2.55777638144
absolute error = 7.810e-31
relative error = 2.188e-29 %
Correct digits = 31
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) = 38.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37906.1MB, alloc=44.3MB, time=466.93
x[1] = 0.5038 1.798
h = 0.0001 0.003
y2[1] (numeric) = 1.77029261375 3.05313392419
y2[1] (closed_form) = 2.49731635283 2.5711844998
absolute error = 0.8723
relative error = 24.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.49731635283 2.5711844998
y1[1] (closed_form) = 2.49731635283 2.5711844998
absolute error = 7.810e-31
relative error = 2.179e-29 %
Correct digits = 31
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) = 38.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37952.9MB, alloc=44.3MB, time=467.50
memory used=38000.4MB, alloc=44.3MB, time=468.09
x[1] = 0.5039 1.801
h = 0.001 0.001
y2[1] (numeric) = 1.77539888112 3.0637468073
y2[1] (closed_form) = 2.50184755801 2.57920259052
absolute error = 0.8732
relative error = 24.3 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.50184755801 2.57920259052
y1[1] (closed_form) = 2.50184755801 2.57920259052
absolute error = 7.071e-31
relative error = 1.968e-29 %
Correct digits = 31
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) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38047.3MB, alloc=44.3MB, time=468.67
memory used=38094.4MB, alloc=44.3MB, time=469.26
x[1] = 0.5049 1.802
h = 0.0001 0.004
y2[1] (numeric) = 1.78054061028 3.0743831239
y2[1] (closed_form) = 2.50599606249 2.58050278477
absolute error = 0.8776
relative error = 24.4 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.50599606249 2.58050278477
y1[1] (closed_form) = 2.50599606249 2.58050278477
absolute error = 7.810e-31
relative error = 2.171e-29 %
Correct digits = 31
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) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38140.8MB, alloc=44.3MB, time=469.82
memory used=38187.8MB, alloc=44.3MB, time=470.41
x[1] = 0.505 1.806
h = 0.003 0.006
y2[1] (numeric) = 1.78571801691 3.085042882
y2[1] (closed_form) = 2.51198643104 2.59127977001
absolute error = 0.8782
relative error = 24.33 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.51198643104 2.59127977001
y1[1] (closed_form) = 2.51198643104 2.59127977001
absolute error = 7.071e-31
relative error = 1.959e-29 %
Correct digits = 31
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) = 38.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38234.3MB, alloc=44.3MB, time=470.98
x[1] = 0.508 1.812
h = 0.0001 0.005
y2[1] (numeric) = 1.79093131706 3.09572608971
y2[1] (closed_form) = 2.52885382557 2.60340049252
absolute error = 0.8871
relative error = 24.44 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.52885382557 2.60340049252
y1[1] (closed_form) = 2.52885382557 2.60340049252
absolute error = 7.810e-31
relative error = 2.152e-29 %
Correct digits = 31
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) = 38.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38280.9MB, alloc=44.3MB, time=471.55
memory used=38328.0MB, alloc=44.3MB, time=472.12
x[1] = 0.5081 1.817
h = 0.0001 0.003
y2[1] (numeric) = 1.79618072895 3.10643275344
y2[1] (closed_form) = 2.53639590654 2.61701788508
absolute error = 0.8874
relative error = 24.35 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.53639590654 2.61701788508
y1[1] (closed_form) = 2.53639590654 2.61701788508
absolute error = 7.810e-31
relative error = 2.143e-29 %
Correct digits = 31
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) = 38.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38374.7MB, alloc=44.3MB, time=472.70
memory used=38422.2MB, alloc=44.3MB, time=473.29
x[1] = 0.5082 1.82
h = 0.001 0.001
y2[1] (numeric) = 1.80146647324 3.11716287834
y2[1] (closed_form) = 2.54105149735 2.62516046725
absolute error = 0.8883
relative error = 24.31 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.54105149735 2.62516046725
y1[1] (closed_form) = 2.54105149735 2.62516046725
absolute error = 7.810e-31
relative error = 2.138e-29 %
Correct digits = 31
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) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38468.8MB, alloc=44.3MB, time=473.86
memory used=38515.7MB, alloc=44.3MB, time=474.44
x[1] = 0.5092 1.821
h = 0.001 0.003
y2[1] (numeric) = 1.80678877136 3.12791647017
y2[1] (closed_form) = 2.54528304152 2.62646342561
absolute error = 0.8927
relative error = 24.41 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.54528304152 2.62646342561
y1[1] (closed_form) = 2.54528304152 2.62646342561
absolute error = 7.810e-31
relative error = 2.135e-29 %
Correct digits = 31
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) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38562.2MB, alloc=44.3MB, time=475.01
x[1] = 0.5102 1.824
h = 0.0001 0.004
y2[1] (numeric) = 1.81214784483 3.13869353481
y2[1] (closed_form) = 2.55246404434 2.63330629674
absolute error = 0.8964
relative error = 24.44 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.55246404434 2.63330629674
y1[1] (closed_form) = 2.55246404434 2.63330629674
absolute error = 7.071e-31
relative error = 1.928e-29 %
Correct digits = 31
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) = 38.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38608.7MB, alloc=44.3MB, time=475.57
memory used=38655.5MB, alloc=44.3MB, time=476.15
x[1] = 0.5103 1.828
h = 0.003 0.006
y2[1] (numeric) = 1.81754391534 3.14949407817
y2[1] (closed_form) = 2.55864955826 2.64427592448
absolute error = 0.8969
relative error = 24.38 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.55864955826 2.64427592448
y1[1] (closed_form) = 2.55864955826 2.64427592448
absolute error = 7.810e-31
relative error = 2.123e-29 %
Correct digits = 31
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) = 38.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38701.9MB, alloc=44.3MB, time=476.73
memory used=38749.0MB, alloc=44.3MB, time=477.31
x[1] = 0.5133 1.834
h = 0.0001 0.005
y2[1] (numeric) = 1.82297720511 3.1603181062
y2[1] (closed_form) = 2.57595278916 2.65655029309
absolute error = 0.906
relative error = 24.48 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.57595278916 2.65655029309
y1[1] (closed_form) = 2.57595278916 2.65655029309
absolute error = 7.211e-31
relative error = 1.949e-29 %
Correct digits = 31
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) = 38.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38795.4MB, alloc=44.3MB, time=477.87
memory used=38842.5MB, alloc=44.3MB, time=478.45
x[1] = 0.5134 1.839
h = 0.0001 0.003
y2[1] (numeric) = 1.82844793858 3.17116562314
y2[1] (closed_form) = 2.5837408941 2.67041167214
absolute error = 0.9062
relative error = 24.39 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.5837408941 2.67041167214
y1[1] (closed_form) = 2.5837408941 2.67041167214
absolute error = 6.403e-31
relative error = 1.723e-29 %
Correct digits = 31
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) = 38.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38889.4MB, alloc=44.3MB, time=479.03
x[1] = 0.5135 1.842
h = 0.001 0.001
y2[1] (numeric) = 1.83395634269 3.18203663188
y2[1] (closed_form) = 2.58854669439 2.67869932449
absolute error = 0.9071
relative error = 24.35 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.58854669439 2.67869932449
y1[1] (closed_form) = 2.58854669439 2.67869932449
absolute error = 7.211e-31
relative error = 1.936e-29 %
Correct digits = 31
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) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38936.4MB, alloc=44.3MB, time=479.64
memory used=38983.4MB, alloc=44.3MB, time=480.22
x[1] = 0.5145 1.843
h = 0.001 0.003
y2[1] (numeric) = 1.83950264514 3.19293113596
y2[1] (closed_form) = 2.59287681815 2.68000380539
absolute error = 0.9114
relative error = 24.44 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.59287681815 2.68000380539
y1[1] (closed_form) = 2.59287681815 2.68000380539
absolute error = 7.211e-31
relative error = 1.934e-29 %
Correct digits = 31
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) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39029.9MB, alloc=44.3MB, time=480.79
memory used=39076.9MB, alloc=44.3MB, time=481.37
x[1] = 0.5155 1.846
h = 0.0001 0.004
y2[1] (numeric) = 1.84508707376 3.20384913905
y2[1] (closed_form) = 2.60025396363 2.68694833093
absolute error = 0.9151
relative error = 24.47 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.60025396363 2.68694833093
y1[1] (closed_form) = 2.60025396363 2.68694833093
absolute error = 7.211e-31
relative error = 1.929e-29 %
Correct digits = 31
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) = 38.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39123.5MB, alloc=44.3MB, time=481.94
memory used=39170.3MB, alloc=44.3MB, time=482.51
x[1] = 0.5156 1.85
h = 0.003 0.006
y2[1] (numeric) = 1.85070985652 3.21479064482
y2[1] (closed_form) = 2.60664000133 2.69811415991
absolute error = 0.9156
relative error = 24.41 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.60664000133 2.69811415991
y1[1] (closed_form) = 2.60664000133 2.69811415991
absolute error = 6.708e-31
relative error = 1.788e-29 %
Correct digits = 31
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) = 38.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39216.8MB, alloc=44.3MB, time=483.08
x[1] = 0.5186 1.856
h = 0.0001 0.005
y2[1] (numeric) = 1.85637122196 3.225755657
y2[1] (closed_form) = 2.62438982014 2.71054373536
absolute error = 0.9248
relative error = 24.51 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.62438982014 2.71054373536
y1[1] (closed_form) = 2.62438982014 2.71054373536
absolute error = 6.403e-31
relative error = 1.697e-29 %
Correct digits = 31
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) = 38.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39263.7MB, alloc=44.3MB, time=483.66
memory used=39310.5MB, alloc=44.3MB, time=484.24
x[1] = 0.5187 1.861
h = 0.0001 0.003
y2[1] (numeric) = 1.86207140087 3.23674417757
y2[1] (closed_form) = 2.63243073254 2.72465360429
absolute error = 0.925
relative error = 24.42 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.63243073254 2.72465360429
y1[1] (closed_form) = 2.63243073254 2.72465360429
absolute error = 7.211e-31
relative error = 1.903e-29 %
Correct digits = 31
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) = 38.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39357.1MB, alloc=44.3MB, time=484.81
memory used=39404.5MB, alloc=44.3MB, time=485.40
x[1] = 0.5188 1.864
h = 0.001 0.001
y2[1] (numeric) = 1.86781062659 3.24775620709
y2[1] (closed_form) = 2.63739086621 2.73308898455
absolute error = 0.9258
relative error = 24.38 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.63739086621 2.73308898455
y1[1] (closed_form) = 2.63739086621 2.73308898455
absolute error = 7.211e-31
relative error = 1.899e-29 %
Correct digits = 31
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) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39451.2MB, alloc=44.3MB, time=485.98
memory used=39498.2MB, alloc=44.3MB, time=486.56
x[1] = 0.5198 1.865
h = 0.001 0.003
y2[1] (numeric) = 1.87358913324 3.25879174679
y2[1] (closed_form) = 2.641821848 2.73439457288
absolute error = 0.9301
relative error = 24.46 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.641821848 2.73439457288
y1[1] (closed_form) = 2.641821848 2.73439457288
absolute error = 6.403e-31
relative error = 1.684e-29 %
Correct digits = 31
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) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39544.7MB, alloc=44.3MB, time=487.13
x[1] = 0.5208 1.868
h = 0.0001 0.004
y2[1] (numeric) = 1.87940715507 3.26985079806
y2[1] (closed_form) = 2.64940011912 2.74144219853
absolute error = 0.9339
relative error = 24.5 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.64940011912 2.74144219853
y1[1] (closed_form) = 2.64940011912 2.74144219853
absolute error = 6.403e-31
relative error = 1.680e-29 %
Correct digits = 31
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) = 38.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39591.6MB, alloc=44.3MB, time=487.70
memory used=39638.3MB, alloc=44.3MB, time=488.27
x[1] = 0.5209 1.872
h = 0.003 0.006
y2[1] (numeric) = 1.88526492651 3.28093336224
y2[1] (closed_form) = 2.65599219623 2.75280783015
absolute error = 0.9343
relative error = 24.43 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.65599219623 2.75280783015
y1[1] (closed_form) = 2.65599219623 2.75280783015
absolute error = 5.831e-31
relative error = 1.524e-29 %
Correct digits = 31
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) = 38.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39684.8MB, alloc=44.3MB, time=488.84
memory used=39731.8MB, alloc=44.3MB, time=489.42
x[1] = 0.5239 1.878
h = 0.0001 0.005
y2[1] (numeric) = 1.89116268252 3.29203944078
y2[1] (closed_form) = 2.67419959429 2.7653941398
absolute error = 0.9437
relative error = 24.53 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.67419959429 2.7653941398
y1[1] (closed_form) = 2.67419959429 2.7653941398
absolute error = 7.211e-31
relative error = 1.875e-29 %
Correct digits = 31
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) = 38.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39778.4MB, alloc=44.3MB, time=489.99
memory used=39825.5MB, alloc=44.3MB, time=490.57
x[1] = 0.524 1.883
h = 0.0001 0.003
y2[1] (numeric) = 1.89710066038 3.30316903328
y2[1] (closed_form) = 2.68250027086 2.77975705634
absolute error = 0.9438
relative error = 24.43 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.68250027086 2.77975705634
y1[1] (closed_form) = 2.68250027086 2.77975705634
absolute error = 6.708e-31
relative error = 1.737e-29 %
Correct digits = 31
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) = 39.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39872.2MB, alloc=44.3MB, time=491.14
x[1] = 0.5241 1.886
h = 0.001 0.001
y2[1] (numeric) = 1.90307909997 3.31432213792
y2[1] (closed_form) = 2.68761896662 2.78834285361
absolute error = 0.9445
relative error = 24.39 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.68761896662 2.78834285361
y1[1] (closed_form) = 2.68761896662 2.78834285361
absolute error = 6.708e-31
relative error = 1.732e-29 %
Correct digits = 31
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) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39919.5MB, alloc=44.3MB, time=491.73
memory used=39966.2MB, alloc=44.3MB, time=492.31
x[1] = 0.5251 1.887
h = 0.001 0.003
y2[1] (numeric) = 1.90909824197 3.32549875353
y2[1] (closed_form) = 2.69215313111 2.78964911122
absolute error = 0.9488
relative error = 24.47 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.69215313111 2.78964911122
y1[1] (closed_form) = 2.69215313111 2.78964911122
absolute error = 6.708e-31
relative error = 1.730e-29 %
Correct digits = 31
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) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40012.7MB, alloc=44.3MB, time=492.88
memory used=40059.8MB, alloc=44.3MB, time=493.45
x[1] = 0.5261 1.89
h = 0.0001 0.004
y2[1] (numeric) = 1.91515832721 3.33669887912
y2[1] (closed_form) = 2.69993762662 2.79680128276
absolute error = 0.9526
relative error = 24.5 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.69993762662 2.79680128276
y1[1] (closed_form) = 2.69993762662 2.79680128276
absolute error = 6.708e-31
relative error = 1.726e-29 %
Correct digits = 31
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) = 39.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40106.2MB, alloc=44.3MB, time=494.02
memory used=40153.3MB, alloc=44.3MB, time=494.59
x[1] = 0.5262 1.894
h = 0.003 0.006
y2[1] (numeric) = 1.92125959666 3.34792251365
y2[1] (closed_form) = 2.70674139927 2.8083703615
absolute error = 0.9529
relative error = 24.43 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.70674139927 2.8083703615
y1[1] (closed_form) = 2.70674139927 2.8083703615
absolute error = 6.708e-31
relative error = 1.720e-29 %
Correct digits = 31
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) = 39.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40199.8MB, alloc=44.3MB, time=495.16
memory used=40246.8MB, alloc=44.3MB, time=495.74
x[1] = 0.5292 1.9
h = 0.0001 0.005
y2[1] (numeric) = 1.92740229189 3.35916965617
y2[1] (closed_form) = 2.7254176131 2.82111489744
absolute error = 0.9625
relative error = 24.54 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.7254176131 2.82111489744
y1[1] (closed_form) = 2.7254176131 2.82111489744
absolute error = 6.708e-31
relative error = 1.710e-29 %
Correct digits = 31
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) = 39.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40293.3MB, alloc=44.3MB, time=496.30
x[1] = 0.5293 1.905
h = 0.0001 0.003
y2[1] (numeric) = 1.93358665678 3.37044030385
y2[1] (closed_form) = 2.733985188 2.8357354741
absolute error = 0.9626
relative error = 24.44 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.733985188 2.8357354741
y1[1] (closed_form) = 2.733985188 2.8357354741
absolute error = 5.831e-31
relative error = 1.480e-29 %
Correct digits = 31
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) = 39.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40340.0MB, alloc=44.3MB, time=496.88
memory used=40387.5MB, alloc=44.3MB, time=497.47
x[1] = 0.5294 1.908
h = 0.001 0.001
y2[1] (numeric) = 1.93981293791 3.38173445238
y2[1] (closed_form) = 2.73926678195 2.84447440907
absolute error = 0.9632
relative error = 24.39 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.73926678195 2.84447440907
y1[1] (closed_form) = 2.73926678195 2.84447440907
absolute error = 6.708e-31
relative error = 1.699e-29 %
Correct digits = 31
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) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40434.4MB, alloc=44.3MB, time=498.05
memory used=40481.4MB, alloc=44.3MB, time=498.62
x[1] = 0.5304 1.909
h = 0.0001 0.004
y2[1] (numeric) = 1.94608138266 3.39305209814
y2[1] (closed_form) = 2.74390650101 2.84578087407
absolute error = 0.9675
relative error = 24.47 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.74390650101 2.84578087407
y1[1] (closed_form) = 2.74390650101 2.84578087407
absolute error = 5.831e-31
relative error = 1.475e-29 %
Correct digits = 31
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) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40527.9MB, alloc=44.3MB, time=499.19
memory used=40574.9MB, alloc=44.3MB, time=499.77
x[1] = 0.5305 1.913
h = 0.003 0.006
y2[1] (numeric) = 1.95239223855 3.40439323765
y2[1] (closed_form) = 2.75089464989 2.85753064089
absolute error = 0.9678
relative error = 24.4 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.75089464989 2.85753064089
y1[1] (closed_form) = 2.75089464989 2.85753064089
absolute error = 6.708e-31
relative error = 1.691e-29 %
Correct digits = 31
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) = 39.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40621.5MB, alloc=44.3MB, time=500.34
x[1] = 0.5335 1.919
h = 0.0001 0.005
y2[1] (numeric) = 1.95874575354 3.4157578676
y2[1] (closed_form) = 2.76998168555 2.87041831057
absolute error = 0.9775
relative error = 24.5 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.76998168555 2.87041831057
y1[1] (closed_form) = 2.76998168555 2.87041831057
absolute error = 5.831e-31
relative error = 1.462e-29 %
Correct digits = 31
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) = 39.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40668.0MB, alloc=44.3MB, time=500.90
memory used=40715.0MB, alloc=44.3MB, time=501.48
x[1] = 0.5336 1.924
h = 0.0001 0.003
y2[1] (numeric) = 1.96514217798 3.4271459827
y2[1] (closed_form) = 2.77878170411 2.88526770653
absolute error = 0.9776
relative error = 24.4 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.77878170411 2.88526770653
y1[1] (closed_form) = 2.77878170411 2.88526770653
absolute error = 7.211e-31
relative error = 1.800e-29 %
Correct digits = 31
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) = 39.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40761.7MB, alloc=44.3MB, time=502.05
memory used=40809.1MB, alloc=44.3MB, time=502.65
x[1] = 0.5337 1.927
h = 0.001 0.001
y2[1] (numeric) = 1.97158176492 3.43855757619
y2[1] (closed_form) = 2.78420520264 2.89414267305
absolute error = 0.9781
relative error = 24.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.78420520264 2.89414267305
y1[1] (closed_form) = 2.78420520264 2.89414267305
absolute error = 7.211e-31
relative error = 1.796e-29 %
Correct digits = 31
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) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40855.8MB, alloc=44.3MB, time=503.22
memory used=40902.7MB, alloc=44.3MB, time=503.80
x[1] = 0.5347 1.928
h = 0.001 0.003
y2[1] (numeric) = 1.97806476823 3.44999264198
y2[1] (closed_form) = 2.78893772112 2.8954502247
absolute error = 0.9824
relative error = 24.44 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.78893772112 2.8954502247
y1[1] (closed_form) = 2.78893772112 2.8954502247
absolute error = 7.616e-31
relative error = 1.894e-29 %
Correct digits = 31
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) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40949.3MB, alloc=44.3MB, time=504.37
x[1] = 0.5357 1.931
h = 0.0001 0.004
y2[1] (numeric) = 1.98459144194 3.46145117412
y2[1] (closed_form) = 2.79711864415 2.90280338338
absolute error = 0.986
relative error = 24.46 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.79711864415 2.90280338338
y1[1] (closed_form) = 2.79711864415 2.90280338338
absolute error = 6.708e-31
relative error = 1.664e-29 %
Correct digits = 31
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) = 39.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40995.9MB, alloc=44.3MB, time=504.93
memory used=41042.8MB, alloc=44.3MB, time=505.51
x[1] = 0.5358 1.935
h = 0.003 0.006
y2[1] (numeric) = 1.99116204026 3.47293316666
y2[1] (closed_form) = 2.80432935455 2.91476356601
absolute error = 0.9863
relative error = 24.38 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.80432935455 2.91476356601
y1[1] (closed_form) = 2.80432935455 2.91476356601
absolute error = 6.708e-31
relative error = 1.658e-29 %
Correct digits = 31
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) = 39.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41089.3MB, alloc=44.3MB, time=506.07
memory used=41136.3MB, alloc=44.3MB, time=506.65
x[1] = 0.5388 1.941
h = 0.0001 0.005
y2[1] (numeric) = 1.99777681797 3.48443861373
y2[1] (closed_form) = 2.82390676918 2.9278122789
absolute error = 0.9962
relative error = 24.49 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.82390676918 2.9278122789
y1[1] (closed_form) = 2.82390676918 2.9278122789
absolute error = 6.708e-31
relative error = 1.649e-29 %
Correct digits = 31
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) = 39.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41182.8MB, alloc=44.3MB, time=507.22
memory used=41229.9MB, alloc=44.3MB, time=507.80
x[1] = 0.5389 1.946
h = 0.0001 0.003
y2[1] (numeric) = 2.00443603232 3.49596750745
y2[1] (closed_form) = 2.83298739173 2.94292815528
absolute error = 0.9962
relative error = 24.39 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.83298739173 2.94292815528
y1[1] (closed_form) = 2.83298739173 2.94292815528
absolute error = 7.211e-31
relative error = 1.765e-29 %
Correct digits = 31
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) = 39.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41276.7MB, alloc=44.3MB, time=508.38
x[1] = 0.539 1.949
h = 0.001 0.001
y2[1] (numeric) = 2.01113994329 3.50751983841
y2[1] (closed_form) = 2.83858211836 2.95196146174
absolute error = 0.9966
relative error = 24.34 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.83858211836 2.95196146174
y1[1] (closed_form) = 2.83858211836 2.95196146174
absolute error = 7.211e-31
relative error = 1.761e-29 %
Correct digits = 31
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) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41323.6MB, alloc=44.3MB, time=508.96
memory used=41370.6MB, alloc=44.3MB, time=509.54
x[1] = 0.54 1.95
h = 0.001 0.003
y2[1] (numeric) = 2.01788881172 3.51909559787
y2[1] (closed_form) = 2.84342474007 2.95326832507
absolute error = 1.001
relative error = 24.41 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.84342474007 2.95326832507
y1[1] (closed_form) = 2.84342474007 2.95326832507
absolute error = 7.211e-31
relative error = 1.759e-29 %
Correct digits = 31
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) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41417.0MB, alloc=44.3MB, time=510.10
memory used=41464.0MB, alloc=44.3MB, time=510.68
x[1] = 0.541 1.953
h = 0.0001 0.004
y2[1] (numeric) = 2.02468289863 3.53069477727
y2[1] (closed_form) = 2.85182711982 2.96073022699
absolute error = 1.005
relative error = 24.44 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.85182711982 2.96073022699
y1[1] (closed_form) = 2.85182711982 2.96073022699
absolute error = 7.211e-31
relative error = 1.754e-29 %
Correct digits = 31
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) = 39.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41510.4MB, alloc=44.3MB, time=511.26
memory used=41557.4MB, alloc=44.3MB, time=511.84
x[1] = 0.5411 1.957
h = 0.003 0.006
y2[1] (numeric) = 2.03152246518 3.54231736801
y2[1] (closed_form) = 2.85926646858 2.97290459669
absolute error = 1.005
relative error = 24.36 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.85926646858 2.97290459669
y1[1] (closed_form) = 2.85926646858 2.97290459669
absolute error = 8.062e-31
relative error = 1.955e-29 %
Correct digits = 31
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) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41604.0MB, alloc=44.3MB, time=512.40
x[1] = 0.5441 1.963
h = 0.0001 0.005
y2[1] (numeric) = 2.03840777317 3.55396336158
y2[1] (closed_form) = 2.87934623117 2.98611573619
absolute error = 1.015
relative error = 24.46 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.87934623117 2.98611573619
y1[1] (closed_form) = 2.87934623117 2.98611573619
absolute error = 8.602e-31
relative error = 2.074e-29 %
Correct digits = 31
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) = 39.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41650.8MB, alloc=44.3MB, time=512.97
memory used=41697.7MB, alloc=44.3MB, time=513.54
x[1] = 0.5442 1.968
h = 0.0001 0.003
y2[1] (numeric) = 2.04533908686 3.56563274741
y2[1] (closed_form) = 2.88871512307 3.00150286692
absolute error = 1.015
relative error = 24.36 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.88871512307 3.00150286692
y1[1] (closed_form) = 2.88871512307 3.00150286692
absolute error = 8.602e-31
relative error = 2.065e-29 %
Correct digits = 31
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) = 40.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41744.2MB, alloc=44.3MB, time=514.12
memory used=41791.7MB, alloc=44.3MB, time=514.71
x[1] = 0.5443 1.971
h = 0.001 0.001
y2[1] (numeric) = 2.05231667332 3.57732551335
y2[1] (closed_form) = 2.89448573528 3.01069732701
absolute error = 1.015
relative error = 24.3 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.89448573528 3.01069732701
y1[1] (closed_form) = 2.89448573528 3.01069732701
absolute error = 8.602e-31
relative error = 2.060e-29 %
Correct digits = 31
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) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41838.4MB, alloc=44.3MB, time=515.28
memory used=41885.4MB, alloc=44.3MB, time=515.86
x[1] = 0.5453 1.972
h = 0.001 0.003
y2[1] (numeric) = 2.05934080053 3.58904164793
y2[1] (closed_form) = 2.89944097289 3.01200296845
absolute error = 1.019
relative error = 24.38 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.89944097289 3.01200296845
y1[1] (closed_form) = 2.89944097289 3.01200296845
absolute error = 9.434e-31
relative error = 2.257e-29 %
Correct digits = 31
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) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41932.0MB, alloc=44.3MB, time=516.43
x[1] = 0.5463 1.975
h = 0.0001 0.004
y2[1] (numeric) = 2.0664117366 3.60078113985
y2[1] (closed_form) = 2.90807038043 3.01957505609
absolute error = 1.023
relative error = 24.4 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.90807038043 3.01957505609
y1[1] (closed_form) = 2.90807038043 3.01957505609
absolute error = 1.00e-30
relative error = 2.385e-29 %
Correct digits = 31
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) = 40.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41978.8MB, alloc=44.3MB, time=517.00
memory used=42025.6MB, alloc=44.3MB, time=517.57
x[1] = 0.5464 1.979
h = 0.003 0.006
y2[1] (numeric) = 2.07352974984 3.61254397781
y2[1] (closed_form) = 2.91574459861 3.03196742845
absolute error = 1.023
relative error = 24.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.91574459861 3.03196742845
y1[1] (closed_form) = 2.91574459861 3.03196742845
absolute error = 8.602e-31
relative error = 2.045e-29 %
Correct digits = 31
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) = 40.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42072.1MB, alloc=44.3MB, time=518.14
memory used=42119.1MB, alloc=44.3MB, time=518.71
x[1] = 0.5494 1.985
h = 0.0001 0.005
y2[1] (numeric) = 2.08069510916 3.62433015055
y2[1] (closed_form) = 2.93633894504 3.04534233485
absolute error = 1.033
relative error = 24.42 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.93633894504 3.04534233485
y1[1] (closed_form) = 2.93633894504 3.04534233485
absolute error = 8.602e-31
relative error = 2.033e-29 %
Correct digits = 31
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) = 40.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42165.6MB, alloc=44.3MB, time=519.28
memory used=42212.5MB, alloc=44.3MB, time=519.88
x[1] = 0.5495 1.99
h = 0.0001 0.003
y2[1] (numeric) = 2.08790808602 3.63613964472
y2[1] (closed_form) = 2.94600396634 3.06100555027
absolute error = 1.033
relative error = 24.32 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.94600396634 3.06100555027
y1[1] (closed_form) = 2.94600396634 3.06100555027
absolute error = 8.602e-31
relative error = 2.025e-29 %
Correct digits = 31
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) = 40.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42259.3MB, alloc=44.3MB, time=520.46
x[1] = 0.5496 1.993
h = 0.001 0.001
y2[1] (numeric) = 2.09516895473 3.64797244533
y2[1] (closed_form) = 2.95195523939 3.07036401017
absolute error = 1.033
relative error = 24.26 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.95195523939 3.07036401017
y1[1] (closed_form) = 2.95195523939 3.07036401017
absolute error = 9.220e-31
relative error = 2.165e-29 %
Correct digits = 31
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) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42306.7MB, alloc=44.3MB, time=521.05
memory used=42353.4MB, alloc=44.3MB, time=521.62
x[1] = 0.5506 1.994
h = 0.001 0.003
y2[1] (numeric) = 2.10247799053 3.65982853809
y2[1] (closed_form) = 2.95702565659 3.07166786934
absolute error = 1.037
relative error = 24.33 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.95702565659 3.07166786934
y1[1] (closed_form) = 2.95702565659 3.07166786934
absolute error = 1.00e-30
relative error = 2.345e-29 %
Correct digits = 31
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) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42399.8MB, alloc=44.3MB, time=522.19
memory used=42446.9MB, alloc=44.3MB, time=522.77
x[1] = 0.5516 1.997
h = 0.0001 0.004
y2[1] (numeric) = 2.1098354688 3.67170790887
y2[1] (closed_form) = 2.96588779222 3.07935158244
absolute error = 1.041
relative error = 24.35 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.96588779222 3.07935158244
y1[1] (closed_form) = 2.96588779222 3.07935158244
absolute error = 9.220e-31
relative error = 2.156e-29 %
Correct digits = 31
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) = 40.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42493.4MB, alloc=44.3MB, time=523.34
memory used=42540.3MB, alloc=44.3MB, time=523.91
x[1] = 0.5517 2.001
h = 0.003 0.006
y2[1] (numeric) = 2.11724166511 3.68361054354
y2[1] (closed_form) = 2.97380326878 3.09196581766
absolute error = 1.041
relative error = 24.27 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.97380326878 3.09196581766
y1[1] (closed_form) = 2.97380326878 3.09196581766
absolute error = 9.220e-31
relative error = 2.149e-29 %
Correct digits = 31
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) = 40.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42586.7MB, alloc=44.3MB, time=524.47
memory used=42633.7MB, alloc=44.3MB, time=525.05
x[1] = 0.5547 2.007
h = 0.0001 0.005
y2[1] (numeric) = 2.12469685567 3.69553642802
y2[1] (closed_form) = 2.99492470776 3.10550578593
absolute error = 1.051
relative error = 24.37 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.99492470776 3.10550578593
y1[1] (closed_form) = 2.99492470776 3.10550578593
absolute error = 9.220e-31
relative error = 2.137e-29 %
Correct digits = 31
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) = 40.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42680.2MB, alloc=44.3MB, time=525.62
x[1] = 0.5548 2.012
h = 0.0001 0.003
y2[1] (numeric) = 2.13220131928 3.70748554608
y2[1] (closed_form) = 3.00489391789 3.12144997321
absolute error = 1.051
relative error = 24.26 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.00489391789 3.12144997321
y1[1] (closed_form) = 3.00489391789 3.12144997321
absolute error = 9.220e-31
relative error = 2.128e-29 %
Correct digits = 31
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) = 40.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42726.9MB, alloc=44.3MB, time=526.18
memory used=42774.2MB, alloc=44.3MB, time=526.78
x[1] = 0.5549 2.015
h = 0.001 0.001
y2[1] (numeric) = 2.13975533763 3.71945787979
y2[1] (closed_form) = 3.01103074767 3.13097531169
absolute error = 1.051
relative error = 24.2 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.01103074767 3.13097531169
y1[1] (closed_form) = 3.01103074767 3.13097531169
absolute error = 9.220e-31
relative error = 2.122e-29 %
Correct digits = 31
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) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42821.0MB, alloc=44.3MB, time=527.35
memory used=42868.1MB, alloc=44.3MB, time=527.93
x[1] = 0.5559 2.016
h = 0.0001 0.004
y2[1] (numeric) = 2.14735919337 3.73145341192
y2[1] (closed_form) = 3.01621896027 3.13227680055
absolute error = 1.055
relative error = 24.27 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.01621896027 3.13227680055
y1[1] (closed_form) = 3.01621896027 3.13227680055
absolute error = 8.485e-31
relative error = 1.951e-29 %
Correct digits = 31
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) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42914.6MB, alloc=44.3MB, time=528.50
memory used=42961.7MB, alloc=44.3MB, time=529.08
x[1] = 0.556 2.02
h = 0.003 0.006
y2[1] (numeric) = 2.15501316933 3.74347212548
y2[1] (closed_form) = 3.02434463728 3.14508811377
absolute error = 1.055
relative error = 24.19 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.02434463728 3.14508811377
y1[1] (closed_form) = 3.02434463728 3.14508811377
absolute error = 8.485e-31
relative error = 1.945e-29 %
Correct digits = 31
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) = 40.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43008.2MB, alloc=44.3MB, time=529.64
x[1] = 0.559 2.026
h = 0.0001 0.005
y2[1] (numeric) = 2.1627175488 3.75551400356
y2[1] (closed_form) = 3.04592802297 3.1587776491
absolute error = 1.066
relative error = 24.29 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.04592802297 3.1587776491
y1[1] (closed_form) = 3.04592802297 3.1587776491
absolute error = 8.485e-31
relative error = 1.934e-29 %
Correct digits = 31
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) = 40.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43054.7MB, alloc=44.3MB, time=530.20
memory used=43101.8MB, alloc=44.3MB, time=530.78
x[1] = 0.5591 2.031
h = 0.0001 0.003
y2[1] (numeric) = 2.17047261769 3.76757902706
y2[1] (closed_form) = 3.05616225107 3.17497140266
absolute error = 1.066
relative error = 24.18 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.05616225107 3.17497140266
y1[1] (closed_form) = 3.05616225107 3.17497140266
absolute error = 9.220e-31
relative error = 2.092e-29 %
Correct digits = 31
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) = 40.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43148.3MB, alloc=44.3MB, time=531.36
memory used=43195.9MB, alloc=44.3MB, time=531.95
x[1] = 0.5592 2.034
h = 0.001 0.001
y2[1] (numeric) = 2.17827866488 3.77966717513
y2[1] (closed_form) = 3.06246078148 3.18464500699
absolute error = 1.066
relative error = 24.12 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.06246078148 3.18464500699
y1[1] (closed_form) = 3.06246078148 3.18464500699
absolute error = 8.485e-31
relative error = 1.921e-29 %
Correct digits = 31
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) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43242.6MB, alloc=44.3MB, time=532.52
memory used=43289.5MB, alloc=44.3MB, time=533.10
x[1] = 0.5602 2.035
h = 0.001 0.003
y2[1] (numeric) = 2.18613598022 3.79177842764
y2[1] (closed_form) = 3.06775256195 3.18594540945
absolute error = 1.07
relative error = 24.19 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.06775256195 3.18594540945
y1[1] (closed_form) = 3.06775256195 3.18594540945
absolute error = 8.485e-31
relative error = 1.919e-29 %
Correct digits = 31
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) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43336.0MB, alloc=44.3MB, time=533.68
x[1] = 0.5612 2.038
h = 0.0001 0.004
y2[1] (numeric) = 2.19404485371 3.80391276466
y2[1] (closed_form) = 3.07706200658 3.19384359015
absolute error = 1.073
relative error = 24.2 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.07706200658 3.19384359015
y1[1] (closed_form) = 3.07706200658 3.19384359015
absolute error = 9.220e-31
relative error = 2.079e-29 %
Correct digits = 31
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) = 41.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43382.5MB, alloc=44.3MB, time=534.25
memory used=43429.5MB, alloc=44.3MB, time=534.83
x[1] = 0.5613 2.042
h = 0.003 0.006
y2[1] (numeric) = 2.20200557555 3.81607016623
y2[1] (closed_form) = 3.08544121655 3.20688414955
absolute error = 1.073
relative error = 24.11 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.08544121655 3.20688414955
y1[1] (closed_form) = 3.08544121655 3.20688414955
absolute error = 9.220e-31
relative error = 2.072e-29 %
Correct digits = 31
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) = 41.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43476.0MB, alloc=44.3MB, time=535.40
memory used=43523.0MB, alloc=44.3MB, time=535.98
x[1] = 0.5643 2.048
h = 0.0001 0.005
y2[1] (numeric) = 2.21001843659 3.82825061244
y2[1] (closed_form) = 3.10757570324 3.2207411846
absolute error = 1.084
relative error = 24.22 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.10757570324 3.2207411846
y1[1] (closed_form) = 3.10757570324 3.2207411846
absolute error = 9.220e-31
relative error = 2.060e-29 %
Correct digits = 31
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) = 41.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43569.5MB, alloc=44.3MB, time=536.54
memory used=43616.5MB, alloc=44.3MB, time=537.12
x[1] = 0.5644 2.053
h = 0.0001 0.003
y2[1] (numeric) = 2.21808373038 3.8404540811
y2[1] (closed_form) = 3.11812960437 3.2372252581
absolute error = 1.083
relative error = 24.11 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.11812960437 3.2372252581
y1[1] (closed_form) = 3.11812960437 3.2372252581
absolute error = 9.220e-31
relative error = 2.051e-29 %
Correct digits = 31
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) = 41.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43663.3MB, alloc=44.3MB, time=537.70
x[1] = 0.5645 2.056
h = 0.001 0.001
y2[1] (numeric) = 2.22620175348 3.85268054824
y2[1] (closed_form) = 3.12462309739 3.24707124707
absolute error = 1.083
relative error = 24.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.12462309739 3.24707124707
y1[1] (closed_form) = 3.12462309739 3.24707124707
absolute error = 8.485e-31
relative error = 1.883e-29 %
Correct digits = 31
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) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43710.2MB, alloc=44.3MB, time=538.28
memory used=43757.1MB, alloc=44.3MB, time=538.86
x[1] = 0.5655 2.057
h = 0.001 0.003
y2[1] (numeric) = 2.23437280343 3.86492999064
y2[1] (closed_form) = 3.13003769077 3.24836814098
absolute error = 1.087
relative error = 24.1 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.13003769077 3.24836814098
y1[1] (closed_form) = 3.13003769077 3.24836814098
absolute error = 9.220e-31
relative error = 2.044e-29 %
Correct digits = 31
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) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43803.6MB, alloc=44.3MB, time=539.42
memory used=43850.6MB, alloc=44.3MB, time=540.00
x[1] = 0.5665 2.06
h = 0.0001 0.004
y2[1] (numeric) = 2.24259717795 3.87720238523
y2[1] (closed_form) = 3.13959689371 3.25638211815
absolute error = 1.091
relative error = 24.12 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.13959689371 3.25638211815
y1[1] (closed_form) = 3.13959689371 3.25638211815
absolute error = 9.220e-31
relative error = 2.038e-29 %
Correct digits = 31
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) = 41.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43897.1MB, alloc=44.3MB, time=540.57
memory used=43944.1MB, alloc=44.3MB, time=541.14
x[1] = 0.5666 2.064
h = 0.003 0.006
y2[1] (numeric) = 2.25087517496 3.88949770893
y2[1] (closed_form) = 3.1482364982 3.26965591504
absolute error = 1.091
relative error = 24.03 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.1482364982 3.26965591504
y1[1] (closed_form) = 3.1482364982 3.26965591504
absolute error = 1.063e-30
relative error = 2.342e-29 %
Correct digits = 31
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) = 41.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43990.7MB, alloc=44.3MB, time=541.71
x[1] = 0.5696 2.07
h = 0.0001 0.005
y2[1] (numeric) = 2.25920709305 3.90181593874
y2[1] (closed_form) = 3.17093540923 3.2836816054
absolute error = 1.102
relative error = 24.13 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.17093540923 3.2836816054
y1[1] (closed_form) = 3.17093540923 3.2836816054
absolute error = 1.063e-30
relative error = 2.329e-29 %
Correct digits = 31
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) = 41.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44037.4MB, alloc=44.3MB, time=542.28
memory used=44084.3MB, alloc=44.3MB, time=542.85
x[1] = 0.5697 2.075
h = 0.0001 0.003
y2[1] (numeric) = 2.26759323353 3.91415704928
y2[1] (closed_form) = 3.18181763952 3.30046105296
absolute error = 1.101
relative error = 24.02 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.18181763952 3.30046105296
y1[1] (closed_form) = 3.18181763952 3.30046105296
absolute error = 1.063e-30
relative error = 2.319e-29 %
Correct digits = 31
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) = 41.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44131.0MB, alloc=44.3MB, time=543.42
memory used=44178.3MB, alloc=44.3MB, time=544.01
x[1] = 0.5698 2.078
h = 0.001 0.001
y2[1] (numeric) = 2.27603390082 3.92652101335
y2[1] (closed_form) = 3.18851135195 3.31048240117
absolute error = 1.101
relative error = 23.95 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.18851135195 3.31048240117
y1[1] (closed_form) = 3.18851135195 3.31048240117
absolute error = 1.063e-30
relative error = 2.313e-29 %
Correct digits = 31
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) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44225.1MB, alloc=44.3MB, time=544.59
memory used=44272.1MB, alloc=44.3MB, time=545.17
x[1] = 0.5708 2.079
h = 0.001 0.003
y2[1] (numeric) = 2.28452940032 3.93890780449
y2[1] (closed_form) = 3.19405152932 3.31177511504
absolute error = 1.105
relative error = 24.01 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.19405152932 3.31177511504
y1[1] (closed_form) = 3.19405152932 3.31177511504
absolute error = 1.063e-30
relative error = 2.310e-29 %
Correct digits = 31
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) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44318.5MB, alloc=44.3MB, time=545.74
x[1] = 0.5718 2.082
h = 0.0001 0.004
y2[1] (numeric) = 2.29308003762 3.95131739642
y2[1] (closed_form) = 3.20386671783 3.31990631307
absolute error = 1.108
relative error = 24.02 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.20386671783 3.31990631307
y1[1] (closed_form) = 3.20386671783 3.31990631307
absolute error = 1.063e-30
relative error = 2.304e-29 %
Correct digits = 31
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) = 41.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44365.3MB, alloc=44.3MB, time=546.30
memory used=44412.1MB, alloc=44.3MB, time=546.87
x[1] = 0.5719 2.086
h = 0.003 0.006
y2[1] (numeric) = 2.30168611852 3.96374976286
y2[1] (closed_form) = 3.21277375154 3.33341738436
absolute error = 1.108
relative error = 23.93 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.21277375154 3.33341738436
y1[1] (closed_form) = 3.21277375154 3.33341738436
absolute error = 1.063e-30
relative error = 2.296e-29 %
Correct digits = 31
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) = 41.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44458.5MB, alloc=44.3MB, time=547.44
memory used=44505.6MB, alloc=44.3MB, time=548.02
x[1] = 0.5749 2.092
h = 0.0001 0.005
y2[1] (numeric) = 2.3103479495 3.97620487754
y2[1] (closed_form) = 3.23605070687 3.34761283087
absolute error = 1.119
relative error = 24.03 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.23605070687 3.34761283087
y1[1] (closed_form) = 3.23605070687 3.34761283087
absolute error = 1.063e-30
relative error = 2.283e-29 %
Correct digits = 31
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) = 41.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44552.2MB, alloc=44.3MB, time=548.58
memory used=44599.4MB, alloc=44.3MB, time=549.16
x[1] = 0.575 2.097
h = 0.0001 0.003
y2[1] (numeric) = 2.31906583982 3.98868271183
y2[1] (closed_form) = 3.24727014106 3.36469276468
absolute error = 1.118
relative error = 23.92 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.24727014106 3.36469276468
y1[1] (closed_form) = 3.24727014106 3.36469276468
absolute error = 1.131e-30
relative error = 2.419e-29 %
Correct digits = 31
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) = 42.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44646.1MB, alloc=44.3MB, time=549.74
x[1] = 0.5751 2.1
h = 0.001 0.001
y2[1] (numeric) = 2.32784010189 4.00118323517
y2[1] (closed_form) = 3.25416946186 3.37489248002
absolute error = 1.118
relative error = 23.85 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.25416946186 3.37489248002
y1[1] (closed_form) = 3.25416946186 3.37489248002
absolute error = 1.131e-30
relative error = 2.413e-29 %
Correct digits = 31
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) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44693.3MB, alloc=44.3MB, time=550.32
memory used=44740.2MB, alloc=44.3MB, time=550.90
x[1] = 0.5761 2.101
h = 0.001 0.003
y2[1] (numeric) = 2.33667104915 4.01370641777
y2[1] (closed_form) = 3.25983805061 3.37618031115
absolute error = 1.122
relative error = 23.91 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.25983805061 3.37618031115
y1[1] (closed_form) = 3.25983805061 3.37618031115
absolute error = 1.063e-30
relative error = 2.265e-29 %
Correct digits = 31
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) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44786.7MB, alloc=44.3MB, time=551.47
memory used=44833.8MB, alloc=44.3MB, time=552.05
x[1] = 0.5771 2.104
h = 0.0001 0.004
y2[1] (numeric) = 2.34555899522 4.02625223002
y2[1] (closed_form) = 3.269915596 3.38443014816
absolute error = 1.125
relative error = 23.91 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.269915596 3.38443014816
y1[1] (closed_form) = 3.269915596 3.38443014816
absolute error = 1.140e-30
relative error = 2.423e-29 %
Correct digits = 31
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) = 42.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44880.2MB, alloc=44.3MB, time=552.61
memory used=44927.1MB, alloc=44.3MB, time=553.19
x[1] = 0.5772 2.108
h = 0.003 0.006
y2[1] (numeric) = 2.35450425395 4.03882064228
y2[1] (closed_form) = 3.27909727085 3.39818257659
absolute error = 1.125
relative error = 23.82 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.27909727085 3.39818257659
y1[1] (closed_form) = 3.27909727085 3.39818257659
absolute error = 1.131e-30
relative error = 2.396e-29 %
Correct digits = 31
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) = 42.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44973.6MB, alloc=44.3MB, time=553.75
x[1] = 0.5802 2.114
h = 0.0001 0.005
y2[1] (numeric) = 2.36350713986 4.05141162499
y2[1] (closed_form) = 3.30296619363 3.41254882267
absolute error = 1.136
relative error = 23.92 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.30296619363 3.41254882267
y1[1] (closed_form) = 3.30296619363 3.41254882267
absolute error = 1.131e-30
relative error = 2.382e-29 %
Correct digits = 31
memory used=45020.7MB, alloc=44.3MB, time=554.33
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) = 42.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45067.3MB, alloc=44.3MB, time=554.90
x[1] = 0.5803 2.119
h = 0.0001 0.003
y2[1] (numeric) = 2.37256797033 4.06402514609
y2[1] (closed_form) = 3.31453193025 3.4299344133
absolute error = 1.136
relative error = 23.81 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.31453193025 3.4299344133
y1[1] (closed_form) = 3.31453193025 3.4299344133
absolute error = 1.204e-30
relative error = 2.525e-29 %
Correct digits = 31
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) = 42.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45113.8MB, alloc=44.3MB, time=555.46
memory used=45161.3MB, alloc=44.3MB, time=556.06
x[1] = 0.5804 2.122
h = 0.001 0.001
y2[1] (numeric) = 2.38168706592 4.07666117156
y2[1] (closed_form) = 3.32164238373 3.440315537
absolute error = 1.135
relative error = 23.74 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.32164238373 3.440315537
y1[1] (closed_form) = 3.32164238373 3.440315537
absolute error = 1.140e-30
relative error = 2.384e-29 %
Correct digits = 31
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) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45208.0MB, alloc=44.3MB, time=556.63
memory used=45255.0MB, alloc=44.3MB, time=557.21
x[1] = 0.5814 2.123
h = 0.0001 0.004
y2[1] (numeric) = 2.39086474829 4.08931966817
y2[1] (closed_form) = 3.32744226864 3.44159775053
absolute error = 1.139
relative error = 23.79 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.32744226864 3.44159775053
y1[1] (closed_form) = 3.32744226864 3.44159775053
absolute error = 1.140e-30
relative error = 2.382e-29 %
Correct digits = 31
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) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45301.4MB, alloc=44.3MB, time=557.78
memory used=45348.4MB, alloc=44.3MB, time=558.35
x[1] = 0.5815 2.127
h = 0.003 0.006
y2[1] (numeric) = 2.40010133927 4.1020006029
y2[1] (closed_form) = 3.33686331695 3.45556462738
absolute error = 1.138
relative error = 23.69 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.33686331695 3.45556462738
y1[1] (closed_form) = 3.33686331695 3.45556462738
absolute error = 1.131e-30
relative error = 2.355e-29 %
Correct digits = 31
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) = 42.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45394.9MB, alloc=44.3MB, time=558.92
x[1] = 0.5845 2.133
h = 0.0001 0.005
y2[1] (numeric) = 2.40939716123 4.11470394283
y2[1] (closed_form) = 3.36125112078 3.47008596468
absolute error = 1.15
relative error = 23.8 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.36125112078 3.47008596468
y1[1] (closed_form) = 3.36125112078 3.47008596468
absolute error = 1.131e-30
relative error = 2.342e-29 %
Correct digits = 31
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) = 42.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45441.4MB, alloc=44.3MB, time=559.48
memory used=45488.4MB, alloc=44.3MB, time=560.06
x[1] = 0.5846 2.138
h = 0.0001 0.003
y2[1] (numeric) = 2.41875253941 4.12742965255
y2[1] (closed_form) = 3.3731186778 3.48774311659
absolute error = 1.149
relative error = 23.68 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.3731186778 3.48774311659
y1[1] (closed_form) = 3.3731186778 3.48774311659
absolute error = 1.131e-30
relative error = 2.332e-29 %
Correct digits = 31
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) = 42.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45535.2MB, alloc=44.3MB, time=560.64
memory used=45582.6MB, alloc=44.3MB, time=561.23
x[1] = 0.5847 2.141
h = 0.001 0.001
y2[1] (numeric) = 2.42816780232 4.14017769459
y2[1] (closed_form) = 3.38041318584 3.49828545858
absolute error = 1.148
relative error = 23.61 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.38041318584 3.49828545858
y1[1] (closed_form) = 3.38041318584 3.49828545858
absolute error = 1.131e-30
relative error = 2.326e-29 %
Correct digits = 31
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) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45629.2MB, alloc=44.3MB, time=561.80
memory used=45676.2MB, alloc=44.3MB, time=562.38
x[1] = 0.5857 2.142
h = 0.001 0.003
y2[1] (numeric) = 2.43764327953 4.15294803231
y2[1] (closed_form) = 3.38632852029 3.49956383476
absolute error = 1.152
relative error = 23.65 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.38632852029 3.49956383476
y1[1] (closed_form) = 3.38632852029 3.49956383476
absolute error = 1.131e-30
relative error = 2.323e-29 %
Correct digits = 31
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) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45722.8MB, alloc=44.3MB, time=562.95
x[1] = 0.5867 2.145
h = 0.0001 0.004
y2[1] (numeric) = 2.44717930084 4.16574062922
y2[1] (closed_form) = 3.39691026223 3.50804149198
absolute error = 1.155
relative error = 23.66 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.39691026223 3.50804149198
y1[1] (closed_form) = 3.39691026223 3.50804149198
absolute error = 1.204e-30
relative error = 2.466e-29 %
Correct digits = 31
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) = 42.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45769.3MB, alloc=44.3MB, time=563.52
memory used=45816.3MB, alloc=44.3MB, time=564.09
x[1] = 0.5868 2.149
h = 0.003 0.006
y2[1] (numeric) = 2.45677619623 4.17855544884
y2[1] (closed_form) = 3.40661980788 3.52225753658
absolute error = 1.155
relative error = 23.56 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.40661980788 3.52225753658
y1[1] (closed_form) = 3.40661980788 3.52225753658
absolute error = 1.204e-30
relative error = 2.457e-29 %
Correct digits = 31
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) = 43.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45862.8MB, alloc=44.3MB, time=564.65
memory used=45909.9MB, alloc=44.3MB, time=565.23
x[1] = 0.5898 2.155
h = 0.0001 0.005
y2[1] (numeric) = 2.46643429644 4.1913924547
y2[1] (closed_form) = 3.43162630562 3.53695162734
absolute error = 1.166
relative error = 23.66 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.43162630562 3.53695162734
y1[1] (closed_form) = 3.43162630562 3.53695162734
absolute error = 1.204e-30
relative error = 2.443e-29 %
Correct digits = 31
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) = 43.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45956.4MB, alloc=44.3MB, time=565.80
memory used=46003.4MB, alloc=44.3MB, time=566.37
x[1] = 0.5899 2.16
h = 0.0001 0.003
y2[1] (numeric) = 2.47615393511 4.20425160777
y2[1] (closed_form) = 3.44385764621 3.55492432831
absolute error = 1.165
relative error = 23.55 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.44385764621 3.55492432831
y1[1] (closed_form) = 3.44385764621 3.55492432831
absolute error = 1.204e-30
relative error = 2.433e-29 %
Correct digits = 31
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) = 43.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46050.1MB, alloc=44.3MB, time=566.95
x[1] = 0.59 2.163
h = 0.001 0.001
y2[1] (numeric) = 2.48593544924 4.21713286691
y2[1] (closed_form) = 3.45137390054 3.5656538966
absolute error = 1.165
relative error = 23.47 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.45137390054 3.5656538966
y1[1] (closed_form) = 3.45137390054 3.5656538966
absolute error = 1.204e-30
relative error = 2.427e-29 %
Correct digits = 31
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) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46097.1MB, alloc=44.3MB, time=567.53
memory used=46144.1MB, alloc=44.3MB, time=568.11
x[1] = 0.591 2.164
h = 0.001 0.003
y2[1] (numeric) = 2.49577917693 4.23003619179
y2[1] (closed_form) = 3.45742606549 3.56692523469
absolute error = 1.168
relative error = 23.51 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.45742606549 3.56692523469
y1[1] (closed_form) = 3.45742606549 3.56692523469
absolute error = 1.204e-30
relative error = 2.424e-29 %
Correct digits = 31
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) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46190.4MB, alloc=44.3MB, time=568.68
memory used=46237.4MB, alloc=44.3MB, time=569.25
x[1] = 0.592 2.167
h = 0.0001 0.004
y2[1] (numeric) = 2.50568545647 4.24296154227
y2[1] (closed_form) = 3.46828919926 3.57552562754
absolute error = 1.171
relative error = 23.52 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.46828919926 3.57552562754
y1[1] (closed_form) = 3.46828919926 3.57552562754
absolute error = 1.281e-30
relative error = 2.571e-29 %
Correct digits = 31
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) = 43.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46283.8MB, alloc=44.3MB, time=569.82
memory used=46330.8MB, alloc=44.3MB, time=570.40
x[1] = 0.5921 2.171
h = 0.003 0.006
y2[1] (numeric) = 2.51565462638 4.25590887818
y2[1] (closed_form) = 3.47829498449 3.58999505687
absolute error = 1.171
relative error = 23.42 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.47829498449 3.58999505687
y1[1] (closed_form) = 3.47829498449 3.58999505687
absolute error = 1.281e-30
relative error = 2.562e-29 %
Correct digits = 31
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) = 43.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46377.2MB, alloc=44.3MB, time=570.96
x[1] = 0.5951 2.177
h = 0.0001 0.005
y2[1] (numeric) = 2.52568702594 4.26887815942
y2[1] (closed_form) = 3.5039350041 3.60486276852
absolute error = 1.182
relative error = 23.52 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.5039350041 3.60486276852
y1[1] (closed_form) = 3.5039350041 3.60486276852
absolute error = 1.281e-30
relative error = 2.547e-29 %
Correct digits = 31
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) = 43.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46423.9MB, alloc=44.3MB, time=571.53
memory used=46470.8MB, alloc=44.3MB, time=572.11
x[1] = 0.5952 2.182
h = 0.0001 0.003
y2[1] (numeric) = 2.53578299739 4.28186934318
y2[1] (closed_form) = 3.51653989636 3.62315636013
absolute error = 1.181
relative error = 23.4 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.51653989636 3.62315636013
y1[1] (closed_form) = 3.51653989636 3.62315636013
absolute error = 1.345e-30
relative error = 2.665e-29 %
Correct digits = 31
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) = 43.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46517.3MB, alloc=44.3MB, time=572.68
memory used=46564.8MB, alloc=44.3MB, time=573.27
x[1] = 0.5953 2.185
h = 0.001 0.001
y2[1] (numeric) = 2.54594288638 4.29488238453
y2[1] (closed_form) = 3.52428382614 3.63407629366
absolute error = 1.181
relative error = 23.32 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.52428382614 3.63407629366
y1[1] (closed_form) = 3.52428382614 3.63407629366
absolute error = 1.345e-30
relative error = 2.658e-29 %
Correct digits = 31
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) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46611.5MB, alloc=44.3MB, time=573.84
memory used=46658.5MB, alloc=44.3MB, time=574.42
x[1] = 0.5963 2.186
h = 0.001 0.003
y2[1] (numeric) = 2.55616703969 4.30791723934
y2[1] (closed_form) = 3.53047587741 3.63533976182
absolute error = 1.184
relative error = 23.36 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.53047587741 3.63533976182
y1[1] (closed_form) = 3.53047587741 3.63533976182
absolute error = 1.345e-30
relative error = 2.655e-29 %
Correct digits = 31
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) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46704.9MB, alloc=44.3MB, time=574.99
x[1] = 0.5973 2.189
h = 0.0001 0.004
y2[1] (numeric) = 2.56645580432 4.32097386368
y2[1] (closed_form) = 3.54162736153 3.64406427794
absolute error = 1.187
relative error = 23.36 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.54162736153 3.64406427794
y1[1] (closed_form) = 3.54162736153 3.64406427794
absolute error = 1.414e-30
relative error = 2.783e-29 %
Correct digits = 31
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) = 43.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46751.7MB, alloc=44.3MB, time=575.56
memory used=46798.5MB, alloc=44.3MB, time=576.13
x[1] = 0.5974 2.193
h = 0.003 0.006
y2[1] (numeric) = 2.57680952749 4.33405221361
y2[1] (closed_form) = 3.55193732273 3.65879135542
absolute error = 1.186
relative error = 23.26 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.55193732273 3.65879135542
y1[1] (closed_form) = 3.55193732273 3.65879135542
absolute error = 1.414e-30
relative error = 2.773e-29 %
Correct digits = 31
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) = 44.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46845.0MB, alloc=44.3MB, time=576.69
memory used=46892.0MB, alloc=44.3MB, time=577.27
x[1] = 0.6004 2.199
h = 0.0001 0.005
y2[1] (numeric) = 2.58722855717 4.3471522452
y2[1] (closed_form) = 3.57822602149 3.67383348676
absolute error = 1.198
relative error = 23.36 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.57822602149 3.67383348676
y1[1] (closed_form) = 3.57822602149 3.67383348676
absolute error = 1.345e-30
relative error = 2.623e-29 %
Correct digits = 31
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) = 44.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46938.5MB, alloc=44.3MB, time=577.83
memory used=46985.6MB, alloc=44.3MB, time=578.41
x[1] = 0.6005 2.204
h = 0.0001 0.003
y2[1] (numeric) = 2.59771324439 4.36027391178
y2[1] (closed_form) = 3.59121447866 3.69245336982
absolute error = 1.197
relative error = 23.24 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.59121447866 3.69245336982
y1[1] (closed_form) = 3.59121447866 3.69245336982
absolute error = 1.273e-30
relative error = 2.471e-29 %
Correct digits = 31
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) = 44.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47032.3MB, alloc=44.3MB, time=578.98
x[1] = 0.6006 2.207
h = 0.001 0.001
y2[1] (numeric) = 2.60826394362 4.3734171645
y2[1] (closed_form) = 3.59919216125 3.7035668412
absolute error = 1.196
relative error = 23.16 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.59919216125 3.7035668412
y1[1] (closed_form) = 3.59919216125 3.7035668412
absolute error = 1.273e-30
relative error = 2.465e-29 %
Correct digits = 31
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) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47079.5MB, alloc=44.3MB, time=579.57
memory used=47126.1MB, alloc=44.3MB, time=580.14
x[1] = 0.6016 2.208
h = 0.001 0.003
y2[1] (numeric) = 2.61888101053 4.38658195529
y2[1] (closed_form) = 3.6055272166 3.70482157139
absolute error = 1.199
relative error = 23.2 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.6055272166 3.70482157139
y1[1] (closed_form) = 3.6055272166 3.70482157139
absolute error = 1.345e-30
relative error = 2.602e-29 %
Correct digits = 31
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) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47172.6MB, alloc=44.3MB, time=580.71
memory used=47219.6MB, alloc=44.3MB, time=581.28
x[1] = 0.6026 2.211
h = 0.0001 0.004
y2[1] (numeric) = 2.62956480097 4.39976823631
y2[1] (closed_form) = 3.61697417 3.71367158775
absolute error = 1.202
relative error = 23.19 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.61697417 3.71367158775
y1[1] (closed_form) = 3.61697417 3.71367158775
absolute error = 1.204e-30
relative error = 2.323e-29 %
Correct digits = 31
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) = 44.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47266.0MB, alloc=44.3MB, time=581.85
memory used=47313.0MB, alloc=44.3MB, time=582.43
x[1] = 0.6027 2.215
h = 0.003 0.006
y2[1] (numeric) = 2.64031567103 4.41297595969
y2[1] (closed_form) = 3.62759644233 3.72866062332
absolute error = 1.201
relative error = 23.09 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.62759644233 3.72866062332
y1[1] (closed_form) = 3.62759644233 3.72866062332
absolute error = 1.345e-30
relative error = 2.586e-29 %
Correct digits = 31
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) = 44.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47359.4MB, alloc=44.3MB, time=583.00
memory used=47406.5MB, alloc=44.3MB, time=583.57
x[1] = 0.6057 2.221
h = 0.0001 0.005
y2[1] (numeric) = 2.6511339776 4.42620507759
y2[1] (closed_form) = 3.65454931394 3.74387790143
absolute error = 1.213
relative error = 23.19 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.65454931394 3.74387790143
y1[1] (closed_form) = 3.65454931394 3.74387790143
absolute error = 1.345e-30
relative error = 2.571e-29 %
Correct digits = 31
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) = 44.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47453.0MB, alloc=44.3MB, time=584.14
x[1] = 0.6058 2.226
h = 0.0001 0.003
y2[1] (numeric) = 2.66202008063 4.43945553934
y2[1] (closed_form) = 3.66793160025 3.76282953601
absolute error = 1.212
relative error = 23.07 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.66793160025 3.76282953601
y1[1] (closed_form) = 3.66793160025 3.76282953601
absolute error = 1.345e-30
relative error = 2.560e-29 %
Correct digits = 31
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) = 44.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47499.6MB, alloc=44.3MB, time=584.70
memory used=47547.0MB, alloc=44.3MB, time=585.30
x[1] = 0.6059 2.229
h = 0.001 0.001
y2[1] (numeric) = 2.67297434362 4.452727292
y2[1] (closed_form) = 3.67614926471 3.77413975159
absolute error = 1.211
relative error = 22.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.67614926471 3.77413975159
y1[1] (closed_form) = 3.67614926471 3.77413975159
absolute error = 1.281e-30
relative error = 2.431e-29 %
Correct digits = 31
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) = 44.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47593.8MB, alloc=44.3MB, time=585.88
memory used=47640.9MB, alloc=44.3MB, time=586.45
x[1] = 0.6069 2.23
h = 0.0001 0.004
y2[1] (numeric) = 2.68399713128 4.46602028347
y2[1] (closed_form) = 3.68263050506 3.77538483842
absolute error = 1.214
relative error = 23.02 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.68263050506 3.77538483842
y1[1] (closed_form) = 3.68263050506 3.77538483842
absolute error = 1.345e-30
relative error = 2.551e-29 %
Correct digits = 31
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) = 44.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47687.2MB, alloc=44.3MB, time=587.02
memory used=47734.1MB, alloc=44.3MB, time=587.59
x[1] = 0.607 2.234
h = 0.003 0.006
y2[1] (numeric) = 2.69508880853 4.4793344619
y2[1] (closed_form) = 3.69352508289 3.79060670154
absolute error = 1.213
relative error = 22.92 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.69352508289 3.79060670154
y1[1] (closed_form) = 3.69352508289 3.79060670154
absolute error = 1.345e-30
relative error = 2.542e-29 %
Correct digits = 31
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) = 45.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47780.7MB, alloc=44.3MB, time=588.16
x[1] = 0.61 2.24
h = 0.0001 0.005
y2[1] (numeric) = 2.7062497409 4.49266977553
y2[1] (closed_form) = 3.72106022476 3.80598343431
absolute error = 1.225
relative error = 23.02 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.72106022476 3.80598343431
y1[1] (closed_form) = 3.72106022476 3.80598343431
absolute error = 1.345e-30
relative error = 2.528e-29 %
Correct digits = 31
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) = 45.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47827.1MB, alloc=44.3MB, time=588.72
memory used=47874.2MB, alloc=44.3MB, time=589.30
x[1] = 0.6101 2.245
h = 0.0001 0.003
y2[1] (numeric) = 2.71748029703 4.50602616973
y2[1] (closed_form) = 3.73478587995 3.82522990964
absolute error = 1.224
relative error = 22.9 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.73478587995 3.82522990964
y1[1] (closed_form) = 3.73478587995 3.82522990964
absolute error = 1.421e-30
relative error = 2.659e-29 %
Correct digits = 31
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) = 45.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47920.8MB, alloc=44.3MB, time=589.87
memory used=47968.3MB, alloc=44.3MB, time=590.46
x[1] = 0.6102 2.248
h = 0.001 0.001
y2[1] (numeric) = 2.72878084918 4.51940358752
y2[1] (closed_form) = 3.74321282313 3.83671503191
absolute error = 1.223
relative error = 22.81 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.74321282313 3.83671503191
y1[1] (closed_form) = 3.74321282313 3.83671503191
absolute error = 1.421e-30
relative error = 2.652e-29 %
Correct digits = 31
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) = 45.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48014.9MB, alloc=44.3MB, time=591.04
memory used=48061.9MB, alloc=44.3MB, time=591.62
x[1] = 0.6112 2.249
h = 0.001 0.003
y2[1] (numeric) = 2.7401517708 4.53280197279
y2[1] (closed_form) = 3.74982262126 3.8379528578
absolute error = 1.226
relative error = 22.84 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.74982262126 3.8379528578
y1[1] (closed_form) = 3.74982262126 3.8379528578
absolute error = 1.500e-30
relative error = 2.796e-29 %
Correct digits = 31
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) = 45.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48108.4MB, alloc=44.3MB, time=592.18
x[1] = 0.6122 2.252
h = 0.0001 0.004
y2[1] (numeric) = 2.75159343558 4.54622126963
y2[1] (closed_form) = 3.76183735255 3.84704375246
absolute error = 1.229
relative error = 22.83 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.76183735255 3.84704375246
y1[1] (closed_form) = 3.76183735255 3.84704375246
absolute error = 1.500e-30
relative error = 2.788e-29 %
Correct digits = 31
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) = 45.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48154.9MB, alloc=44.3MB, time=592.75
memory used=48201.9MB, alloc=44.3MB, time=593.32
x[1] = 0.6123 2.256
h = 0.003 0.006
y2[1] (numeric) = 2.76310621744 4.55966142209
y2[1] (closed_form) = 3.77305987175 3.86253582025
absolute error = 1.227
relative error = 22.73 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.77305987175 3.86253582025
y1[1] (closed_form) = 3.77305987175 3.86253582025
absolute error = 1.562e-30
relative error = 2.893e-29 %
Correct digits = 31
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) = 45.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48248.4MB, alloc=44.3MB, time=593.89
memory used=48295.5MB, alloc=44.3MB, time=594.47
x[1] = 0.6153 2.262
h = 0.0001 0.005
y2[1] (numeric) = 2.77469049114 4.57312237426
y2[1] (closed_form) = 3.80128893047 3.87808904471
absolute error = 1.24
relative error = 22.83 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.80128893047 3.87808904471
y1[1] (closed_form) = 3.80128893047 3.87808904471
absolute error = 1.562e-30
relative error = 2.876e-29 %
Correct digits = 31
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) = 45.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48341.9MB, alloc=44.3MB, time=595.04
memory used=48389.0MB, alloc=44.3MB, time=595.61
x[1] = 0.6154 2.267
h = 0.0001 0.003
y2[1] (numeric) = 2.7863466346 4.58660406724
y2[1] (closed_form) = 3.81542813586 3.89767771929
absolute error = 1.238
relative error = 22.7 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.81542813586 3.89767771929
y1[1] (closed_form) = 3.81542813586 3.89767771929
absolute error = 1.562e-30
relative error = 2.864e-29 %
Correct digits = 31
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) = 45.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48435.9MB, alloc=44.3MB, time=596.19
x[1] = 0.6155 2.27
h = 0.001 0.001
y2[1] (numeric) = 2.79807502944 4.60010643974
y2[1] (closed_form) = 3.82410702873 3.90936572043
absolute error = 1.237
relative error = 22.62 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.82410702873 3.90936572043
y1[1] (closed_form) = 3.82410702873 3.90936572043
absolute error = 1.562e-30
relative error = 2.856e-29 %
Correct digits = 31
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) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48482.7MB, alloc=44.3MB, time=596.77
memory used=48529.7MB, alloc=44.3MB, time=597.35
x[1] = 0.6165 2.271
h = 0.001 0.003
y2[1] (numeric) = 2.80987605851 4.61362943135
y2[1] (closed_form) = 3.83086911506 3.91059215462
absolute error = 1.24
relative error = 22.64 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.83086911506 3.91059215462
y1[1] (closed_form) = 3.83086911506 3.91059215462
absolute error = 1.562e-30
relative error = 2.853e-29 %
Correct digits = 31
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) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48576.2MB, alloc=44.3MB, time=597.92
memory used=48623.2MB, alloc=44.3MB, time=598.49
x[1] = 0.6175 2.274
h = 0.0001 0.004
y2[1] (numeric) = 2.82175010489 4.62717298182
y2[1] (closed_form) = 3.84320058341 3.91981251202
absolute error = 1.242
relative error = 22.63 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.84320058341 3.91981251202
y1[1] (closed_form) = 3.84320058341 3.91981251202
absolute error = 1.562e-30
relative error = 2.845e-29 %
Correct digits = 31
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) = 46.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48669.5MB, alloc=44.3MB, time=599.06
memory used=48716.5MB, alloc=44.3MB, time=599.65
x[1] = 0.6176 2.278
h = 0.003 0.006
y2[1] (numeric) = 2.83369755191 4.64073703093
y2[1] (closed_form) = 3.85475977361 3.93557923036
absolute error = 1.241
relative error = 22.53 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.85475977361 3.93557923036
y1[1] (closed_form) = 3.85475977361 3.93557923036
absolute error = 1.562e-30
relative error = 2.836e-29 %
Correct digits = 31
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) = 46.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48763.0MB, alloc=44.3MB, time=600.21
x[1] = 0.6206 2.284
h = 0.0001 0.005
y2[1] (numeric) = 2.84571878373 4.65432151843
y2[1] (closed_form) = 3.88369924671 3.95130945406
absolute error = 1.254
relative error = 22.63 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.88369924671 3.95130945406
y1[1] (closed_form) = 3.88369924671 3.95130945406
absolute error = 1.628e-30
relative error = 2.938e-29 %
Correct digits = 31
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) = 46.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48809.7MB, alloc=44.3MB, time=600.78
memory used=48856.6MB, alloc=44.3MB, time=601.36
x[1] = 0.6207 2.289
h = 0.0001 0.003
y2[1] (numeric) = 2.85781418778 4.66792638105
y2[1] (closed_form) = 3.89826301712 3.9712459613
absolute error = 1.252
relative error = 22.5 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.89826301712 3.9712459613
y1[1] (closed_form) = 3.89826301712 3.9712459613
absolute error = 1.703e-30
relative error = 3.060e-29 %
Correct digits = 31
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) = 46.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48903.2MB, alloc=44.3MB, time=601.92
memory used=48950.5MB, alloc=44.3MB, time=602.52
x[1] = 0.6208 2.292
h = 0.001 0.001
y2[1] (numeric) = 2.8699841552 4.68155155302
y2[1] (closed_form) = 3.90720054244 3.98314014607
absolute error = 1.25
relative error = 22.41 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.90720054244 3.98314014607
y1[1] (closed_form) = 3.90720054244 3.98314014607
absolute error = 1.703e-30
relative error = 3.052e-29 %
Correct digits = 31
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) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48997.4MB, alloc=44.3MB, time=603.10
memory used=49044.4MB, alloc=44.3MB, time=603.69
x[1] = 0.6218 2.293
h = 0.001 0.003
y2[1] (numeric) = 2.88222907844 4.69519696947
y2[1] (closed_form) = 3.914118286 3.98435417068
absolute error = 1.253
relative error = 22.43 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.914118286 3.98435417068
y1[1] (closed_form) = 3.914118286 3.98435417068
absolute error = 1.780e-30
relative error = 3.188e-29 %
Correct digits = 30
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) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49091.0MB, alloc=44.3MB, time=604.26
x[1] = 0.6228 2.296
h = 0.0001 0.004
y2[1] (numeric) = 2.89454935015 4.70886256573
y2[1] (closed_form) = 3.92677426394 3.99370531867
absolute error = 1.256
relative error = 22.42 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.92677426394 3.99370531867
y1[1] (closed_form) = 3.92677426394 3.99370531867
absolute error = 1.780e-30
relative error = 3.179e-29 %
Correct digits = 30
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) = 46.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49137.5MB, alloc=44.3MB, time=604.82
memory used=49184.3MB, alloc=44.3MB, time=605.40
x[1] = 0.6229 2.3
h = 0.003 0.006
y2[1] (numeric) = 2.90694536327 4.72254827708
y2[1] (closed_form) = 3.93867907232 4.00975118017
absolute error = 1.254
relative error = 22.31 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.93867907232 4.00975118017
y1[1] (closed_form) = 3.93867907232 4.00975118017
absolute error = 1.640e-30
relative error = 2.918e-29 %
Correct digits = 31
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) = 46.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49230.8MB, alloc=44.3MB, time=605.96
memory used=49277.9MB, alloc=44.3MB, time=606.54
x[1] = 0.6259 2.306
h = 0.0001 0.005
y2[1] (numeric) = 2.91941751157 4.73625403886
y2[1] (closed_form) = 3.96834582255 4.02565882568
absolute error = 1.267
relative error = 22.41 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.96834582255 4.02565882568
y1[1] (closed_form) = 3.96834582255 4.02565882568
absolute error = 1.703e-30
relative error = 3.013e-29 %
Correct digits = 31
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) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49324.5MB, alloc=44.3MB, time=607.10
memory used=49371.6MB, alloc=44.3MB, time=607.68
x[1] = 0.626 2.311
h = 0.0001 0.003
y2[1] (numeric) = 2.93196619214 4.74997978324
y2[1] (closed_form) = 3.98334544747 4.04594885855
absolute error = 1.265
relative error = 22.29 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.98334544747 4.04594885855
y1[1] (closed_form) = 3.98334544747 4.04594885855
absolute error = 1.640e-30
relative error = 2.889e-29 %
Correct digits = 31
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) = 47.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49418.3MB, alloc=44.3MB, time=608.26
x[1] = 0.6261 2.314
h = 0.001 0.001
y2[1] (numeric) = 2.94459180587 4.76372543984
y2[1] (closed_form) = 3.992548454 4.0580525654
absolute error = 1.263
relative error = 22.19 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.992548454 4.0580525654
y1[1] (closed_form) = 3.992548454 4.0580525654
absolute error = 1.703e-30
relative error = 2.991e-29 %
Correct digits = 31
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) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49465.4MB, alloc=44.3MB, time=608.84
memory used=49512.3MB, alloc=44.3MB, time=609.42
x[1] = 0.6271 2.315
h = 0.001 0.003
y2[1] (numeric) = 2.95729475496 4.77749093917
y2[1] (closed_form) = 3.99962529186 4.05925312059
absolute error = 1.266
relative error = 22.21 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.99962529186 4.05925312059
y1[1] (closed_form) = 3.99962529186 4.05925312059
absolute error = 1.780e-30
relative error = 3.124e-29 %
Correct digits = 31
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) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49558.8MB, alloc=44.3MB, time=609.98
memory used=49605.8MB, alloc=44.3MB, time=610.56
x[1] = 0.6281 2.318
h = 0.0001 0.004
y2[1] (numeric) = 2.97007544188 4.79127621198
y2[1] (closed_form) = 4.01261373041 4.06873637096
absolute error = 1.268
relative error = 22.2 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.01261373041 4.06873637096
y1[1] (closed_form) = 4.01261373041 4.06873637096
absolute error = 1.780e-30
relative error = 3.116e-29 %
Correct digits = 31
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) = 47.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49652.2MB, alloc=44.3MB, time=611.12
memory used=49699.1MB, alloc=44.3MB, time=611.70
x[1] = 0.6282 2.322
h = 0.003 0.006
y2[1] (numeric) = 2.98293426933 4.80508118896
y2[1] (closed_form) = 4.02487332681 4.08506591489
absolute error = 1.267
relative error = 22.08 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.02487332681 4.08506591489
y1[1] (closed_form) = 4.02487332681 4.08506591489
absolute error = 1.703e-30
relative error = 2.970e-29 %
Correct digits = 31
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) = 47.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49745.4MB, alloc=44.3MB, time=612.26
memory used=49792.4MB, alloc=44.3MB, time=612.84
x[1] = 0.6312 2.328
h = 0.0001 0.005
y2[1] (numeric) = 2.99587164088 4.81890580083
y2[1] (closed_form) = 4.05528458987 4.10115131606
absolute error = 1.28
relative error = 22.19 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.05528458987 4.10115131606
y1[1] (closed_form) = 4.05528458987 4.10115131606
absolute error = 1.780e-30
relative error = 3.087e-29 %
Correct digits = 31
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) = 47.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49839.0MB, alloc=44.3MB, time=613.40
x[1] = 0.6313 2.333
h = 0.0001 0.003
y2[1] (numeric) = 3.0088879635 4.83274997506
y2[1] (closed_form) = 4.07073163997 4.12180062707
absolute error = 1.278
relative error = 22.06 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.07073163997 4.12180062707
y1[1] (closed_form) = 4.07073163997 4.12180062707
absolute error = 1.703e-30
relative error = 2.940e-29 %
Correct digits = 31
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) = 47.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49885.6MB, alloc=44.3MB, time=613.97
memory used=49932.9MB, alloc=44.3MB, time=614.57
x[1] = 0.6314 2.336
h = 0.001 0.001
y2[1] (numeric) = 3.02198364801 4.84661363652
y2[1] (closed_form) = 4.08020714636 4.13411722804
absolute error = 1.276
relative error = 21.96 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.08020714636 4.13411722804
y1[1] (closed_form) = 4.08020714636 4.13411722804
absolute error = 1.769e-30
relative error = 3.046e-29 %
Correct digits = 31
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) = 47.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49979.7MB, alloc=44.3MB, time=615.14
memory used=50026.8MB, alloc=44.3MB, time=615.72
x[1] = 0.6324 2.337
h = 0.0001 0.004
y2[1] (numeric) = 3.03515910659 4.86049671098
y2[1] (closed_form) = 4.08744658502 4.13530321073
absolute error = 1.278
relative error = 21.98 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.08744658502 4.13530321073
y1[1] (closed_form) = 4.08744658502 4.13530321073
absolute error = 1.844e-30
relative error = 3.171e-29 %
Correct digits = 30
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) = 47.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50073.3MB, alloc=44.3MB, time=616.30
memory used=50120.3MB, alloc=44.3MB, time=616.88
x[1] = 0.6325 2.341
h = 0.003 0.006
y2[1] (numeric) = 3.04841475168 4.87439912445
y2[1] (closed_form) = 4.10001563431 4.15188498863
absolute error = 1.276
relative error = 21.87 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.10001563431 4.15188498863
y1[1] (closed_form) = 4.10001563431 4.15188498863
absolute error = 1.769e-30
relative error = 3.032e-29 %
Correct digits = 31
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) = 48.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50166.7MB, alloc=44.3MB, time=617.45
x[1] = 0.6355 2.347
h = 0.0001 0.005
y2[1] (numeric) = 3.06175099641 4.88832080308
y2[1] (closed_form) = 4.13107972055 4.1681327478
absolute error = 1.289
relative error = 21.97 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.13107972055 4.1681327478
y1[1] (closed_form) = 4.13107972055 4.1681327478
absolute error = 1.769e-30
relative error = 3.015e-29 %
Correct digits = 31
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) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50213.2MB, alloc=44.3MB, time=618.01
memory used=50260.2MB, alloc=44.3MB, time=618.59
x[1] = 0.6356 2.352
h = 0.0001 0.003
y2[1] (numeric) = 3.0751682573 4.90226166969
y2[1] (closed_form) = 4.1469170103 4.18910148795
absolute error = 1.287
relative error = 21.84 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.1469170103 4.18910148795
y1[1] (closed_form) = 4.1469170103 4.18910148795
absolute error = 1.769e-30
relative error = 3.001e-29 %
Correct digits = 31
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) = 48.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50306.9MB, alloc=44.3MB, time=619.16
memory used=50354.4MB, alloc=44.3MB, time=619.76
x[1] = 0.6357 2.355
h = 0.001 0.001
y2[1] (numeric) = 3.0886669548 4.91622164443
y2[1] (closed_form) = 4.15663023723 4.20160742994
absolute error = 1.285
relative error = 21.74 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.15663023723 4.20160742994
y1[1] (closed_form) = 4.15663023723 4.20160742994
absolute error = 1.769e-30
relative error = 2.993e-29 %
Correct digits = 31
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) = 48.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50401.0MB, alloc=44.3MB, time=620.33
memory used=50448.0MB, alloc=44.3MB, time=620.91
x[1] = 0.6367 2.356
h = 0.001 0.003
y2[1] (numeric) = 3.10224751076 4.93020064835
y2[1] (closed_form) = 4.16401269139 4.20278194686
absolute error = 1.287
relative error = 21.75 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.16401269139 4.20278194686
y1[1] (closed_form) = 4.16401269139 4.20278194686
absolute error = 1.844e-30
relative error = 3.117e-29 %
Correct digits = 31
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) = 48.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50494.5MB, alloc=44.3MB, time=621.48
x[1] = 0.6377 2.359
h = 0.0001 0.004
y2[1] (numeric) = 3.11591034727 4.94419860274
y2[1] (closed_form) = 4.17763994142 4.21251863259
absolute error = 1.289
relative error = 21.73 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.17763994142 4.21251863259
y1[1] (closed_form) = 4.17763994142 4.21251863259
absolute error = 1.769e-30
relative error = 2.982e-29 %
Correct digits = 31
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) = 48.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50540.9MB, alloc=44.3MB, time=622.04
memory used=50587.9MB, alloc=44.3MB, time=622.62
x[1] = 0.6378 2.363
h = 0.003 0.006
y2[1] (numeric) = 3.1296558867 4.95821542883
y2[1] (closed_form) = 4.19058139701 4.2293927791
absolute error = 1.287
relative error = 21.62 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.19058139701 4.2293927791
y1[1] (closed_form) = 4.19058139701 4.2293927791
absolute error = 1.844e-30
relative error = 3.097e-29 %
Correct digits = 31
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) = 48.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50634.2MB, alloc=44.3MB, time=623.18
memory used=50681.3MB, alloc=44.3MB, time=623.76
x[1] = 0.6408 2.369
h = 0.0001 0.005
y2[1] (numeric) = 3.14348455233 4.97225104787
y2[1] (closed_form) = 4.22242308632 4.24581888182
absolute error = 1.301
relative error = 21.72 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.22242308632 4.24581888182
y1[1] (closed_form) = 4.22242308632 4.24581888182
absolute error = 1.844e-30
relative error = 3.079e-29 %
Correct digits = 31
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) = 49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50727.8MB, alloc=44.3MB, time=624.36
memory used=50775.0MB, alloc=44.3MB, time=624.94
x[1] = 0.6409 2.374
h = 0.0001 0.003
y2[1] (numeric) = 3.1573967709 4.98630537772
y2[1] (closed_form) = 4.23873003246 4.2671579084
absolute error = 1.299
relative error = 21.59 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.23873003246 4.2671579084
y1[1] (closed_form) = 4.23873003246 4.2671579084
absolute error = 1.769e-30
relative error = 2.941e-29 %
Correct digits = 31
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) = 49.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50821.8MB, alloc=44.3MB, time=625.52
x[1] = 0.641 2.377
h = 0.001 0.001
y2[1] (numeric) = 3.17139297319 5.00037833346
y2[1] (closed_form) = 4.24872924415 4.27988319678
absolute error = 1.296
relative error = 21.49 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.24872924415 4.27988319678
y1[1] (closed_form) = 4.24872924415 4.27988319678
absolute error = 1.769e-30
relative error = 2.934e-29 %
Correct digits = 31
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) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50868.7MB, alloc=44.3MB, time=626.11
memory used=50915.6MB, alloc=44.3MB, time=626.69
x[1] = 0.642 2.378
h = 0.001 0.003
y2[1] (numeric) = 3.1854735914 5.01446983109
y2[1] (closed_form) = 4.25628102758 4.28104101275
absolute error = 1.298
relative error = 21.5 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.25628102758 4.28104101275
y1[1] (closed_form) = 4.25628102758 4.28104101275
absolute error = 1.769e-30
relative error = 2.931e-29 %
Correct digits = 31
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) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50962.2MB, alloc=44.3MB, time=627.26
memory used=51009.2MB, alloc=44.3MB, time=627.84
x[1] = 0.643 2.381
h = 0.0001 0.004
y2[1] (numeric) = 3.19963905797 5.02857978685
y2[1] (closed_form) = 4.27026449028 4.29091355576
absolute error = 1.3
relative error = 21.48 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.27026449028 4.29091355576
y1[1] (closed_form) = 4.27026449028 4.29091355576
absolute error = 1.769e-30
relative error = 2.922e-29 %
Correct digits = 31
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) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51055.7MB, alloc=44.3MB, time=628.40
memory used=51102.7MB, alloc=44.3MB, time=628.98
x[1] = 0.6431 2.385
h = 0.003 0.006
y2[1] (numeric) = 3.21388980563 5.04270811694
y2[1] (closed_form) = 4.28358818782 4.30808474599
absolute error = 1.298
relative error = 21.36 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.28358818782 4.30808474599
y1[1] (closed_form) = 4.28358818782 4.30808474599
absolute error = 1.769e-30
relative error = 2.912e-29 %
Correct digits = 31
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) = 49.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51149.2MB, alloc=44.3MB, time=629.55
x[1] = 0.6461 2.391
h = 0.0001 0.005
y2[1] (numeric) = 3.22822626803 5.05685473755
y2[1] (closed_form) = 4.3162258284 4.32468925527
absolute error = 1.311
relative error = 21.46 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.3162258284 4.32468925527
y1[1] (closed_form) = 4.3162258284 4.32468925527
absolute error = 1.844e-30
relative error = 3.018e-29 %
Correct digits = 31
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) = 49.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51195.9MB, alloc=44.3MB, time=630.11
memory used=51243.0MB, alloc=44.3MB, time=630.69
x[1] = 0.6462 2.396
h = 0.0001 0.003
y2[1] (numeric) = 3.24264888236 5.07101956139
y2[1] (closed_form) = 4.33301484229 4.34640449415
absolute error = 1.309
relative error = 21.33 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.33301484229 4.34640449415
y1[1] (closed_form) = 4.33301484229 4.34640449415
absolute error = 1.780e-30
relative error = 2.901e-29 %
Correct digits = 31
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) = 50.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51289.8MB, alloc=44.3MB, time=631.26
memory used=51337.2MB, alloc=44.3MB, time=631.86
x[1] = 0.6463 2.399
h = 0.001 0.001
y2[1] (numeric) = 3.25715808992 5.08520249832
y2[1] (closed_form) = 4.34330756538 4.35935259868
absolute error = 1.306
relative error = 21.23 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.34330756538 4.35935259868
y1[1] (closed_form) = 4.34330756538 4.35935259868
absolute error = 1.780e-30
relative error = 2.893e-29 %
Correct digits = 31
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) = 50.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51383.8MB, alloc=44.3MB, time=632.43
memory used=51430.8MB, alloc=44.3MB, time=633.01
x[1] = 0.6473 2.4
h = 0.001 0.003
y2[1] (numeric) = 3.27175433345 5.09940345913
y2[1] (closed_form) = 4.35103239112 4.36049248037
absolute error = 1.308
relative error = 21.23 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.35103239112 4.36049248037
y1[1] (closed_form) = 4.35103239112 4.36049248037
absolute error = 1.703e-30
relative error = 2.765e-29 %
Correct digits = 31
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) = 50.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51477.3MB, alloc=44.3MB, time=633.58
x[1] = 0.6483 2.403
h = 0.0001 0.004
y2[1] (numeric) = 3.28643805597 5.11362235485
y2[1] (closed_form) = 4.36538074432 4.37050212057
absolute error = 1.31
relative error = 21.21 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.36538074432 4.37050212057
y1[1] (closed_form) = 4.36538074432 4.37050212057
absolute error = 1.703e-30
relative error = 2.757e-29 %
Correct digits = 31
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) = 50.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51524.0MB, alloc=44.3MB, time=634.14
memory used=51570.7MB, alloc=44.3MB, time=634.72
x[1] = 0.6484 2.407
h = 0.003 0.006
y2[1] (numeric) = 3.30120970076 5.12785909646
y2[1] (closed_form) = 4.37909676302 4.38797507595
absolute error = 1.307
relative error = 21.09 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.37909676302 4.38797507595
y1[1] (closed_form) = 4.37909676302 4.38797507595
absolute error = 1.640e-30
relative error = 2.646e-29 %
Correct digits = 31
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) = 50.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51617.2MB, alloc=44.3MB, time=635.28
memory used=51664.3MB, alloc=44.3MB, time=635.86
x[1] = 0.6514 2.413
h = 0.0001 0.005
y2[1] (numeric) = 3.31606971206 5.14211359494
y2[1] (closed_form) = 4.41254910758 4.40475795047
absolute error = 1.321
relative error = 21.19 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.41254910758 4.40475795047
y1[1] (closed_form) = 4.41254910758 4.40475795047
absolute error = 1.703e-30
relative error = 2.731e-29 %
Correct digits = 31
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) = 50.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51710.8MB, alloc=44.3MB, time=636.42
memory used=51757.7MB, alloc=44.3MB, time=637.00
x[1] = 0.6515 2.418
h = 0.0001 0.003
y2[1] (numeric) = 3.33101853773 5.15638575769
y2[1] (closed_form) = 4.42983290809 4.42685538664
absolute error = 1.319
relative error = 21.06 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.42983290809 4.42685538664
y1[1] (closed_form) = 4.42983290809 4.42685538664
absolute error = 1.780e-30
relative error = 2.843e-29 %
Correct digits = 31
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) = 50.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51804.5MB, alloc=44.3MB, time=637.58
x[1] = 0.6516 2.421
h = 0.001 0.001
y2[1] (numeric) = 3.34605662977 5.17067548916
y2[1] (closed_form) = 4.44042685499 4.44002981021
absolute error = 1.316
relative error = 20.96 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.44042685499 4.44002981021
y1[1] (closed_form) = 4.44042685499 4.44002981021
absolute error = 1.703e-30
relative error = 2.712e-29 %
Correct digits = 31
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) = 51.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51851.7MB, alloc=44.3MB, time=638.16
memory used=51898.4MB, alloc=44.3MB, time=638.74
x[1] = 0.6526 2.422
h = 0.001 0.003
y2[1] (numeric) = 3.3611844417 5.18498269477
y2[1] (closed_form) = 4.44832851081 4.44115047575
absolute error = 1.317
relative error = 20.96 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.44832851081 4.44115047575
y1[1] (closed_form) = 4.44832851081 4.44115047575
absolute error = 1.703e-30
relative error = 2.709e-29 %
Correct digits = 31
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) = 51.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51944.8MB, alloc=44.3MB, time=639.30
memory used=51991.8MB, alloc=44.3MB, time=639.88
x[1] = 0.6536 2.425
h = 0.0001 0.004
y2[1] (numeric) = 3.3764024273 5.19930728016
y2[1] (closed_form) = 4.46305063068 4.45129843048
absolute error = 1.319
relative error = 20.93 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.46305063068 4.45129843048
y1[1] (closed_form) = 4.46305063068 4.45129843048
absolute error = 1.703e-30
relative error = 2.702e-29 %
Correct digits = 31
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) = 51.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52038.2MB, alloc=44.3MB, time=640.45
memory used=52085.2MB, alloc=44.3MB, time=641.02
x[1] = 0.6537 2.429
h = 0.003 0.006
y2[1] (numeric) = 3.39171104063 5.21364915094
y2[1] (closed_form) = 4.47716929898 4.46907791851
absolute error = 1.316
relative error = 20.81 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.47716929898 4.46907791851
y1[1] (closed_form) = 4.47716929898 4.46907791851
absolute error = 1.628e-30
relative error = 2.573e-29 %
Correct digits = 31
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) = 51.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52131.7MB, alloc=44.3MB, time=641.59
x[1] = 0.6567 2.435
h = 0.0001 0.005
y2[1] (numeric) = 3.40711073674 5.22800821269
y2[1] (closed_form) = 4.51145551328 4.48603900829
absolute error = 1.33
relative error = 20.91 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.51145551328 4.48603900829
memory used=52178.8MB, alloc=44.3MB, time=642.16
y1[1] (closed_form) = 4.51145551328 4.48603900829
absolute error = 1.703e-30
relative error = 2.677e-29 %
Correct digits = 31
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) = 51.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52225.4MB, alloc=44.3MB, time=642.73
x[1] = 0.6568 2.44
h = 0.0001 0.003
y2[1] (numeric) = 3.42260197433 5.24238436733
y2[1] (closed_form) = 4.529247134 4.50852468558
absolute error = 1.328
relative error = 20.78 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.529247134 4.50852468558
y1[1] (closed_form) = 4.529247134 4.50852468558
absolute error = 1.703e-30
relative error = 2.665e-29 %
Correct digits = 31
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) = 51.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52271.9MB, alloc=44.3MB, time=643.30
memory used=52319.2MB, alloc=44.3MB, time=643.90
x[1] = 0.6569 2.443
h = 0.001 0.001
y2[1] (numeric) = 3.43818521636 5.25677751374
y2[1] (closed_form) = 4.54015020724 4.52192896401
absolute error = 1.325
relative error = 20.67 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.54015020724 4.52192896401
y1[1] (closed_form) = 4.54015020724 4.52192896401
absolute error = 1.628e-30
relative error = 2.540e-29 %
Correct digits = 31
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) = 51.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52366.0MB, alloc=44.3MB, time=644.47
memory used=52413.0MB, alloc=44.3MB, time=645.05
x[1] = 0.6579 2.444
h = 0.0001 0.004
y2[1] (numeric) = 3.45386092731 5.27118755177
y2[1] (closed_form) = 4.54823255705 4.52302908153
absolute error = 1.326
relative error = 20.67 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.54823255705 4.52302908153
y1[1] (closed_form) = 4.54823255705 4.52302908153
absolute error = 1.628e-30
relative error = 2.538e-29 %
Correct digits = 31
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) = 51.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52459.5MB, alloc=44.3MB, time=645.62
memory used=52506.6MB, alloc=44.3MB, time=646.20
x[1] = 0.658 2.448
h = 0.003 0.006
y2[1] (numeric) = 3.46962957197 5.28561438157
y2[1] (closed_form) = 4.56270254849 4.54108124387
absolute error = 1.323
relative error = 20.54 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.56270254849 4.54108124387
y1[1] (closed_form) = 4.56270254849 4.54108124387
absolute error = 1.628e-30
relative error = 2.529e-29 %
Correct digits = 31
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) = 52.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52553.2MB, alloc=44.3MB, time=646.76
x[1] = 0.661 2.454
h = 0.0001 0.005
y2[1] (numeric) = 3.48549161588 5.30005790337
y2[1] (closed_form) = 4.59772008088 4.55820578055
absolute error = 1.337
relative error = 20.65 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.59772008088 4.55820578055
y1[1] (closed_form) = 4.59772008088 4.55820578055
absolute error = 1.703e-30
relative error = 2.630e-29 %
Correct digits = 31
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) = 52.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52599.7MB, alloc=44.3MB, time=647.32
memory used=52646.7MB, alloc=44.3MB, time=647.90
x[1] = 0.6611 2.459
h = 0.0001 0.003
y2[1] (numeric) = 3.50144752829 5.31451801366
y2[1] (closed_form) = 4.61595477519 4.58103679374
absolute error = 1.334
relative error = 20.52 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.61595477519 4.58103679374
y1[1] (closed_form) = 4.61595477519 4.58103679374
absolute error = 1.703e-30
relative error = 2.619e-29 %
Correct digits = 31
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) = 52.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52693.4MB, alloc=44.3MB, time=648.47
memory used=52740.8MB, alloc=44.3MB, time=649.07
x[1] = 0.6612 2.462
h = 0.001 0.001
y2[1] (numeric) = 3.51749778273 5.3289946058
y2[1] (closed_form) = 4.62712761469 4.59464559397
absolute error = 1.331
relative error = 20.41 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.62712761469 4.59464559397
y1[1] (closed_form) = 4.62712761469 4.59464559397
absolute error = 1.703e-30
relative error = 2.612e-29 %
Correct digits = 31
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) = 52.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52787.3MB, alloc=44.3MB, time=649.64
memory used=52834.4MB, alloc=44.3MB, time=650.22
x[1] = 0.6622 2.463
h = 0.001 0.003
y2[1] (numeric) = 3.53364285435 5.34348757414
y2[1] (closed_form) = 4.63536892048 4.59572913514
absolute error = 1.332
relative error = 20.4 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.63536892048 4.59572913514
y1[1] (closed_form) = 4.63536892048 4.59572913514
absolute error = 1.703e-30
relative error = 2.609e-29 %
Correct digits = 31
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) = 52.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52880.8MB, alloc=44.3MB, time=650.78
x[1] = 0.6632 2.466
h = 0.0001 0.004
y2[1] (numeric) = 3.54988321853 5.35799681329
y2[1] (closed_form) = 4.65080917389 4.60614232864
absolute error = 1.333
relative error = 20.37 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.65080917389 4.60614232864
y1[1] (closed_form) = 4.65080917389 4.60614232864
absolute error = 1.628e-30
relative error = 2.487e-29 %
Correct digits = 31
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) = 52.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52927.3MB, alloc=44.3MB, time=651.35
memory used=52974.3MB, alloc=44.3MB, time=651.92
x[1] = 0.6633 2.47
h = 0.003 0.006
y2[1] (numeric) = 3.566219351 5.37252221779
y2[1] (closed_form) = 4.6657016591 4.62451014697
absolute error = 1.33
relative error = 20.24 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.6657016591 4.62451014697
y1[1] (closed_form) = 4.6657016591 4.62451014697
absolute error = 1.703e-30
relative error = 2.592e-29 %
Correct digits = 31
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) = 53.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53020.8MB, alloc=44.3MB, time=652.49
memory used=53067.8MB, alloc=44.3MB, time=653.07
x[1] = 0.6663 2.476
h = 0.0001 0.005
y2[1] (numeric) = 3.58265172847 5.38706368217
y2[1] (closed_form) = 4.70158985853 4.64181255524
absolute error = 1.344
relative error = 20.35 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.70158985853 4.64181255524
y1[1] (closed_form) = 4.70158985853 4.64181255524
absolute error = 1.628e-30
relative error = 2.464e-29 %
Correct digits = 31
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) = 53.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53114.3MB, alloc=44.3MB, time=653.64
memory used=53161.4MB, alloc=44.3MB, time=654.22
x[1] = 0.6664 2.481
h = 0.0001 0.003
y2[1] (numeric) = 3.59918083144 5.40162109709
y2[1] (closed_form) = 4.72035741483 4.66504337581
absolute error = 1.341
relative error = 20.21 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.72035741483 4.66504337581
y1[1] (closed_form) = 4.72035741483 4.66504337581
absolute error = 1.628e-30
relative error = 2.453e-29 %
Correct digits = 31
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) = 53.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53208.2MB, alloc=44.3MB, time=654.80
x[1] = 0.6665 2.484
h = 0.001 0.001
y2[1] (numeric) = 3.61580714481 5.41619435001
y2[1] (closed_form) = 4.73185456364 4.67888879678
absolute error = 1.338
relative error = 20.1 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.73185456364 4.67888879678
y1[1] (closed_form) = 4.73185456364 4.67888879678
absolute error = 1.628e-30
relative error = 2.446e-29 %
Correct digits = 31
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) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53255.0MB, alloc=44.3MB, time=655.38
memory used=53302.0MB, alloc=44.3MB, time=655.96
x[1] = 0.6675 2.485
h = 0.001 0.003
y2[1] (numeric) = 3.6325311551 5.43078332939
y2[1] (closed_form) = 4.74028397821 4.67994922159
absolute error = 1.338
relative error = 20.09 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.74028397821 4.67994922159
y1[1] (closed_form) = 4.74028397821 4.67994922159
absolute error = 1.628e-30
relative error = 2.444e-29 %
Correct digits = 31
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) = 53.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53348.5MB, alloc=44.3MB, time=656.52
memory used=53395.6MB, alloc=44.3MB, time=657.10
x[1] = 0.6685 2.488
h = 0.0001 0.004
y2[1] (numeric) = 3.64935334911 5.44538792392
y2[1] (closed_form) = 4.75612451186 4.69050418762
absolute error = 1.34
relative error = 20.06 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.75612451186 4.69050418762
y1[1] (closed_form) = 4.75612451186 4.69050418762
absolute error = 1.628e-30
relative error = 2.437e-29 %
Correct digits = 31
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) = 53.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53442.0MB, alloc=44.3MB, time=657.67
memory used=53489.0MB, alloc=44.3MB, time=658.24
x[1] = 0.6686 2.492
h = 0.003 0.006
y2[1] (numeric) = 3.66627421394 5.46000802227
y2[1] (closed_form) = 4.77145056436 4.70919256305
absolute error = 1.336
relative error = 19.93 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.77145056436 4.70919256305
y1[1] (closed_form) = 4.77145056436 4.70919256305
absolute error = 1.628e-30
relative error = 2.428e-29 %
Correct digits = 31
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) = 54.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53535.5MB, alloc=44.3MB, time=658.81
x[1] = 0.6716 2.498
h = 0.0001 0.005
y2[1] (numeric) = 3.68329423774 5.47464351306
y2[1] (closed_form) = 4.80822982829 4.7266723617
absolute error = 1.351
relative error = 20.04 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.80822982829 4.7266723617
y1[1] (closed_form) = 4.80822982829 4.7266723617
absolute error = 1.628e-30
relative error = 2.414e-29 %
Correct digits = 31
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) = 54.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53582.3MB, alloc=44.3MB, time=659.38
memory used=53629.3MB, alloc=44.3MB, time=659.95
x[1] = 0.6717 2.503
h = 0.0001 0.003
y2[1] (numeric) = 3.7004139125 5.48929428094
y2[1] (closed_form) = 4.82754422098 4.7503092042
absolute error = 1.348
relative error = 19.9 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.82754422098 4.7503092042
y1[1] (closed_form) = 4.82754422098 4.7503092042
absolute error = 1.697e-30
relative error = 2.506e-29 %
Correct digits = 31
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) = 54.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53676.0MB, alloc=44.3MB, time=660.52
memory used=53723.4MB, alloc=44.3MB, time=661.12
x[1] = 0.6718 2.506
h = 0.001 0.001
y2[1] (numeric) = 3.71763373469 5.50396020727
y2[1] (closed_form) = 4.8393741499 4.76439487701
absolute error = 1.344
relative error = 19.78 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.8393741499 4.76439487701
y1[1] (closed_form) = 4.8393741499 4.76439487701
absolute error = 1.628e-30
relative error = 2.397e-29 %
Correct digits = 31
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) = 54.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53770.1MB, alloc=44.3MB, time=661.69
memory used=53817.1MB, alloc=44.3MB, time=662.27
x[1] = 0.6728 2.507
h = 0.001 0.003
y2[1] (numeric) = 3.73495420244 5.51864117442
y2[1] (closed_form) = 4.84799576374 4.76543070305
absolute error = 1.344
relative error = 19.77 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.84799576374 4.76543070305
y1[1] (closed_form) = 4.84799576374 4.76543070305
absolute error = 1.628e-30
relative error = 2.395e-29 %
Correct digits = 31
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) = 54.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53863.6MB, alloc=44.3MB, time=662.85
x[1] = 0.6738 2.51
h = 0.0001 0.004
y2[1] (numeric) = 3.75237581417 5.53333706502
y2[1] (closed_form) = 4.86424626128 4.77612855955
absolute error = 1.345
relative error = 19.73 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.86424626128 4.77612855955
y1[1] (closed_form) = 4.86424626128 4.77612855955
absolute error = 1.697e-30
relative error = 2.489e-29 %
Correct digits = 31
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) = 55.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53910.3MB, alloc=44.3MB, time=663.42
memory used=53957.1MB, alloc=44.3MB, time=663.99
x[1] = 0.6739 2.514
h = 0.003 0.006
y2[1] (numeric) = 3.76989906861 5.54804776161
y2[1] (closed_form) = 4.88001722702 4.79514243824
absolute error = 1.341
relative error = 19.61 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.88001722702 4.79514243824
y1[1] (closed_form) = 4.88001722702 4.79514243824
absolute error = 1.628e-30
relative error = 2.379e-29 %
Correct digits = 31
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) = 55.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54003.7MB, alloc=44.3MB, time=664.56
memory used=54050.8MB, alloc=44.3MB, time=665.14
x[1] = 0.6769 2.52
h = 0.0001 0.005
y2[1] (numeric) = 3.78752446556 5.56277314676
y2[1] (closed_form) = 4.91770840057 4.81279901914
absolute error = 1.356
relative error = 19.71 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.91770840057 4.81279901914
y1[1] (closed_form) = 4.91770840057 4.81279901914
absolute error = 1.628e-30
relative error = 2.366e-29 %
Correct digits = 31
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) = 55.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54097.4MB, alloc=44.3MB, time=665.70
memory used=54144.4MB, alloc=44.3MB, time=666.28
x[1] = 0.677 2.525
h = 0.0001 0.003
y2[1] (numeric) = 3.80525250872 5.5775130989
y2[1] (closed_form) = 4.93758394804 4.83684815568
absolute error = 1.353
relative error = 19.58 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.93758394804 4.83684815568
y1[1] (closed_form) = 4.93758394804 4.83684815568
absolute error = 1.628e-30
relative error = 2.355e-29 %
Correct digits = 31
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) = 55.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54191.2MB, alloc=44.3MB, time=666.86
x[1] = 0.6771 2.528
h = 0.001 0.001
y2[1] (numeric) = 3.82308370636 5.59226749309
y2[1] (closed_form) = 4.94975533565 4.85117774336
absolute error = 1.349
relative error = 19.46 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.94975533565 4.85117774336
y1[1] (closed_form) = 4.94975533565 4.85117774336
absolute error = 1.628e-30
relative error = 2.349e-29 %
Correct digits = 31
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) = 56.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54238.3MB, alloc=44.3MB, time=667.44
memory used=54285.2MB, alloc=44.3MB, time=668.02
x[1] = 0.6781 2.529
h = 0.001 0.003
y2[1] (numeric) = 3.84101856845 5.60703620543
y2[1] (closed_form) = 4.95857332111 4.85218743216
absolute error = 1.349
relative error = 19.44 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.95857332111 4.85218743216
y1[1] (closed_form) = 4.95857332111 4.85218743216
absolute error = 1.628e-30
relative error = 2.346e-29 %
Correct digits = 31
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) = 56.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54331.7MB, alloc=44.3MB, time=668.59
memory used=54378.8MB, alloc=44.3MB, time=669.20
x[1] = 0.6791 2.532
h = 0.0001 0.004
y2[1] (numeric) = 3.85905760525 5.62181911225
y2[1] (closed_form) = 4.97524368644 4.86302926663
absolute error = 1.35
relative error = 19.4 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.97524368644 4.86302926663
y1[1] (closed_form) = 4.97524368644 4.86302926663
absolute error = 1.628e-30
relative error = 2.340e-29 %
Correct digits = 31
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) = 56.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54425.2MB, alloc=44.3MB, time=669.77
memory used=54472.0MB, alloc=44.3MB, time=670.34
x[1] = 0.6792 2.536
h = 0.003 0.006
y2[1] (numeric) = 3.87720132736 5.63661608984
y2[1] (closed_form) = 4.99147119016 4.88237363938
absolute error = 1.346
relative error = 19.27 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.99147119016 4.88237363938
y1[1] (closed_form) = 4.99147119016 4.88237363938
absolute error = 1.628e-30
relative error = 2.331e-29 %
Correct digits = 31
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) = 56.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54518.5MB, alloc=44.3MB, time=670.90
x[1] = 0.6822 2.542
h = 0.0001 0.005
y2[1] (numeric) = 3.89545024645 5.65142701445
y2[1] (closed_form) = 5.03009557541 4.9002062623
absolute error = 1.361
relative error = 19.38 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.03009557541 4.9002062623
y1[1] (closed_form) = 5.03009557541 4.9002062623
absolute error = 1.628e-30
relative error = 2.318e-29 %
Correct digits = 31
memory used=54565.5MB, alloc=44.3MB, time=671.48
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) = 56.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54612.2MB, alloc=44.3MB, time=672.05
x[1] = 0.6823 2.547
h = 0.0001 0.003
y2[1] (numeric) = 3.91380487817 5.66625175813
y2[1] (closed_form) = 5.05054694806 4.9246740221
absolute error = 1.357
relative error = 19.24 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.05054694806 4.9246740221
y1[1] (closed_form) = 5.05054694806 4.9246740221
absolute error = 1.703e-30
relative error = 2.414e-29 %
Correct digits = 31
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) = 57.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54658.9MB, alloc=44.3MB, time=672.62
memory used=54706.4MB, alloc=44.3MB, time=673.22
x[1] = 0.6824 2.55
h = 0.001 0.001
y2[1] (numeric) = 3.93226574281 5.68109018944
y2[1] (closed_form) = 5.06306868549 4.93925121926
absolute error = 1.352
relative error = 19.12 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.06306868549 4.93925121926
y1[1] (closed_form) = 5.06306868549 4.93925121926
absolute error = 1.703e-30
relative error = 2.408e-29 %
Correct digits = 31
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) = 57.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54753.1MB, alloc=44.3MB, time=673.80
memory used=54800.1MB, alloc=44.3MB, time=674.39
x[1] = 0.6834 2.551
h = 0.0001 0.004
y2[1] (numeric) = 3.95083336242 5.69594217798
y2[1] (closed_form) = 5.07208729836 4.94023317466
absolute error = 1.352
relative error = 19.1 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.07208729836 4.94023317466
y1[1] (closed_form) = 5.07208729836 4.94023317466
absolute error = 1.703e-30
relative error = 2.405e-29 %
Correct digits = 31
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) = 57.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54846.6MB, alloc=44.3MB, time=674.96
x[1] = 0.6835 2.555
h = 0.003 0.006
y2[1] (numeric) = 3.96950825938 5.71080759368
y2[1] (closed_form) = 5.08871328253 4.95987168794
absolute error = 1.348
relative error = 18.97 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.08871328253 4.95987168794
y1[1] (closed_form) = 5.08871328253 4.95987168794
absolute error = 1.640e-30
relative error = 2.308e-29 %
Correct digits = 31
memory used=54893.6MB, alloc=44.3MB, time=675.55
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) = 57.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54940.1MB, alloc=44.3MB, time=676.12
x[1] = 0.6865 2.561
h = 0.0001 0.005
y2[1] (numeric) = 3.98829095689 5.72568630654
y2[1] (closed_form) = 5.12815627694 4.97786661488
absolute error = 1.363
relative error = 19.08 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.12815627694 4.97786661488
y1[1] (closed_form) = 5.12815627694 4.97786661488
absolute error = 1.703e-30
relative error = 2.383e-29 %
Correct digits = 31
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) = 57.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54986.7MB, alloc=44.3MB, time=676.70
memory used=55033.8MB, alloc=44.3MB, time=677.29
x[1] = 0.6866 2.566
h = 0.0001 0.003
y2[1] (numeric) = 4.0071819822 5.74057818227
y2[1] (closed_form) = 5.14911023287 5.00270692683
absolute error = 1.36
relative error = 18.94 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.14911023287 5.00270692683
y1[1] (closed_form) = 5.14911023287 5.00270692683
absolute error = 1.628e-30
relative error = 2.268e-29 %
Correct digits = 31
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) = 58.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55080.4MB, alloc=44.3MB, time=677.88
memory used=55127.8MB, alloc=44.3MB, time=678.48
x[1] = 0.6867 2.569
h = 0.001 0.001
y2[1] (numeric) = 4.02618186725 5.75548308302
y2[1] (closed_form) = 5.16193781543 5.01750456186
absolute error = 1.354
relative error = 18.82 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.16193781543 5.01750456186
y1[1] (closed_form) = 5.16193781543 5.01750456186
absolute error = 1.703e-30
relative error = 2.366e-29 %
Correct digits = 31
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) = 58.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55174.4MB, alloc=44.3MB, time=679.06
x[1] = 0.6877 2.57
h = 0.001 0.003
y2[1] (numeric) = 4.04529114578 5.77040087199
y2[1] (closed_form) = 5.17113295182 5.01846378221
absolute error = 1.354
relative error = 18.79 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.17113295182 5.01846378221
y1[1] (closed_form) = 5.17113295182 5.01846378221
absolute error = 1.703e-30
relative error = 2.363e-29 %
Correct digits = 31
memory used=55221.4MB, alloc=44.3MB, time=679.64
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) = 58.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55268.0MB, alloc=44.3MB, time=680.22
x[1] = 0.6887 2.573
h = 0.0001 0.004
y2[1] (numeric) = 4.06451035183 5.78533141262
y2[1] (closed_form) = 5.18860998293 5.02958159913
absolute error = 1.355
relative error = 18.74 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.18860998293 5.02958159913
y1[1] (closed_form) = 5.18860998293 5.02958159913
absolute error = 1.844e-30
relative error = 2.552e-29 %
Correct digits = 31
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) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55314.5MB, alloc=44.3MB, time=680.80
memory used=55361.5MB, alloc=44.3MB, time=681.38
x[1] = 0.6888 2.577
h = 0.003 0.006
y2[1] (numeric) = 4.08384001979 5.80027456833
y2[1] (closed_form) = 5.20571483943 5.04956015707
absolute error = 1.35
relative error = 18.61 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.20571483943 5.04956015707
y1[1] (closed_form) = 5.20571483943 5.04956015707
absolute error = 1.844e-30
relative error = 2.542e-29 %
Correct digits = 31
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) = 58.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55408.1MB, alloc=44.3MB, time=681.96
memory used=55455.0MB, alloc=44.3MB, time=682.55
x[1] = 0.6918 2.583
h = 0.0001 0.005
y2[1] (numeric) = 4.10328068516 5.81523020244
y2[1] (closed_form) = 5.24613194566 5.06772964592
absolute error = 1.366
relative error = 18.72 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.24613194566 5.06772964592
y1[1] (closed_form) = 5.24613194566 5.06772964592
absolute error = 1.844e-30
relative error = 2.528e-29 %
Correct digits = 31
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) = 59.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55501.6MB, alloc=44.3MB, time=683.13
memory used=55548.8MB, alloc=44.3MB, time=683.72
x[1] = 0.6919 2.588
h = 0.0001 0.003
y2[1] (numeric) = 4.12283288757 5.83019817391
y2[1] (closed_form) = 5.26768991294 5.09300069347
absolute error = 1.362
relative error = 18.58 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.26768991294 5.09300069347
y1[1] (closed_form) = 5.26768991294 5.09300069347
absolute error = 1.844e-30
relative error = 2.517e-29 %
Correct digits = 31
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) = 59.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55595.5MB, alloc=44.3MB, time=684.31
x[1] = 0.692 2.591
h = 0.001 0.001
y2[1] (numeric) = 4.14249717144 5.84517833798
y2[1] (closed_form) = 5.28088492741 5.10805300755
absolute error = 1.356
relative error = 18.46 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.28088492741 5.10805300755
y1[1] (closed_form) = 5.28088492741 5.10805300755
absolute error = 1.844e-30
relative error = 2.510e-29 %
Correct digits = 31
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) = 59.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55642.4MB, alloc=44.3MB, time=684.91
memory used=55689.3MB, alloc=44.3MB, time=685.50
x[1] = 0.693 2.592
h = 0.001 0.003
y2[1] (numeric) = 4.16227408302 5.86017055098
y2[1] (closed_form) = 5.29028885844 5.10898141798
absolute error = 1.355
relative error = 18.43 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.29028885844 5.10898141798
y1[1] (closed_form) = 5.29028885844 5.10898141798
absolute error = 1.844e-30
relative error = 2.507e-29 %
Correct digits = 31
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) = 59.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55735.9MB, alloc=44.3MB, time=686.08
memory used=55783.0MB, alloc=44.3MB, time=686.67
x[1] = 0.694 2.595
h = 0.0001 0.004
y2[1] (numeric) = 4.18216416888 5.87517466949
y2[1] (closed_form) = 5.30821533779 5.12024626641
absolute error = 1.356
relative error = 18.38 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.30821533779 5.12024626641
y1[1] (closed_form) = 5.30821533779 5.12024626641
absolute error = 1.844e-30
relative error = 2.500e-29 %
Correct digits = 31
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) = 59.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55829.5MB, alloc=44.3MB, time=687.24
memory used=55876.4MB, alloc=44.3MB, time=687.83
x[1] = 0.6941 2.599
h = 0.003 0.006
y2[1] (numeric) = 4.20216797595 5.89019055005
y2[1] (closed_form) = 5.32581152448 5.14056998853
absolute error = 1.351
relative error = 18.25 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.32581152448 5.14056998853
y1[1] (closed_form) = 5.32581152448 5.14056998853
absolute error = 1.844e-30
relative error = 2.491e-29 %
Correct digits = 31
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) = 60.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55922.9MB, alloc=44.3MB, time=688.40
x[1] = 0.6971 2.605
h = 0.0001 0.005
y2[1] (numeric) = 4.22228605228 5.90521804912
y2[1] (closed_form) = 5.36722540705 5.15891289718
absolute error = 1.367
relative error = 18.36 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.36722540705 5.15891289718
y1[1] (closed_form) = 5.36722540705 5.15891289718
absolute error = 1.921e-30
relative error = 2.580e-29 %
Correct digits = 31
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) = 60.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55969.6MB, alloc=44.3MB, time=688.98
memory used=56016.8MB, alloc=44.3MB, time=689.57
x[1] = 0.6972 2.61
h = 0.0001 0.003
y2[1] (numeric) = 4.24251895014 5.92025701864
y2[1] (closed_form) = 5.38940310811 5.18462117427
absolute error = 1.363
relative error = 18.22 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.38940310811 5.18462117427
y1[1] (closed_form) = 5.38940310811 5.18462117427
absolute error = 1.921e-30
relative error = 2.569e-29 %
Correct digits = 31
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) = 61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56063.3MB, alloc=44.3MB, time=690.15
memory used=56110.8MB, alloc=44.3MB, time=690.76
x[1] = 0.6973 2.613
h = 0.001 0.001
y2[1] (numeric) = 4.26286722665 5.93530730676
y2[1] (closed_form) = 5.40297508086 5.19993195279
absolute error = 1.357
relative error = 18.09 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.40297508086 5.19993195279
y1[1] (closed_form) = 5.40297508086 5.19993195279
absolute error = 1.921e-30
relative error = 2.562e-29 %
Correct digits = 31
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) = 61.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56157.4MB, alloc=44.3MB, time=691.34
memory used=56204.4MB, alloc=44.3MB, time=691.93
x[1] = 0.6983 2.614
h = 0.001 0.003
y2[1] (numeric) = 4.28333144083 5.95036876271
y2[1] (closed_form) = 5.41259231051 5.20082778343
absolute error = 1.355
relative error = 18.06 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.41259231051 5.20082778343
y1[1] (closed_form) = 5.41259231051 5.20082778343
absolute error = 1.921e-30
relative error = 2.559e-29 %
Correct digits = 31
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) = 61.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56250.9MB, alloc=44.3MB, time=692.52
x[1] = 0.6993 2.617
h = 0.0001 0.004
y2[1] (numeric) = 4.30391215203 5.965441236
y2[1] (closed_form) = 5.43097903838 5.21224061848
absolute error = 1.356
relative error = 18.01 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.43097903838 5.21224061848
y1[1] (closed_form) = 5.43097903838 5.21224061848
absolute error = 1.921e-30
relative error = 2.552e-29 %
Correct digits = 31
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) = 61.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56297.5MB, alloc=44.3MB, time=693.10
memory used=56344.4MB, alloc=44.3MB, time=693.68
x[1] = 0.6994 2.621
h = 0.003 0.006
y2[1] (numeric) = 4.32460991994 5.98052457606
y2[1] (closed_form) = 5.4490793176 5.23291466709
absolute error = 1.35
relative error = 17.87 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.4490793176 5.23291466709
y1[1] (closed_form) = 5.4490793176 5.23291466709
absolute error = 1.921e-30
relative error = 2.543e-29 %
Correct digits = 31
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) = 61.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56390.9MB, alloc=44.3MB, time=694.26
memory used=56437.8MB, alloc=44.3MB, time=694.84
x[1] = 0.7024 2.627
h = 0.0001 0.005
y2[1] (numeric) = 4.34542530544 5.99561863227
y2[1] (closed_form) = 5.49151313593 5.25142970004
absolute error = 1.367
relative error = 17.98 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.49151313593 5.25142970004
y1[1] (closed_form) = 5.49151313593 5.25142970004
absolute error = 2.000e-30
relative error = 2.632e-29 %
Correct digits = 31
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) = 62.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56484.3MB, alloc=44.3MB, time=695.42
memory used=56531.4MB, alloc=44.3MB, time=696.01
x[1] = 0.7025 2.632
h = 0.0001 0.003
y2[1] (numeric) = 4.36635887364 6.01072324933
y2[1] (closed_form) = 5.51432667772 5.27758175544
absolute error = 1.362
relative error = 17.85 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.51432667772 5.27758175544
y1[1] (closed_form) = 5.51432667772 5.27758175544
absolute error = 2.000e-30
relative error = 2.620e-29 %
Correct digits = 31
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) = 62.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56578.3MB, alloc=44.3MB, time=696.60
x[1] = 0.7026 2.635
h = 0.001 0.001
y2[1] (numeric) = 4.38741119464 6.02583826808
y2[1] (closed_form) = 5.52828536726 5.29315481371
absolute error = 1.356
relative error = 17.72 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.52828536726 5.29315481371
y1[1] (closed_form) = 5.52828536726 5.29315481371
absolute error = 2.000e-30
relative error = 2.613e-29 %
Correct digits = 31
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) = 62.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56625.3MB, alloc=44.3MB, time=697.20
memory used=56672.2MB, alloc=44.3MB, time=697.79
x[1] = 0.7036 2.636
h = 0.001 0.003
y2[1] (numeric) = 4.40858284048 6.04096353044
y2[1] (closed_form) = 5.53812048918 5.29401623007
absolute error = 1.354
relative error = 17.68 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.53812048918 5.29401623007
y1[1] (closed_form) = 5.53812048918 5.29401623007
absolute error = 2.000e-30
relative error = 2.610e-29 %
Correct digits = 31
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) = 62.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56718.7MB, alloc=44.3MB, time=698.37
memory used=56765.7MB, alloc=44.3MB, time=698.95
x[1] = 0.7046 2.639
h = 0.0001 0.004
y2[1] (numeric) = 4.42987438352 6.05609887859
y2[1] (closed_form) = 5.55697851016 5.30557796701
absolute error = 1.354
relative error = 17.62 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.55697851016 5.30557796701
y1[1] (closed_form) = 5.55697851016 5.30557796701
absolute error = 2.000e-30
relative error = 2.603e-29 %
Correct digits = 31
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) = 63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56812.1MB, alloc=44.3MB, time=699.53
memory used=56859.0MB, alloc=44.3MB, time=700.12
x[1] = 0.7047 2.643
h = 0.003 0.006
y2[1] (numeric) = 4.45128639648 6.07124415465
y2[1] (closed_form) = 5.5755959558 5.32660754657
absolute error = 1.349
relative error = 17.49 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.5755959558 5.32660754657
y1[1] (closed_form) = 5.5755959558 5.32660754657
absolute error = 2.062e-30
relative error = 2.674e-29 %
Correct digits = 31
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) = 63.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56905.6MB, alloc=44.3MB, time=700.70
x[1] = 0.7077 2.649
h = 0.0001 0.005
y2[1] (numeric) = 4.47281945328 6.08639920068
y2[1] (closed_form) = 5.61907337448 5.34529324893
absolute error = 1.365
relative error = 17.6 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.61907337448 5.34529324893
y1[1] (closed_form) = 5.61907337448 5.34529324893
absolute error = 2.140e-30
relative error = 2.759e-29 %
Correct digits = 31
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) = 63.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56952.4MB, alloc=44.3MB, time=701.28
memory used=56999.0MB, alloc=44.3MB, time=701.87
x[1] = 0.7078 2.654
h = 0.0001 0.003
y2[1] (numeric) = 4.49447413217 6.10156385395
y2[1] (closed_form) = 5.64253925732 5.37189568543
absolute error = 1.36
relative error = 17.46 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.64253925732 5.37189568543
y1[1] (closed_form) = 5.64253925732 5.37189568543
absolute error = 2.140e-30
relative error = 2.747e-29 %
Correct digits = 31
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) = 64.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57045.5MB, alloc=44.3MB, time=702.46
memory used=57092.8MB, alloc=44.3MB, time=703.06
x[1] = 0.7079 2.657
h = 0.001 0.001
y2[1] (numeric) = 4.51625101647 6.11673794772
y2[1] (closed_form) = 5.65689465966 5.38773486814
absolute error = 1.354
relative error = 17.33 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.65689465966 5.38773486814
y1[1] (closed_form) = 5.65689465966 5.38773486814
absolute error = 2.140e-30
relative error = 2.739e-29 %
Correct digits = 31
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) = 64.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57139.6MB, alloc=44.3MB, time=703.65
memory used=57186.7MB, alloc=44.3MB, time=704.24
x[1] = 0.7089 2.658
h = 0.0001 0.004
y2[1] (numeric) = 4.53815069146 6.13192131636
y2[1] (closed_form) = 5.66695235879 5.38855996923
absolute error = 1.352
relative error = 17.28 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.66695235879 5.38855996923
y1[1] (closed_form) = 5.66695235879 5.38855996923
absolute error = 2.140e-30
relative error = 2.737e-29 %
Correct digits = 31
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) = 64.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57233.2MB, alloc=44.3MB, time=704.81
x[1] = 0.709 2.662
h = 0.003 0.006
y2[1] (numeric) = 4.56017374282 6.14711379459
y2[1] (closed_form) = 5.6860213562 5.40990615561
absolute error = 1.346
relative error = 17.15 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.6860213562 5.40990615561
y1[1] (closed_form) = 5.6860213562 5.40990615561
absolute error = 2.220e-30
relative error = 2.829e-29 %
Correct digits = 31
memory used=57280.0MB, alloc=44.3MB, time=705.40
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) = 64.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57326.6MB, alloc=44.3MB, time=705.98
x[1] = 0.712 2.668
h = 0.0001 0.005
y2[1] (numeric) = 4.58232075714 6.16231521719
y2[1] (closed_form) = 5.73041440826 5.42875029776
absolute error = 1.362
relative error = 17.26 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.73041440826 5.42875029776
y1[1] (closed_form) = 5.73041440826 5.42875029776
absolute error = 2.280e-30
relative error = 2.889e-29 %
Correct digits = 31
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) = 65.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57373.3MB, alloc=44.3MB, time=706.56
memory used=57420.3MB, alloc=44.3MB, time=707.16
x[1] = 0.7121 2.673
h = 0.0001 0.003
y2[1] (numeric) = 4.60459232539 6.17752541407
y2[1] (closed_form) = 5.75444985165 5.45575378092
absolute error = 1.358
relative error = 17.12 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.75444985165 5.45575378092
y1[1] (closed_form) = 5.75444985165 5.45575378092
absolute error = 2.280e-30
relative error = 2.876e-29 %
Correct digits = 31
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) = 65.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57467.1MB, alloc=44.3MB, time=707.74
memory used=57514.5MB, alloc=44.3MB, time=708.35
x[1] = 0.7122 2.676
h = 0.001 0.001
y2[1] (numeric) = 4.6269890437 6.19274421103
y2[1] (closed_form) = 5.76915168808 5.47183002762
absolute error = 1.351
relative error = 16.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.76915168808 5.47183002762
y1[1] (closed_form) = 5.76915168808 5.47183002762
absolute error = 2.202e-30
relative error = 2.770e-29 %
Correct digits = 31
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) = 65.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57561.3MB, alloc=44.3MB, time=708.94
x[1] = 0.7132 2.677
h = 0.001 0.003
y2[1] (numeric) = 4.64951151018 6.207971435
y2[1] (closed_form) = 5.77940526148 5.47262502427
absolute error = 1.348
relative error = 16.94 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.77940526148 5.47262502427
y1[1] (closed_form) = 5.77940526148 5.47262502427
absolute error = 2.220e-30
relative error = 2.790e-29 %
Correct digits = 31
memory used=57608.3MB, alloc=44.3MB, time=709.53
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) = 65.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57654.9MB, alloc=44.3MB, time=710.12
x[1] = 0.7142 2.68
h = 0.0001 0.004
y2[1] (numeric) = 4.67216032332 6.22320691317
y2[1] (closed_form) = 5.79916870601 5.48447205971
absolute error = 1.348
relative error = 16.88 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.79916870601 5.48447205971
y1[1] (closed_form) = 5.79916870601 5.48447205971
absolute error = 2.220e-30
relative error = 2.782e-29 %
Correct digits = 31
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) = 66.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57701.4MB, alloc=44.3MB, time=710.70
memory used=57748.4MB, alloc=44.3MB, time=711.29
x[1] = 0.7143 2.684
h = 0.003 0.006
y2[1] (numeric) = 4.69493608198 6.23845047267
y2[1] (closed_form) = 5.81877998797 5.50618373601
absolute error = 1.341
relative error = 16.74 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.81877998797 5.50618373601
y1[1] (closed_form) = 5.81877998797 5.50618373601
absolute error = 2.220e-30
relative error = 2.772e-29 %
Correct digits = 31
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) = 66.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57795.0MB, alloc=44.3MB, time=711.87
memory used=57842.0MB, alloc=44.3MB, time=712.46
x[1] = 0.7173 2.69
h = 0.0001 0.005
y2[1] (numeric) = 4.71783938626 6.25370194055
y2[1] (closed_form) = 5.86426207717 5.5251956914
absolute error = 1.358
relative error = 16.86 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.86426207717 5.5251956914
y1[1] (closed_form) = 5.86426207717 5.5251956914
absolute error = 2.220e-30
relative error = 2.756e-29 %
Correct digits = 31
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) = 66.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57888.6MB, alloc=44.3MB, time=713.05
memory used=57935.7MB, alloc=44.3MB, time=713.65
x[1] = 0.7174 2.695
h = 0.0001 0.003
y2[1] (numeric) = 4.74087084074 6.26896113882
y2[1] (closed_form) = 5.88898156298 5.55266219087
absolute error = 1.353
relative error = 16.72 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.88898156298 5.55266219087
y1[1] (closed_form) = 5.88898156298 5.55266219087
absolute error = 2.220e-30
relative error = 2.743e-29 %
Correct digits = 31
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) = 67.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57982.4MB, alloc=44.3MB, time=714.25
x[1] = 0.7175 2.698
h = 0.001 0.001
y2[1] (numeric) = 4.76403105523 6.28422788529
y2[1] (closed_form) = 5.90409931665 5.56901191832
absolute error = 1.346
relative error = 16.58 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.90409931665 5.56901191832
y1[1] (closed_form) = 5.90409931665 5.56901191832
absolute error = 2.220e-30
relative error = 2.736e-29 %
Correct digits = 31
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) = 67.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58029.3MB, alloc=44.3MB, time=714.84
memory used=58076.4MB, alloc=44.3MB, time=715.42
x[1] = 0.7185 2.699
h = 0.001 0.003
y2[1] (numeric) = 4.7873206416 6.29950199887
y2[1] (closed_form) = 5.91458445834 5.56976693711
absolute error = 1.343
relative error = 16.53 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.91458445834 5.56976693711
y1[1] (closed_form) = 5.91458445834 5.56976693711
absolute error = 2.220e-30
relative error = 2.733e-29 %
Correct digits = 31
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) = 67.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58122.8MB, alloc=44.3MB, time=715.99
memory used=58169.8MB, alloc=44.3MB, time=716.59
x[1] = 0.7195 2.702
h = 0.0001 0.004
y2[1] (numeric) = 4.81074021209 6.3147832988
y2[1] (closed_form) = 5.93485217969 5.5817653948
absolute error = 1.342
relative error = 16.47 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.93485217969 5.5817653948
y1[1] (closed_form) = 5.93485217969 5.5817653948
absolute error = 2.302e-30
relative error = 2.826e-29 %
Correct digits = 31
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) = 67.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58216.3MB, alloc=44.3MB, time=717.18
memory used=58263.4MB, alloc=44.3MB, time=717.76
x[1] = 0.7196 2.706
h = 0.003 0.006
y2[1] (numeric) = 4.83429037932 6.33007160421
y2[1] (closed_form) = 5.95501975098 5.60384788617
absolute error = 1.335
relative error = 16.33 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.95501975098 5.60384788617
y1[1] (closed_form) = 5.95501975098 5.60384788617
absolute error = 2.220e-30
relative error = 2.715e-29 %
Correct digits = 31
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) = 68.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58309.7MB, alloc=44.3MB, time=718.34
x[1] = 0.7226 2.712
h = 0.0001 0.005
y2[1] (numeric) = 4.85797175719 6.34536673414
y2[1] (closed_form) = 6.00161604755 5.62302571555
absolute error = 1.353
relative error = 16.45 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.00161604755 5.62302571555
y1[1] (closed_form) = 6.00161604755 5.62302571555
absolute error = 2.220e-30
relative error = 2.700e-29 %
Correct digits = 31
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) = 68.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58356.3MB, alloc=44.3MB, time=718.91
memory used=58403.3MB, alloc=44.3MB, time=719.50
x[1] = 0.7227 2.717
h = 0.0001 0.003
y2[1] (numeric) = 4.88178496415 6.36066850249
y2[1] (closed_form) = 6.02703725163 5.65096198892
absolute error = 1.347
relative error = 16.31 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.02703725163 5.65096198892
y1[1] (closed_form) = 6.02703725163 5.65096198892
absolute error = 2.220e-30
relative error = 2.687e-29 %
Correct digits = 31
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) = 69.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58450.0MB, alloc=44.3MB, time=720.10
memory used=58497.4MB, alloc=44.3MB, time=720.72
x[1] = 0.7228 2.72
h = 0.001 0.001
y2[1] (numeric) = 4.90573062395 6.37597671878
y2[1] (closed_form) = 6.04258162813 5.6675891256
absolute error = 1.339
relative error = 16.17 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.04258162813 5.6675891256
y1[1] (closed_form) = 6.04258162813 5.6675891256
absolute error = 2.247e-30
relative error = 2.713e-29 %
Correct digits = 31
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) = 69.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58544.1MB, alloc=44.3MB, time=721.31
memory used=58591.2MB, alloc=44.3MB, time=721.91
x[1] = 0.7238 2.721
h = 0.001 0.003
y2[1] (numeric) = 4.92980936249 6.39129119372
y2[1] (closed_form) = 6.05330329461 5.66830206545
absolute error = 1.336
relative error = 16.11 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.05330329461 5.66830206545
y1[1] (closed_form) = 6.05330329461 5.66830206545
absolute error = 2.220e-30
relative error = 2.677e-29 %
Correct digits = 31
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) = 69.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58637.8MB, alloc=44.3MB, time=722.50
x[1] = 0.7248 2.724
h = 0.0001 0.004
y2[1] (numeric) = 4.95402180602 6.40661173829
y2[1] (closed_form) = 6.07408733153 5.68045268896
absolute error = 1.335
relative error = 16.05 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.07408733153 5.68045268896
y1[1] (closed_form) = 6.07408733153 5.68045268896
absolute error = 2.247e-30
relative error = 2.702e-29 %
Correct digits = 31
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) = 69.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58684.3MB, alloc=44.3MB, time=723.10
memory used=58731.4MB, alloc=44.3MB, time=723.71
x[1] = 0.7249 2.728
h = 0.003 0.006
y2[1] (numeric) = 4.97836858121 6.42193816338
y2[1] (closed_form) = 6.09482553705 5.70291135989
absolute error = 1.328
relative error = 15.91 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.09482553705 5.70291135989
y1[1] (closed_form) = 6.09482553705 5.70291135989
absolute error = 2.247e-30
relative error = 2.692e-29 %
Correct digits = 31
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) = 70.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58777.9MB, alloc=44.3MB, time=724.29
memory used=58824.9MB, alloc=44.3MB, time=724.90
x[1] = 0.7279 2.734
h = 0.0001 0.005
y2[1] (numeric) = 5.002850316 6.4372702798
y2[1] (closed_form) = 6.14256175792 5.72225293979
absolute error = 1.345
relative error = 16.03 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.14256175792 5.72225293979
y1[1] (closed_form) = 6.14256175792 5.72225293979
absolute error = 2.332e-30
relative error = 2.778e-29 %
Correct digits = 31
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) = 70.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58871.5MB, alloc=44.3MB, time=725.49
memory used=58918.6MB, alloc=44.3MB, time=726.10
x[1] = 0.728 2.739
h = 0.0001 0.003
y2[1] (numeric) = 5.02746764297 6.45260789303
y2[1] (closed_form) = 6.1687027856 5.75066579516
absolute error = 1.34
relative error = 15.89 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.1687027856 5.75066579516
y1[1] (closed_form) = 6.1687027856 5.75066579516
absolute error = 2.385e-30
relative error = 2.828e-29 %
Correct digits = 31
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) = 71.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58965.3MB, alloc=44.3MB, time=726.70
x[1] = 0.7281 2.742
h = 0.001 0.001
y2[1] (numeric) = 5.05222120011 6.46795080412
y2[1] (closed_form) = 6.1846847497 5.76757429654
absolute error = 1.332
relative error = 15.75 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.1846847497 5.76757429654
y1[1] (closed_form) = 6.1846847497 5.76757429654
absolute error = 2.385e-30
relative error = 2.821e-29 %
Correct digits = 31
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) = 71.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59012.2MB, alloc=44.3MB, time=727.30
memory used=59059.3MB, alloc=44.3MB, time=727.90
x[1] = 0.7291 2.743
h = 0.001 0.003
y2[1] (numeric) = 5.07711162759 6.48329881525
y2[1] (closed_form) = 6.19564799549 5.768242982
absolute error = 1.328
relative error = 15.68 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.19564799549 5.768242982
y1[1] (closed_form) = 6.19564799549 5.768242982
absolute error = 2.385e-30
relative error = 2.818e-29 %
Correct digits = 31
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) = 71.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59105.8MB, alloc=44.3MB, time=728.50
memory used=59153.0MB, alloc=44.3MB, time=729.11
x[1] = 0.7301 2.746
h = 0.0001 0.004
y2[1] (numeric) = 5.10213956597 6.49865172893
y2[1] (closed_form) = 6.21696065765 5.78054646388
absolute error = 1.326
relative error = 15.62 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.21696065765 5.78054646388
y1[1] (closed_form) = 6.21696065765 5.78054646388
absolute error = 2.385e-30
relative error = 2.810e-29 %
Correct digits = 31
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) = 71.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59199.5MB, alloc=44.3MB, time=729.71
memory used=59246.5MB, alloc=44.3MB, time=730.30
x[1] = 0.7302 2.75
h = 0.003 0.006
y2[1] (numeric) = 5.12730565619 6.51400934753
y2[1] (closed_form) = 6.23828419016 5.80338671727
absolute error = 1.319
relative error = 15.48 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.23828419016 5.80338671727
y1[1] (closed_form) = 6.23828419016 5.80338671727
absolute error = 2.470e-30
relative error = 2.899e-29 %
Correct digits = 31
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) = 72.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59293.1MB, alloc=44.3MB, time=730.88
x[1] = 0.7332 2.756
h = 0.0001 0.005
y2[1] (numeric) = 5.15261054054 6.52937147338
y2[1] (closed_form) = 6.28718661017 5.82288973302
absolute error = 1.337
relative error = 15.6 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.28718661017 5.82288973302
y1[1] (closed_form) = 6.28718661017 5.82288973302
absolute error = 2.470e-30
relative error = 2.882e-29 %
Correct digits = 31
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) = 72.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59339.9MB, alloc=44.3MB, time=731.45
memory used=59386.8MB, alloc=44.3MB, time=732.04
x[1] = 0.7333 2.761
h = 0.0001 0.003
y2[1] (numeric) = 5.178054866 6.5447379033
y2[1] (closed_form) = 6.31406600613 5.8517860279
absolute error = 1.331
relative error = 15.46 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.31406600613 5.8517860279
y1[1] (closed_form) = 6.31406600613 5.8517860279
absolute error = 2.470e-30
relative error = 2.869e-29 %
Correct digits = 31
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) = 73.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59433.4MB, alloc=44.3MB, time=732.62
memory used=59480.9MB, alloc=44.3MB, time=733.23
x[1] = 0.7334 2.764
h = 0.001 0.001
y2[1] (numeric) = 5.20363928505 6.56010842956
y2[1] (closed_form) = 6.33049678774 5.86897987568
absolute error = 1.322
relative error = 15.31 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.33049678774 5.86897987568
y1[1] (closed_form) = 6.33049678774 5.86897987568
absolute error = 2.470e-30
relative error = 2.861e-29 %
Correct digits = 31
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) = 73.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59527.6MB, alloc=44.3MB, time=733.82
memory used=59574.6MB, alloc=44.3MB, time=734.41
x[1] = 0.7344 2.765
h = 0.0001 0.004
y2[1] (numeric) = 5.22936445243 6.57548284559
y2[1] (closed_form) = 6.34170676718 5.8696020548
absolute error = 1.317
relative error = 15.25 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.34170676718 5.8696020548
y1[1] (closed_form) = 6.34170676718 5.8696020548
absolute error = 2.470e-30
relative error = 2.858e-29 %
Correct digits = 31
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) = 73.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59621.1MB, alloc=44.3MB, time=734.98
x[1] = 0.7345 2.769
h = 0.003 0.006
y2[1] (numeric) = 5.25523102329 6.59086094519
y2[1] (closed_form) = 6.36354153305 5.89278233398
absolute error = 1.31
relative error = 15.1 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.36354153305 5.89278233398
y1[1] (closed_form) = 6.36354153305 5.89278233398
absolute error = 2.524e-30
relative error = 2.910e-29 %
Correct digits = 31
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) = 74.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59667.9MB, alloc=44.3MB, time=735.56
memory used=59714.6MB, alloc=44.3MB, time=736.14
x[1] = 0.7375 2.775
h = 0.0001 0.005
y2[1] (numeric) = 5.28123965384 6.60624252223
y2[1] (closed_form) = 6.41346737115 5.91243663179
absolute error = 1.328
relative error = 15.22 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.41346737115 5.91243663179
y1[1] (closed_form) = 6.41346737115 5.91243663179
absolute error = 2.524e-30
relative error = 2.893e-29 %
Correct digits = 31
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) = 74.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59761.0MB, alloc=44.3MB, time=736.71
memory used=59808.0MB, alloc=44.3MB, time=737.30
x[1] = 0.7376 2.78
h = 0.0001 0.003
y2[1] (numeric) = 5.30739100499 6.62162736501
y2[1] (closed_form) = 6.44099165205 5.94176368786
absolute error = 1.322
relative error = 15.08 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.44099165205 5.94176368786
y1[1] (closed_form) = 6.44099165205 5.94176368786
absolute error = 2.524e-30
relative error = 2.880e-29 %
Correct digits = 31
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) = 75.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59854.8MB, alloc=44.3MB, time=737.88
memory used=59902.4MB, alloc=44.3MB, time=738.49
x[1] = 0.7377 2.783
h = 0.001 0.001
y2[1] (numeric) = 5.33368574328 6.63701525713
y2[1] (closed_form) = 6.45781449624 5.95921189356
absolute error = 1.313
relative error = 14.94 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.45781449624 5.95921189356
y1[1] (closed_form) = 6.45781449624 5.95921189356
absolute error = 2.524e-30
relative error = 2.872e-29 %
Correct digits = 31
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) = 75.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59949.1MB, alloc=44.3MB, time=739.07
x[1] = 0.7387 2.784
h = 0.001 0.003
y2[1] (numeric) = 5.36012453754 6.65240598338
y2[1] (closed_form) = 6.46924165275 5.95979520273
absolute error = 1.308
relative error = 14.87 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.46924165275 5.95979520273
y1[1] (closed_form) = 6.46924165275 5.95979520273
absolute error = 2.524e-30
relative error = 2.869e-29 %
Correct digits = 31
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) = 75.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59996.0MB, alloc=44.3MB, time=739.65
memory used=60042.7MB, alloc=44.3MB, time=740.23
x[1] = 0.7397 2.787
h = 0.0001 0.004
y2[1] (numeric) = 5.38670805696 6.66779932886
y2[1] (closed_form) = 6.49156983992 5.97239143227
absolute error = 1.305
relative error = 14.8 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.49156983992 5.97239143227
y1[1] (closed_form) = 6.49156983992 5.97239143227
absolute error = 2.524e-30
relative error = 2.861e-29 %
Correct digits = 31
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) = 76.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60089.3MB, alloc=44.3MB, time=740.81
memory used=60136.3MB, alloc=44.3MB, time=741.40
x[1] = 0.7398 2.791
h = 0.003 0.006
y2[1] (numeric) = 5.41343697118 6.68319507855
y2[1] (closed_form) = 6.51401816056 5.99596363155
absolute error = 1.298
relative error = 14.66 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.51401816056 5.99596363155
y1[1] (closed_form) = 6.51401816056 5.99596363155
absolute error = 2.524e-30
relative error = 2.851e-29 %
Correct digits = 31
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) = 76.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60182.9MB, alloc=44.3MB, time=741.97
memory used=60229.8MB, alloc=44.3MB, time=742.56
x[1] = 0.7428 2.797
h = 0.0001 0.005
y2[1] (numeric) = 5.44031195123 6.69859301734
y2[1] (closed_form) = 6.56516064664 6.01577485375
absolute error = 1.316
relative error = 14.78 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.56516064664 6.01577485375
y1[1] (closed_form) = 6.56516064664 6.01577485375
absolute error = 2.524e-30
relative error = 2.834e-29 %
Correct digits = 31
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) = 77.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60276.3MB, alloc=44.3MB, time=743.13
memory used=60323.3MB, alloc=44.3MB, time=743.72
x[1] = 0.7429 2.802
h = 0.0001 0.003
y2[1] (numeric) = 5.46733367293 6.71399292438
y2[1] (closed_form) = 6.593458924 6.04559847064
absolute error = 1.31
relative error = 14.64 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.593458924 6.04559847064
y1[1] (closed_form) = 6.593458924 6.04559847064
absolute error = 2.608e-30
relative error = 2.915e-29 %
Correct digits = 31
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) = 77.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60370.2MB, alloc=44.3MB, time=744.31
x[1] = 0.743 2.805
h = 0.001 0.001
y2[1] (numeric) = 5.49450281786 6.72939457399
y2[1] (closed_form) = 6.61075216025 6.06333964027
absolute error = 1.3
relative error = 14.49 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.61075216025 6.06333964027
y1[1] (closed_form) = 6.61075216025 6.06333964027
absolute error = 2.608e-30
relative error = 2.907e-29 %
Correct digits = 31
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) = 78.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60417.1MB, alloc=44.3MB, time=744.90
memory used=60464.1MB, alloc=44.3MB, time=745.49
x[1] = 0.744 2.806
h = 0.001 0.003
y2[1] (numeric) = 5.52182006991 6.74479774167
y2[1] (closed_form) = 6.62243594247 6.0638721057
absolute error = 1.294
relative error = 14.41 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.62243594247 6.0638721057
y1[1] (closed_form) = 6.62243594247 6.0638721057
absolute error = 2.524e-30
relative error = 2.811e-29 %
Correct digits = 31
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) = 78.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60510.7MB, alloc=44.3MB, time=746.07
memory used=60557.8MB, alloc=44.3MB, time=746.65
x[1] = 0.745 2.809
h = 0.0001 0.004
y2[1] (numeric) = 5.54928611339 6.76020220328
y2[1] (closed_form) = 6.64532951202 6.0766230277
absolute error = 1.292
relative error = 14.35 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.64532951202 6.0766230277
y1[1] (closed_form) = 6.64532951202 6.0766230277
absolute error = 2.524e-30
relative error = 2.803e-29 %
Correct digits = 31
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) = 78.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60604.2MB, alloc=44.3MB, time=747.23
memory used=60651.1MB, alloc=44.3MB, time=747.81
x[1] = 0.7451 2.813
h = 0.003 0.006
y2[1] (numeric) = 5.57690163302 6.77560773453
y2[1] (closed_form) = 6.66840711958 6.10059265885
absolute error = 1.283
relative error = 14.2 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.66840711958 6.10059265885
y1[1] (closed_form) = 6.66840711958 6.10059265885
absolute error = 2.524e-30
relative error = 2.793e-29 %
Correct digits = 31
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) = 78.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60697.6MB, alloc=44.3MB, time=748.39
x[1] = 0.7481 2.819
h = 0.0001 0.005
y2[1] (numeric) = 5.60466731496 6.79101411101
y2[1] (closed_form) = 6.72079419099 6.12055791047
absolute error = 1.302
relative error = 14.32 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.72079419099 6.12055791047
y1[1] (closed_form) = 6.72079419099 6.12055791047
absolute error = 2.524e-30
relative error = 2.777e-29 %
Correct digits = 31
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) = 79.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60744.3MB, alloc=44.3MB, time=748.96
memory used=60791.4MB, alloc=44.3MB, time=749.55
x[1] = 0.7482 2.824
h = 0.0001 0.003
y2[1] (numeric) = 5.63258385024 6.80642110246
y2[1] (closed_form) = 6.74988632203 6.1508850858
absolute error = 1.295
relative error = 14.19 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.74988632203 6.1508850858
y1[1] (closed_form) = 6.74988632203 6.1508850858
absolute error = 2.581e-30
relative error = 2.826e-29 %
Correct digits = 31
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) = 80.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60838.0MB, alloc=44.3MB, time=750.13
memory used=60885.5MB, alloc=44.3MB, time=750.74
x[1] = 0.7483 2.827
h = 0.001 0.001
y2[1] (numeric) = 5.66065193576 6.82182847361
y2[1] (closed_form) = 6.76766197228 6.16892327487
absolute error = 1.285
relative error = 14.03 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.76766197228 6.16892327487
y1[1] (closed_form) = 6.76766197228 6.16892327487
absolute error = 2.663e-30
relative error = 2.908e-29 %
Correct digits = 31
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) = 80.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=60932.2MB, alloc=44.3MB, time=751.32
memory used=60979.4MB, alloc=44.3MB, time=751.90
x[1] = 0.7493 2.828
h = 0.001 0.003
y2[1] (numeric) = 5.68887227076 6.83723599043
y2[1] (closed_form) = 6.7796078313 6.16940241445
absolute error = 1.279
relative error = 13.95 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.7796078313 6.16940241445
y1[1] (closed_form) = 6.7796078313 6.16940241445
absolute error = 2.608e-30
relative error = 2.845e-29 %
Correct digits = 31
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) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61025.9MB, alloc=44.3MB, time=752.46
x[1] = 0.7503 2.831
h = 0.0001 0.004
y2[1] (numeric) = 5.71724555494 6.85264341921
y2[1] (closed_form) = 6.80308019466 6.18230850318
absolute error = 1.276
relative error = 13.88 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.80308019466 6.18230850318
y1[1] (closed_form) = 6.80308019466 6.18230850318
absolute error = 2.581e-30
relative error = 2.807e-29 %
Correct digits = 31
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) = 80.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61072.5MB, alloc=44.3MB, time=753.03
memory used=61119.4MB, alloc=44.3MB, time=753.60
x[1] = 0.7504 2.835
h = 0.003 0.006
y2[1] (numeric) = 5.7457724884 6.8680505261
y2[1] (closed_form) = 6.8268032009 6.20668111238
absolute error = 1.267
relative error = 13.74 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.8268032009 6.20668111238
y1[1] (closed_form) = 6.8268032009 6.20668111238
absolute error = 2.663e-30
relative error = 2.886e-29 %
Correct digits = 31
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) = 81.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61166.0MB, alloc=44.3MB, time=754.17
memory used=61213.0MB, alloc=44.3MB, time=754.75
x[1] = 0.7534 2.841
h = 0.0001 0.005
y2[1] (numeric) = 5.77445377273 6.88345707715
y2[1] (closed_form) = 6.88046339835 6.22679727845
absolute error = 1.286
relative error = 13.86 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.88046339835 6.22679727845
y1[1] (closed_form) = 6.88046339835 6.22679727845
absolute error = 2.720e-30
relative error = 2.931e-29 %
Correct digits = 31
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) = 82.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61259.5MB, alloc=44.3MB, time=755.32
memory used=61306.5MB, alloc=44.3MB, time=755.90
x[1] = 0.7535 2.846
h = 0.0001 0.003
y2[1] (numeric) = 5.80329011445 6.89886283235
y2[1] (closed_form) = 6.91036971968 6.25763505427
absolute error = 1.279
relative error = 13.72 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.91036971968 6.25763505427
y1[1] (closed_form) = 6.91036971968 6.25763505427
absolute error = 2.720e-30
relative error = 2.918e-29 %
Correct digits = 31
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) = 82.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61353.4MB, alloc=44.3MB, time=756.48
x[1] = 0.7536 2.849
h = 0.001 0.001
y2[1] (numeric) = 5.83228222606 6.91426754659
y2[1] (closed_form) = 6.92864009507 6.2759743412
absolute error = 1.269
relative error = 13.57 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.92864009507 6.2759743412
y1[1] (closed_form) = 6.92864009507 6.2759743412
absolute error = 2.720e-30
relative error = 2.910e-29 %
Correct digits = 31
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) = 83.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61400.4MB, alloc=44.3MB, time=757.06
memory used=61447.5MB, alloc=44.3MB, time=757.65
x[1] = 0.7546 2.85
h = 0.001 0.003
y2[1] (numeric) = 5.86143082247 6.92967097597
y2[1] (closed_form) = 6.94085358901 6.27639758741
absolute error = 1.262
relative error = 13.48 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.94085358901 6.27639758741
y1[1] (closed_form) = 6.94085358901 6.27639758741
absolute error = 2.720e-30
relative error = 2.907e-29 %
Correct digits = 31
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) = 83.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61494.0MB, alloc=44.3MB, time=758.22
memory used=61540.9MB, alloc=44.3MB, time=758.80
x[1] = 0.7556 2.853
h = 0.0001 0.004
y2[1] (numeric) = 5.89073661903 6.94507287695
y2[1] (closed_form) = 6.9649184577 6.28945925286
absolute error = 1.258
relative error = 13.41 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.9649184577 6.28945925286
y1[1] (closed_form) = 6.9649184577 6.28945925286
absolute error = 2.640e-30
relative error = 2.813e-29 %
Correct digits = 31
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) = 83.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61587.3MB, alloc=44.3MB, time=759.36
memory used=61634.3MB, alloc=44.3MB, time=759.94
x[1] = 0.7557 2.857
h = 0.003 0.006
y2[1] (numeric) = 5.92020033155 6.96047300583
y2[1] (closed_form) = 6.9893033626 6.31424041951
absolute error = 1.249
relative error = 13.26 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.9893033626 6.31424041951
y1[1] (closed_form) = 6.9893033626 6.31424041951
absolute error = 2.640e-30
relative error = 2.803e-29 %
Correct digits = 31
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) = 84.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61680.8MB, alloc=44.3MB, time=760.51
x[1] = 0.7587 2.863
h = 0.0001 0.005
y2[1] (numeric) = 5.9498226773 6.97587111879
y2[1] (closed_form) = 7.04426584244 6.33450415695
absolute error = 1.269
relative error = 13.39 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 7.04426584244 6.33450415695
y1[1] (closed_form) = 7.04426584244 6.33450415695
absolute error = 2.720e-30
relative error = 2.871e-29 %
Correct digits = 31
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) = 84.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61727.5MB, alloc=44.3MB, time=761.08
memory used=61774.5MB, alloc=44.3MB, time=761.66
x[1] = 0.7588 2.868
h = 0.0001 0.003
y2[1] (numeric) = 5.97960437861 6.99126696581
y2[1] (closed_form) = 7.07500718095 6.36585961822
absolute error = 1.261
relative error = 13.25 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 7.07500718095 6.36585961822
y1[1] (closed_form) = 7.07500718095 6.36585961822
absolute error = 2.720e-30
relative error = 2.858e-29 %
Correct digits = 31
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) = 85.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61821.3MB, alloc=44.3MB, time=762.23
memory used=61868.8MB, alloc=44.3MB, time=762.82
x[1] = 0.7589 2.871
h = 0.001 0.001
y2[1] (numeric) = 6.00954616387 7.00666029161
y2[1] (closed_form) = 7.09378488842 6.38450410333
absolute error = 1.25
relative error = 13.1 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 7.09378488842 6.38450410333
y1[1] (closed_form) = 7.09378488842 6.38450410333
absolute error = 2.780e-30
relative error = 2.913e-29 %
Correct digits = 31
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) = 86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=61915.4MB, alloc=44.3MB, time=763.40
memory used=61962.5MB, alloc=44.3MB, time=763.98
x[1] = 0.7599 2.872
h = 0.001 0.003
y2[1] (numeric) = 6.03964876395 7.02205084214
y2[1] (closed_form) = 7.1062716844 6.38486880073
absolute error = 1.242
relative error = 13.01 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 7.1062716844 6.38486880073
y1[1] (closed_form) = 7.1062716844 6.38486880073
absolute error = 2.720e-30
relative error = 2.847e-29 %
Correct digits = 31
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) = 86.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=62010.7MB, alloc=44.3MB, time=764.62
Finished!
Maximum Time Reached before Solution Completed!
diff ( y2 , x , 4 ) = y1 - 1.0 ;
diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ;
Iterations = 754
Total Elapsed Time = 12 Minutes 44 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 12 Minutes 44 Seconds
> quit
memory used=62040.4MB, alloc=44.3MB, time=765.00