|\^/| 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) + cos(c(x)));
> end;
exact_soln_y1 := proc(x) return c(1.0) + cos(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
> 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_1,
> array_const_0D0,
> array_const_1D0,
#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_1, array_const_0D0, array_const_1D0,
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_1,
> array_const_0D0,
> array_const_1D0,
#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_1, array_const_0D0, array_const_1D0,
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_1,
> array_const_0D0,
> array_const_1D0,
#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_1, array_const_0D0, array_const_1D0,
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_1,
> array_const_0D0,
> array_const_1D0,
#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_1, array_const_0D0, array_const_1D0,
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_1,
> array_const_0D0,
> array_const_1D0,
#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_1, array_const_0D0, array_const_1D0,
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_1,
> array_const_0D0,
> array_const_1D0,
#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_1, array_const_0D0, array_const_1D0,
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_1,
> array_const_0D0,
> array_const_1D0,
#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 - 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_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 - 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_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 - 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_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_1, array_const_0D0, array_const_1D0,
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 - 11;
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 - 11;
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 - 11;
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_1,
> array_const_0D0,
> array_const_1D0,
#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 neg FULL $eq_no = 1
> array_tmp1[1] := neg(array_y1[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre sub FULL - CONST $eq_no = 2 i = 1
> array_tmp5[1] := array_y2[1] - array_const_1D0[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 neg FULL $eq_no = 1
> array_tmp1[2] := neg(array_y1[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre sub FULL CONST $eq_no = 2 i = 2
> array_tmp5[2] := array_y2[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 neg FULL $eq_no = 1
> array_tmp1[3] := neg(array_y1[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre sub FULL CONST $eq_no = 2 i = 3
> array_tmp5[3] := array_y2[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 neg FULL $eq_no = 1
> array_tmp1[4] := neg(array_y1[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre sub FULL CONST $eq_no = 2 i = 4
> array_tmp5[4] := array_y2[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 neg FULL $eq_no = 1
> array_tmp1[5] := neg(array_y1[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre sub FULL CONST $eq_no = 2 i = 5
> array_tmp5[5] := array_y2[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 neg FULL $eq_no = 1
> array_tmp1[kkk] := neg(array_y1[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> 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_tmp3[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 FULL - NOT FULL sub $eq_no = 2
> array_tmp5[kkk] := array_y2[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_1, array_const_0D0, array_const_1D0,
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] := neg(array_y1[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
if not array_y2_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp5[1] := array_y2[1] - array_const_1D0[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] := neg(array_y1[2]);
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
if not array_y2_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp5[2] := array_y2[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] := neg(array_y1[3]);
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_tmp2[3];
if not array_y2_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp5[3] := array_y2[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] := neg(array_y1[4]);
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_tmp2[4];
if not array_y2_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 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)
end if
end if;
kkk := 5;
array_tmp5[4] := array_y2[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] := neg(array_y1[5]);
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_tmp2[5];
if not array_y2_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 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)
end if
end if;
kkk := 6;
array_tmp5[5] := array_y2[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] := neg(array_y1[kkk]);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := c(array_tmp3[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;
array_tmp5[kkk] := array_y2[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_1,
> array_const_0D0,
> array_const_1D0,
> #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:=16;
> 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..(2) ,(0..40+ 1),[]);
> array_y2_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y2_higher_work2 := Array(0..(2) ,(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 <=2) 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 <=2) 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 <=2) 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_1);
> array_const_1[1] := c(1);
> 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_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] := false;
> array_y2_set_initial[1,3] := false;
> array_y2_set_initial[1,4] := false;
> 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/mtest3postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; ");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = y2 - 1.0 ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=16;");
> 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,"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,"");
> 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) + cos(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,"");
> 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);
> 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 := 1;
> #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 <= 2) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 2 + 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 := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #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 := 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 , 1 ) = neg ( y1 ) + 1.0 ; ");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = y2 - 1.0 ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 19
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T15:18:11-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest3")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = neg ( 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,"mtest3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest3 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> 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 ) = y2 - 1.0 ; ")
> ;
> 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_1, array_const_0D0, array_const_1D0,
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 := 16;
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 .. 2, 0 .. 41, []);
array_y2_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y2_higher_work2 := Array(0 .. 2, 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 <= 2 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 <= 2 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 <= 2 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_1);
array_const_1[1] := c(1);
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_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] := false;
array_y2_set_initial[1, 3] := false;
array_y2_set_initial[1, 4] := false;
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/mtest3postcpx.cpx#################");
omniout_str(ALWAYS,
"diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; ");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0 ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=16;");
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, "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, "");
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) + cos(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, "");
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,");
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omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
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 := 1;
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 <= 2 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 2 + 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 := 2;
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 := 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 , 1 ) = neg ( y1 ) + 1.0 ; ");
omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0 ; ")
;
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T15:18:11-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest3");
logitem_str(html_log_file,
"diff ( y2 , x , 1 ) = neg ( 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,
"mtest3 diffeq.mxt");
logitem_str(html_log_file, "mtest3 maple results");
logitem_str(html_log_file, "OK");
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 ) = y2 - 1.0 ; ");
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=3.7MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/mtest3postcpx.cpx#################
diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ;
diff ( y1 , x , 1 ) = y2 - 1.0 ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=16;
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);
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) + cos(c(x)));
end;
exact_soln_y2 := proc(x)
return(c(1.0) - sin(c(x)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1 0.1
h = 0.0001 0.005
y2[1] (numeric) = 0.899667000159 -0.0996663334921
y2[1] (closed_form) = 0.899667000159 -0.0996663334921
absolute error = 0
relative error = 0 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 1.99998333334 -0.00999998888889
y1[1] (closed_form) = 1.99998333334 -0.00999998888889
absolute error = 0
relative error = 0 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1414
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1414
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54.4MB, alloc=40.3MB, time=0.72
x[1] = 0.1001 0.105
h = 0.0001 0.003
y2[1] (numeric) = 0.899515696926 -0.104666466122
y2[1] (closed_form) = 0.899515696926 -0.104666466122
absolute error = 1e-16
relative error = 1.104e-14 %
Correct digits = 16
h = 0.0001 0.003
y1[1] (numeric) = 2.00048412347 -0.0105122476776
y1[1] (closed_form) = 2.00048412347 -0.0105122476776
absolute error = 0
relative error = 0 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1452
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1452
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=101.9MB, alloc=40.3MB, time=1.35
x[1] = 0.1002 0.108
h = 0.001 0.001
y2[1] (numeric) = 0.899383628196 -0.107667312081
y2[1] (closed_form) = 0.899383628196 -0.107667312081
absolute error = 1e-16
relative error = 1.104e-14 %
Correct digits = 16
h = 0.001 0.001
y1[1] (numeric) = 2.00079256889 -0.0108245151295
y1[1] (closed_form) = 2.00079256889 -0.0108245151295
absolute error = 0
relative error = 0 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1475
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1475
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=149.7MB, alloc=40.3MB, time=1.97
x[1] = 0.1012 0.109
h = 0.001 0.003
y2[1] (numeric) = 0.898371903115 -0.108657179181
y2[1] (closed_form) = 0.898371903115 -0.108657179181
absolute error = 1e-16
relative error = 1.105e-14 %
Correct digits = 16
h = 0.001 0.003
y1[1] (numeric) = 2.00079960894 -0.0110337996083
y1[1] (closed_form) = 2.00079960894 -0.0110337996083
absolute error = 1e-15
relative error = 4.998e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1489
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1489
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1022 0.112
h = 0.0001 0.004
y2[1] (numeric) = 0.897337265253 -0.111648676907
y2[1] (closed_form) = 0.897337265253 -0.111648676907
absolute error = 1.414e-16
relative error = 1.564e-14 %
Correct digits = 16
h = 0.0001 0.004
y1[1] (numeric) = 2.00102792236 -0.0114503883919
y1[1] (closed_form) = 2.00102792236 -0.0114503883919
absolute error = 1e-15
relative error = 4.997e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1518
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1518
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=197.2MB, alloc=40.3MB, time=2.59
x[1] = 0.1023 0.116
h = 0.003 0.006
y2[1] (numeric) = 0.897190494535 -0.115652505773
y2[1] (closed_form) = 0.897190494535 -0.115652505773
absolute error = 2e-16
relative error = 2.211e-14 %
Correct digits = 16
h = 0.003 0.006
y1[1] (numeric) = 2.00147225055 -0.0118726973391
y1[1] (closed_form) = 2.00147225055 -0.0118726973391
absolute error = 1e-15
relative error = 4.996e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.155
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.155
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=245.0MB, alloc=40.3MB, time=3.22
x[1] = 0.1053 0.122
h = 0.0001 0.005
y2[1] (numeric) = 0.894111322239 -0.121625440337
y2[1] (closed_form) = 0.894111322239 -0.121625440337
absolute error = 2.236e-16
relative error = 2.478e-14 %
Correct digits = 16
h = 0.0001 0.005
y1[1] (numeric) = 2.00187103916 -0.0128547054021
y1[1] (closed_form) = 2.00187103916 -0.0128547054021
absolute error = 1e-15
relative error = 4.995e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1616
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1616
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=292.6MB, alloc=40.3MB, time=3.84
x[1] = 0.1054 0.127
h = 0.0001 0.003
y2[1] (numeric) = 0.893945476194 -0.126634997662
y2[1] (closed_form) = 0.893945476194 -0.126634997662
absolute error = 2.236e-16
relative error = 2.477e-14 %
Correct digits = 16
h = 0.0001 0.003
y1[1] (numeric) = 2.00248109187 -0.0133969752478
y1[1] (closed_form) = 2.00248109187 -0.0133969752478
absolute error = 1.000e-15
relative error = 4.994e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1656
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1656
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1055 0.13
h = 0.001 0.001
y2[1] (numeric) = 0.893804521942 -0.129641643138
y2[1] (closed_form) = 0.893804521942 -0.129641643138
absolute error = 2.236e-16
relative error = 2.476e-14 %
Correct digits = 16
h = 0.001 0.001
y1[1] (numeric) = 2.00285489407 -0.0137281638158
y1[1] (closed_form) = 2.00285489407 -0.0137281638158
absolute error = 1e-15
relative error = 4.993e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1681
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1681
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=340.0MB, alloc=40.3MB, time=4.46
x[1] = 0.1065 0.131
h = 0.001 0.003
y2[1] (numeric) = 0.892787808913 -0.130630663334
y2[1] (closed_form) = 0.892787808913 -0.130630663334
absolute error = 1.414e-16
relative error = 1.567e-14 %
Correct digits = 16
h = 0.001 0.003
y1[1] (numeric) = 2.00287832643 -0.0139650037997
y1[1] (closed_form) = 2.00287832643 -0.0139650037997
absolute error = 1e-15
relative error = 4.993e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1695
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1695
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=387.7MB, alloc=40.3MB, time=5.08
x[1] = 0.1075 0.134
h = 0.0001 0.004
y2[1] (numeric) = 0.891742210446 -0.133625537144
y2[1] (closed_form) = 0.891742210446 -0.133625537144
absolute error = 1.414e-16
relative error = 1.568e-14 %
Correct digits = 16
h = 0.0001 0.004
y1[1] (numeric) = 2.00316697577 -0.014420336423
y1[1] (closed_form) = 2.00316697577 -0.014420336423
absolute error = 1e-15
relative error = 4.992e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1725
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1725
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1076 0.138
h = 0.003 0.006
y2[1] (numeric) = 0.891583292474 -0.137637798716
y2[1] (closed_form) = 0.891583292474 -0.137637798716
absolute error = 2.236e-16
relative error = 2.479e-14 %
Correct digits = 16
h = 0.003 0.006
y1[1] (numeric) = 2.00369866804 -0.014867247953
y1[1] (closed_form) = 2.00369866804 -0.014867247953
absolute error = 1e-15
relative error = 4.991e-14 %
Correct digits = 15
memory used=435.4MB, alloc=40.3MB, time=5.70
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1759
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1759
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1106 0.144
h = 0.0001 0.005
y2[1] (numeric) = 0.888479002051 -0.143615303875
y2[1] (closed_form) = 0.888479002051 -0.143615303875
absolute error = 2.236e-16
relative error = 2.484e-14 %
Correct digits = 16
h = 0.0001 0.005
y1[1] (numeric) = 2.00421252288 -0.015948936748
y1[1] (closed_form) = 2.00421252288 -0.015948936748
absolute error = 1.000e-15
relative error = 4.990e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1826
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1826
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=483.0MB, alloc=40.3MB, time=6.32
x[1] = 0.1107 0.149
h = 0.0001 0.003
y2[1] (numeric) = 0.888297369262 -0.148636531188
y2[1] (closed_form) = 0.888297369262 -0.148636531188
absolute error = 2.236e-16
relative error = 2.483e-14 %
Correct digits = 16
h = 0.0001 0.003
y1[1] (numeric) = 2.00493198983 -0.0165216071589
y1[1] (closed_form) = 2.00493198983 -0.0165216071589
absolute error = 1.000e-15
relative error = 4.988e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1869
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1869
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=530.6MB, alloc=40.3MB, time=6.94
x[1] = 0.1108 0.152
h = 0.001 0.001
y2[1] (numeric) = 0.888146764021 -0.151650314108
y2[1] (closed_form) = 0.888146764021 -0.151650314108
absolute error = 2.236e-16
relative error = 2.482e-14 %
Correct digits = 16
h = 0.001 0.001
y1[1] (numeric) = 2.005371242 -0.0168719550168
y1[1] (closed_form) = 2.005371242 -0.0168719550168
absolute error = 1.000e-15
relative error = 4.987e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1895
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1895
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1118 0.153
h = 0.001 0.003
y2[1] (numeric) = 0.887124368844 -0.152638701201
y2[1] (closed_form) = 0.887124368844 -0.152638701201
absolute error = 2.236e-16
relative error = 2.484e-14 %
Correct digits = 16
h = 0.001 0.003
y1[1] (numeric) = 2.00541102212 -0.0171364639514
y1[1] (closed_form) = 2.00541102212 -0.0171364639514
absolute error = 1.000e-15
relative error = 4.987e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1909
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1909
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=578.3MB, alloc=40.3MB, time=7.57
x[1] = 0.1128 0.156
h = 0.0001 0.004
y2[1] (numeric) = 0.886066634603 -0.155638072673
y2[1] (closed_form) = 0.886066634603 -0.155638072673
absolute error = 2e-16
relative error = 2.223e-14 %
Correct digits = 16
h = 0.0001 0.004
y1[1] (numeric) = 2.00576003279 -0.0176308153291
y1[1] (closed_form) = 2.00576003279 -0.0176308153291
absolute error = 1.000e-15
relative error = 4.986e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.194
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.194
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=625.9MB, alloc=40.3MB, time=8.19
x[1] = 0.1129 0.16
h = 0.003 0.006
y2[1] (numeric) = 0.885894561192 -0.159660559171
y2[1] (closed_form) = 0.885894561192 -0.159660559171
absolute error = 2.236e-16
relative error = 2.484e-14 %
Correct digits = 16
h = 0.003 0.006
y1[1] (numeric) = 2.00637922732 -0.0181026571991
y1[1] (closed_form) = 2.00637922732 -0.0181026571991
absolute error = 1.000e-15
relative error = 4.984e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1975
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1975
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=673.6MB, alloc=40.3MB, time=8.82
x[1] = 0.1159 0.166
h = 0.0001 0.005
y2[1] (numeric) = 0.882762343264 -0.165644636231
y2[1] (closed_form) = 0.882762343264 -0.165644636231
absolute error = 2.236e-16
relative error = 2.490e-14 %
Correct digits = 16
h = 0.0001 0.005
y1[1] (numeric) = 2.0070081304 -0.0192846397327
y1[1] (closed_form) = 2.0070081304 -0.0192846397327
absolute error = 1e-17
relative error = 4.982e-16 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2044
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2044
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.116 0.171
h = 0.0001 0.003
y2[1] (numeric) = 0.882563669882 -0.170679780464
y2[1] (closed_form) = 0.882563669882 -0.170679780464
absolute error = 2.236e-16
relative error = 2.488e-14 %
Correct digits = 16
h = 0.0001 0.003
y1[1] (numeric) = 2.00783720606 -0.0198881395948
y1[1] (closed_form) = 2.00783720606 -0.0198881395948
absolute error = 1e-15
relative error = 4.980e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2088
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2088
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=721.1MB, alloc=40.3MB, time=9.44
x[1] = 0.1161 0.174
h = 0.001 0.001
y2[1] (numeric) = 0.88240264212 -0.173702039755
y2[1] (closed_form) = 0.88240264212 -0.173702039755
absolute error = 2.236e-16
relative error = 2.486e-14 %
Correct digits = 16
h = 0.001 0.001
y1[1] (numeric) = 2.00834202675 -0.0202579089155
y1[1] (closed_form) = 2.00834202675 -0.0202579089155
absolute error = 1e-15
relative error = 4.979e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2116
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2116
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=768.8MB, alloc=40.3MB, time=10.06
x[1] = 0.1171 0.175
h = 0.001 0.003
y2[1] (numeric) = 0.881373868153 -0.174690005932
y2[1] (closed_form) = 0.881373868153 -0.174690005932
absolute error = 2e-16
relative error = 2.226e-14 %
Correct digits = 16
h = 0.001 0.003
y1[1] (numeric) = 2.00839811108 -0.0205502166739
y1[1] (closed_form) = 2.00839811108 -0.0205502166739
absolute error = 1e-15
relative error = 4.979e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.213
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.213
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=816.5MB, alloc=40.3MB, time=10.70
x[1] = 0.1181 0.178
h = 0.0001 0.004
y2[1] (numeric) = 0.880302816385 -0.177694995866
y2[1] (closed_form) = 0.880302816385 -0.177694995866
absolute error = 3e-16
relative error = 3.341e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.00880752691 -0.0210838935875
y1[1] (closed_form) = 2.00880752691 -0.0210838935875
absolute error = 1e-15
relative error = 4.978e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2162
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2162
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1182 0.182
h = 0.003 0.006
y2[1] (numeric) = 0.880116570968 -0.181729501103
y2[1] (closed_form) = 0.880116570968 -0.181729501103
absolute error = 2e-16
relative error = 2.225e-14 %
Correct digits = 16
h = 0.003 0.006
y1[1] (numeric) = 2.00951439597 -0.0215810253281
y1[1] (closed_form) = 2.00951439597 -0.0215810253281
absolute error = 1e-15
relative error = 4.976e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2198
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2198
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=864.2MB, alloc=40.3MB, time=11.32
x[1] = 0.1212 0.188
h = 0.0001 0.005
y2[1] (numeric) = 0.876953601894 -0.187722147852
y2[1] (closed_form) = 0.876953601894 -0.187722147852
absolute error = 2e-16
relative error = 2.230e-14 %
Correct digits = 16
h = 0.0001 0.005
y1[1] (numeric) = 2.01025835835 -0.0228639871644
y1[1] (closed_form) = 2.01025835835 -0.0228639871644
absolute error = 1e-15
relative error = 4.974e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2268
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2268
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=911.9MB, alloc=40.3MB, time=11.95
x[1] = 0.1213 0.193
h = 0.0001 0.003
y2[1] (numeric) = 0.876736623054 -0.192773458308
y2[1] (closed_form) = 0.876736623054 -0.192773458308
absolute error = 3e-16
relative error = 3.342e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.01119727997 -0.0234987849821
y1[1] (closed_form) = 2.01119727997 -0.0234987849821
absolute error = 1e-15
relative error = 4.972e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2314
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2314
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=959.5MB, alloc=40.3MB, time=12.57
x[1] = 0.1214 0.196
h = 0.001 0.001
y2[1] (numeric) = 0.87656439451 -0.195805534333
y2[1] (closed_form) = 0.87656439451 -0.195805534333
absolute error = 2e-16
relative error = 2.227e-14 %
Correct digits = 16
h = 0.001 0.001
y1[1] (numeric) = 2.01176781311 -0.0238882620851
y1[1] (closed_form) = 2.01176781311 -0.0238882620851
absolute error = 1.000e-15
relative error = 4.971e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2343
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2343
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1224 0.197
h = 0.0001 0.004
y2[1] (numeric) = 0.8755285423 -0.196793290103
y2[1] (closed_form) = 0.8755285423 -0.196793290103
absolute error = 2e-16
relative error = 2.229e-14 %
Correct digits = 16
h = 0.0001 0.004
y1[1] (numeric) = 2.01184015904 -0.0242085150168
y1[1] (closed_form) = 2.01184015904 -0.0242085150168
absolute error = 1.000e-15
relative error = 4.970e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2357
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2357
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1007.1MB, alloc=40.3MB, time=13.19
x[1] = 0.1225 0.201
h = 0.003 0.006
y2[1] (numeric) = 0.875329449288 -0.200839764217
y2[1] (closed_form) = 0.875329449288 -0.200839764217
absolute error = 3.162e-16
relative error = 3.521e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.01262296704 -0.0247266799437
y1[1] (closed_form) = 2.01262296704 -0.0247266799437
absolute error = 1e-15
relative error = 4.968e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2394
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2394
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1054.8MB, alloc=40.3MB, time=13.82
x[1] = 0.1255 0.207
h = 0.0001 0.005
y2[1] (numeric) = 0.872137871779 -0.206841797121
y2[1] (closed_form) = 0.872137871779 -0.206841797121
absolute error = 3.162e-16
relative error = 3.528e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.01346721491 -0.0260957947093
y1[1] (closed_form) = 2.01346721491 -0.0260957947093
absolute error = 1e-15
relative error = 4.966e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2465
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2465
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1102.6MB, alloc=40.3MB, time=14.44
x[1] = 0.1256 0.212
h = 0.0001 0.003
y2[1] (numeric) = 0.871904343212 -0.211909065234
y2[1] (closed_form) = 0.871904343212 -0.211909065234
absolute error = 2.236e-16
relative error = 2.492e-14 %
Correct digits = 16
h = 0.0001 0.003
y1[1] (numeric) = 2.01450129208 -0.0267566252526
y1[1] (closed_form) = 2.01450129208 -0.0267566252526
absolute error = 1e-15
relative error = 4.964e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2513
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2513
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1257 0.215
h = 0.001 0.001
y2[1] (numeric) = 0.871721983267 -0.214950812089
y2[1] (closed_form) = 0.871721983267 -0.214950812089
absolute error = 2.236e-16
relative error = 2.491e-14 %
Correct digits = 16
h = 0.001 0.001
y1[1] (numeric) = 2.01512876276 -0.0271625284212
y1[1] (closed_form) = 2.01512876276 -0.0271625284212
absolute error = 1e-15
relative error = 4.962e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2542
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2542
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1150.2MB, alloc=40.3MB, time=15.06
x[1] = 0.1267 0.216
h = 0.001 0.003
y2[1] (numeric) = 0.870679476696 -0.215938649698
y2[1] (closed_form) = 0.870679476696 -0.215938649698
absolute error = 2.236e-16
relative error = 2.493e-14 %
Correct digits = 16
h = 0.001 0.003
y1[1] (numeric) = 2.01521540828 -0.0275067724077
y1[1] (closed_form) = 2.01521540828 -0.0275067724077
absolute error = 0
relative error = 0 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2556
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2556
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1198.0MB, alloc=40.3MB, time=15.69
x[1] = 0.1277 0.219
h = 0.0001 0.004
y2[1] (numeric) = 0.86958057139 -0.218957267869
y2[1] (closed_form) = 0.86958057139 -0.218957267869
absolute error = 2.828e-16
relative error = 3.154e-14 %
Correct digits = 16
h = 0.0001 0.004
y1[1] (numeric) = 2.01573788214 -0.0281138296284
y1[1] (closed_form) = 2.01573788214 -0.0281138296284
absolute error = 0
relative error = 0 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.259
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.259
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1245.9MB, alloc=40.3MB, time=16.32
x[1] = 0.1278 0.223
h = 0.003 0.006
y2[1] (numeric) = 0.869365410884 -0.223019117204
y2[1] (closed_form) = 0.869365410884 -0.223019117204
absolute error = 2.828e-16
relative error = 3.151e-14 %
Correct digits = 16
h = 0.003 0.006
y1[1] (numeric) = 2.01660878108 -0.0286580356999
y1[1] (closed_form) = 2.01660878108 -0.0286580356999
absolute error = 0
relative error = 0 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2629
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2629
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1308 0.229
h = 0.0001 0.005
y2[1] (numeric) = 0.86613780782 -0.229033462834
y2[1] (closed_form) = 0.86613780782 -0.229033462834
absolute error = 2.828e-16
relative error = 3.157e-14 %
Correct digits = 16
h = 0.0001 0.005
y1[1] (numeric) = 2.01756819591 -0.0301295987246
y1[1] (closed_form) = 2.01756819591 -0.0301295987246
absolute error = 1e-17
relative error = 4.956e-16 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2701
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2701
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1293.5MB, alloc=40.3MB, time=16.94
x[1] = 0.1309 0.234
h = 0.0001 0.003
y2[1] (numeric) = 0.865883613979 -0.234121106838
y2[1] (closed_form) = 0.865883613979 -0.234121106838
absolute error = 2.828e-16
relative error = 3.153e-14 %
Correct digits = 16
h = 0.0001 0.003
y1[1] (numeric) = 2.01871268108 -0.0308227013598
y1[1] (closed_form) = 2.01871268108 -0.0308227013598
absolute error = 1e-17
relative error = 4.953e-16 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.275
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.275
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1341.4MB, alloc=40.3MB, time=17.57
x[1] = 0.131 0.237
h = 0.001 0.001
y2[1] (numeric) = 0.86568860092 -0.237175179306
y2[1] (closed_form) = 0.86568860092 -0.237175179306
absolute error = 3.606e-16
relative error = 4.017e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.01940620362 -0.0312489074978
y1[1] (closed_form) = 2.01940620362 -0.0312489074978
absolute error = 1.000e-15
relative error = 4.952e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.278
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.278
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1389.1MB, alloc=40.3MB, time=18.20
x[1] = 0.132 0.238
h = 0.001 0.003
y2[1] (numeric) = 0.864637708305 -0.238163201941
y2[1] (closed_form) = 0.864637708305 -0.238163201941
absolute error = 2.236e-16
relative error = 2.493e-14 %
Correct digits = 16
h = 0.001 0.003
y1[1] (numeric) = 2.01950903603 -0.0316214135167
y1[1] (closed_form) = 2.01950903603 -0.0316214135167
absolute error = 2e-17
relative error = 9.902e-16 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2794
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2794
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.133 0.241
h = 0.0001 0.004
y2[1] (numeric) = 0.863522074576 -0.241190657123
y2[1] (closed_form) = 0.863522074576 -0.241190657123
absolute error = 3.162e-16
relative error = 3.527e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.02009214664 -0.0322688500487
y1[1] (closed_form) = 2.02009214664 -0.0322688500487
absolute error = 2e-17
relative error = 9.899e-16 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2828
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2828
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1436.5MB, alloc=44.3MB, time=18.82
x[1] = 0.1331 0.245
h = 0.003 0.006
y2[1] (numeric) = 0.863289801182 -0.245269683389
y2[1] (closed_form) = 0.863289801182 -0.245269683389
absolute error = 3.162e-16
relative error = 3.524e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.02105140668 -0.0328395484898
y1[1] (closed_form) = 2.02105140668 -0.0328395484898
absolute error = 1.000e-15
relative error = 4.948e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2869
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2869
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1484.4MB, alloc=44.3MB, time=19.45
x[1] = 0.1361 0.251
h = 0.0001 0.005
y2[1] (numeric) = 0.860023298375 -0.251298331088
y2[1] (closed_form) = 0.860023298375 -0.251298331088
absolute error = 2.236e-16
relative error = 2.496e-14 %
Correct digits = 16
h = 0.0001 0.005
y1[1] (numeric) = 2.02212608268 -0.0344144544453
y1[1] (closed_form) = 2.02212608268 -0.0344144544453
absolute error = 1.000e-15
relative error = 4.947e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2942
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2942
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1532.1MB, alloc=44.3MB, time=20.08
x[1] = 0.1362 0.256
h = 0.0001 0.003
y2[1] (numeric) = 0.859747136839 -0.256408611272
y2[1] (closed_form) = 0.859747136839 -0.256408611272
absolute error = 2.236e-16
relative error = 2.492e-14 %
Correct digits = 16
h = 0.0001 0.003
y1[1] (numeric) = 2.023381336 -0.035140412088
y1[1] (closed_form) = 2.023381336 -0.035140412088
absolute error = 1.000e-15
relative error = 4.944e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2993
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2993
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1363 0.259
h = 0.001 0.001
y2[1] (numeric) = 0.859538669491 -0.259476356295
y2[1] (closed_form) = 0.859538669491 -0.259476356295
absolute error = 2.236e-16
relative error = 2.490e-14 %
Correct digits = 16
h = 0.001 0.001
y1[1] (numeric) = 2.02414112719 -0.0355872772541
y1[1] (closed_form) = 2.02414112719 -0.0355872772541
absolute error = 4e-17
relative error = 1.976e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3024
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3024
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1579.9MB, alloc=44.3MB, time=20.70
x[1] = 0.1373 0.26
h = 0.001 0.003
y2[1] (numeric) = 0.858478681281 -0.26046476933
y2[1] (closed_form) = 0.858478681281 -0.26046476933
absolute error = 2.236e-16
relative error = 2.492e-14 %
Correct digits = 16
h = 0.001 0.003
y1[1] (numeric) = 2.0242601065 -0.0359882391217
y1[1] (closed_form) = 2.0242601065 -0.0359882391217
absolute error = 4e-17
relative error = 1.976e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3038
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3038
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1627.6MB, alloc=44.3MB, time=21.33
x[1] = 0.1383 0.263
h = 0.0001 0.004
y2[1] (numeric) = 0.85734510443 -0.263502181622
y2[1] (closed_form) = 0.85734510443 -0.263502181622
absolute error = 3.162e-16
relative error = 3.526e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.02490396873 -0.0366764861378
y1[1] (closed_form) = 2.02490396873 -0.0366764861378
absolute error = 5e-17
relative error = 2.469e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3073
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3073
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1384 0.267
h = 0.003 0.006
y2[1] (numeric) = 0.857094660949 -0.267600190372
y2[1] (closed_form) = 0.857094660949 -0.267600190372
absolute error = 3.606e-16
relative error = 4.016e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.02595189411 -0.0372741608594
y1[1] (closed_form) = 2.02595189411 -0.0372741608594
absolute error = 4e-17
relative error = 1.974e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3114
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3114
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1675.4MB, alloc=44.3MB, time=21.95
x[1] = 0.1414 0.273
h = 0.0001 0.005
y2[1] (numeric) = 0.853786363138 -0.273645126931
y2[1] (closed_form) = 0.853786363138 -0.273645126931
absolute error = 3.606e-16
relative error = 4.022e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.02714195396 -0.0389533784147
y1[1] (closed_form) = 2.02714195396 -0.0389533784147
absolute error = 4e-17
relative error = 1.973e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3189
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3189
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1723.0MB, alloc=44.3MB, time=22.58
x[1] = 0.1415 0.278
h = 0.0001 0.003
y2[1] (numeric) = 0.85348691619 -0.278780308783
y2[1] (closed_form) = 0.85348691619 -0.278780308783
absolute error = 3.606e-16
relative error = 4.016e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.02850837843 -0.0397128147928
y1[1] (closed_form) = 2.02850837843 -0.0397128147928
absolute error = 4e-17
relative error = 1.972e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3242
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3242
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1770.9MB, alloc=44.3MB, time=23.20
x[1] = 0.1416 0.281
h = 0.001 0.001
y2[1] (numeric) = 0.853264184056 -0.281863076396
y2[1] (closed_form) = 0.853264184056 -0.281863076396
absolute error = 3.606e-16
relative error = 4.012e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.02933468047 -0.0401807199198
y1[1] (closed_form) = 2.02933468047 -0.0401807199198
absolute error = 4e-17
relative error = 1.971e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3273
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3273
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1426 0.282
h = 0.001 0.003
y2[1] (numeric) = 0.852194386463 -0.282852083264
y2[1] (closed_form) = 0.852194386463 -0.282852083264
absolute error = 3.606e-16
relative error = 4.015e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.0294697674 -0.0406103481919
y1[1] (closed_form) = 2.0294697674 -0.0406103481919
absolute error = 3e-17
relative error = 1.478e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3288
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3288
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1818.7MB, alloc=44.3MB, time=23.82
x[1] = 0.1436 0.285
h = 0.0001 0.004
y2[1] (numeric) = 0.851041641288 -0.285900573122
y2[1] (closed_form) = 0.851041641288 -0.285900573122
absolute error = 3.606e-16
relative error = 4.016e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.0301745143 -0.0413398696397
y1[1] (closed_form) = 2.0301745143 -0.0413398696397
absolute error = 4e-17
relative error = 1.970e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3324
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3324
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1866.4MB, alloc=44.3MB, time=24.44
x[1] = 0.1437 0.289
h = 0.003 0.006
y2[1] (numeric) = 0.85077195781 -0.290019374322
y2[1] (closed_form) = 0.85077195781 -0.290019374322
absolute error = 3.606e-16
relative error = 4.011e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.0313114434 -0.04196503753
y1[1] (closed_form) = 2.0313114434 -0.04196503753
absolute error = 4e-17
relative error = 1.969e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3367
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3367
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1914.2MB, alloc=44.3MB, time=25.07
x[1] = 0.1467 0.295
h = 0.0001 0.005
y2[1] (numeric) = 0.847418946879 -0.296082584212
y2[1] (closed_form) = 0.847418946879 -0.296082584212
absolute error = 4.243e-16
relative error = 4.726e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.03261703805 -0.0437496098217
y1[1] (closed_form) = 2.03261703805 -0.0437496098217
absolute error = 4e-17
relative error = 1.967e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3443
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3443
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1468 0.3
h = 0.0001 0.003
y2[1] (numeric) = 0.847094880379 -0.301244939142
y2[1] (closed_form) = 0.847094880379 -0.301244939142
absolute error = 4.472e-16
relative error = 4.974e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.03409507953 -0.0445431898539
y1[1] (closed_form) = 2.03409507953 -0.0445431898539
absolute error = 5e-17
relative error = 2.458e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3497
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3497
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1961.7MB, alloc=44.3MB, time=25.68
x[1] = 0.1469 0.303
h = 0.001 0.001
y2[1] (numeric) = 0.846857062954 -0.304344082905
y2[1] (closed_form) = 0.846857062954 -0.304344082905
absolute error = 4.472e-16
relative error = 4.970e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.03498816002 -0.0450325409788
y1[1] (closed_form) = 2.03498816002 -0.0450325409788
absolute error = 5e-17
relative error = 2.456e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.353
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.353
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2009.5MB, alloc=44.3MB, time=26.31
x[1] = 0.1479 0.304
h = 0.0001 0.004
y2[1] (numeric) = 0.845776737579 -0.305333885021
y2[1] (closed_form) = 0.845776737579 -0.305333885021
absolute error = 4.472e-16
relative error = 4.973e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.03513931598 -0.0454910630373
y1[1] (closed_form) = 2.03513931598 -0.0454910630373
absolute error = 5e-17
relative error = 2.456e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3544
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3544
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2057.4MB, alloc=44.3MB, time=26.94
x[1] = 0.148 0.308
h = 0.003 0.006
y2[1] (numeric) = 0.845489902933 -0.309472283621
y2[1] (closed_form) = 0.845489902933 -0.309472283621
absolute error = 4.472e-16
relative error = 4.967e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.03635349007 -0.04613926912
y1[1] (closed_form) = 2.03635349007 -0.04613926912
absolute error = 6e-17
relative error = 2.946e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3588
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3588
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.151 0.314
h = 0.0001 0.005
y2[1] (numeric) = 0.842096298724 -0.315553390472
y2[1] (closed_form) = 0.842096298724 -0.315553390472
absolute error = 4.243e-16
relative error = 4.718e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.03775994886 -0.0480140405886
y1[1] (closed_form) = 2.03775994886 -0.0480140405886
absolute error = 6e-17
relative error = 2.944e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3666
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3666
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2105.0MB, alloc=44.3MB, time=27.56
x[1] = 0.1511 0.319
h = 0.0001 0.003
y2[1] (numeric) = 0.841750319442 -0.320741274242
y2[1] (closed_form) = 0.841750319442 -0.320741274242
absolute error = 4.243e-16
relative error = 4.710e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.03933487464 -0.0488362369329
y1[1] (closed_form) = 2.03933487464 -0.0488362369329
absolute error = 5e-17
relative error = 2.451e-15 %
Correct digits = 17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3721
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3721
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2152.8MB, alloc=44.3MB, time=28.19
x[1] = 0.1512 0.322
h = 0.001 0.001
y2[1] (numeric) = 0.841499069002 -0.32385579414
y2[1] (closed_form) = 0.841499069002 -0.32385579414
absolute error = 4.243e-16
relative error = 4.705e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.04028593203 -0.049343592276
y1[1] (closed_form) = 2.04028593203 -0.049343592276
absolute error = 1.002e-15
relative error = 4.909e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3755
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3755
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2200.6MB, alloc=44.3MB, time=28.81
x[1] = 0.1522 0.323
h = 0.001 0.003
y2[1] (numeric) = 0.840409115291 -0.324846577615
y2[1] (closed_form) = 0.840409115291 -0.324846577615
absolute error = 5.000e-16
relative error = 5.549e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.04045123738 -0.0498269893422
y1[1] (closed_form) = 2.04045123738 -0.0498269893422
absolute error = 1.002e-15
relative error = 4.908e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.377
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.377
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1532 0.326
h = 0.0001 0.004
y2[1] (numeric) = 0.839217565523 -0.327918927857
y2[1] (closed_form) = 0.839217565523 -0.327918927857
absolute error = 5.000e-16
relative error = 5.549e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.04127019884 -0.0506339311263
y1[1] (closed_form) = 2.04127019884 -0.0506339311263
absolute error = 1.002e-15
relative error = 4.906e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3807
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3807
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2248.2MB, alloc=44.3MB, time=29.43
x[1] = 0.1533 0.33
h = 0.003 0.006
y2[1] (numeric) = 0.838909484782 -0.332081513707
y2[1] (closed_form) = 0.838909484782 -0.332081513707
absolute error = 4.243e-16
relative error = 4.702e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.04257410438 -0.0513106760591
y1[1] (closed_form) = 2.04257410438 -0.0513106760591
absolute error = 1.002e-15
relative error = 4.906e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3853
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3853
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2296.0MB, alloc=44.3MB, time=30.05
x[1] = 0.1563 0.336
h = 0.0001 0.005
y2[1] (numeric) = 0.83546569413 -0.338184616598
y2[1] (closed_form) = 0.83546569413 -0.338184616598
absolute error = 4.243e-16
relative error = 4.707e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.04409646806 -0.0532929406906
y1[1] (closed_form) = 2.04409646806 -0.0532929406906
absolute error = 7e-17
relative error = 3.423e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3932
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3932
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2343.6MB, alloc=44.3MB, time=30.68
x[1] = 0.1564 0.341
h = 0.0001 0.003
y2[1] (numeric) = 0.835092592413 -0.343403934662
y2[1] (closed_form) = 0.835092592413 -0.343403934662
absolute error = 4.243e-16
relative error = 4.699e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.04578396391 -0.0541506224751
y1[1] (closed_form) = 2.04578396391 -0.0541506224751
absolute error = 7e-17
relative error = 3.420e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3989
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3989
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1565 0.344
h = 0.001 0.001
y2[1] (numeric) = 0.834824717155 -0.346537370287
y2[1] (closed_form) = 0.834824717155 -0.346537370287
absolute error = 5.000e-16
relative error = 5.532e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.046802371 -0.0546802431283
y1[1] (closed_form) = 2.046802371 -0.0546802431283
absolute error = 1.002e-15
relative error = 4.896e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4024
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4024
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2391.4MB, alloc=44.3MB, time=31.30
x[1] = 0.1575 0.345
h = 0.001 0.003
y2[1] (numeric) = 0.833722887673 -0.347529326872
y2[1] (closed_form) = 0.833722887673 -0.347529326872
absolute error = 5.000e-16
relative error = 5.536e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.04698367824 -0.0551930026442
y1[1] (closed_form) = 2.04698367824 -0.0551930026442
absolute error = 1.002e-15
relative error = 4.895e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4039
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4039
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2439.2MB, alloc=44.3MB, time=31.92
x[1] = 0.1585 0.348
h = 0.0001 0.004
y2[1] (numeric) = 0.832508612586 -0.350615979092
y2[1] (closed_form) = 0.832508612586 -0.350615979092
absolute error = 5.000e-16
relative error = 5.535e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.04786401178 -0.0560427270402
y1[1] (closed_form) = 2.04786401178 -0.0560427270402
absolute error = 1.002e-15
relative error = 4.893e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4077
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4077
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2487.0MB, alloc=44.3MB, time=32.54
x[1] = 0.1586 0.352
h = 0.003 0.006
y2[1] (numeric) = 0.8321781745 -0.35480457816
y2[1] (closed_form) = 0.8321781745 -0.35480457816
absolute error = 5.000e-16
relative error = 5.527e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.04925808543 -0.0567486234603
y1[1] (closed_form) = 2.04925808543 -0.0567486234603
absolute error = 2.002e-15
relative error = 9.764e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4124
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4124
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1616 0.358
h = 0.0001 0.005
y2[1] (numeric) = 0.828681203952 -0.360931656483
y2[1] (closed_form) = 0.828681203952 -0.360931656483
absolute error = 5.000e-16
relative error = 5.532e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.05089658578 -0.0588396400566
y1[1] (closed_form) = 2.05089658578 -0.0588396400566
absolute error = 1.003e-15
relative error = 4.889e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4205
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4205
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2534.6MB, alloc=44.3MB, time=33.16
x[1] = 0.1617 0.363
h = 0.0001 0.003
y2[1] (numeric) = 0.828279592456 -0.366184701432
y2[1] (closed_form) = 0.828279592456 -0.366184701432
absolute error = 5.000e-16
relative error = 5.521e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.05269722104 -0.0597335918718
y1[1] (closed_form) = 2.05269722104 -0.0597335918718
absolute error = 1.003e-15
relative error = 4.885e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4264
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4264
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2582.5MB, alloc=44.3MB, time=33.79
x[1] = 0.1618 0.366
h = 0.001 0.001
y2[1] (numeric) = 0.827994239477 -0.369338418916
y2[1] (closed_form) = 0.827994239477 -0.369338418916
absolute error = 4.243e-16
relative error = 4.680e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.05378331863 -0.0602859568118
y1[1] (closed_form) = 2.05378331863 -0.0602859568118
absolute error = 1.003e-15
relative error = 4.883e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.43
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.43
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1628 0.367
h = 0.001 0.003
y2[1] (numeric) = 0.826879800532 -0.370331743901
y2[1] (closed_form) = 0.826879800532 -0.370331743901
absolute error = 5.000e-16
relative error = 5.519e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.05398059082 -0.0608283548403
y1[1] (closed_form) = 2.05398059082 -0.0608283548403
absolute error = 1.003e-15
relative error = 4.882e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4316
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4316
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2630.2MB, alloc=44.3MB, time=34.40
x[1] = 0.1638 0.37
h = 0.0001 0.004
y2[1] (numeric) = 0.825641526649 -0.373433822183
y2[1] (closed_form) = 0.825641526649 -0.373433822183
absolute error = 5.000e-16
relative error = 5.518e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.05492249965 -0.0617214545662
y1[1] (closed_form) = 2.05492249965 -0.0617214545662
absolute error = 2.002e-15
relative error = 9.736e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4355
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4355
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2678.0MB, alloc=44.3MB, time=35.02
x[1] = 0.1639 0.374
h = 0.003 0.006
y2[1] (numeric) = 0.825287603709 -0.377650267082
y2[1] (closed_form) = 0.825287603709 -0.377650267082
absolute error = 5.000e-16
relative error = 5.509e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.05640721236 -0.0624571494307
y1[1] (closed_form) = 2.05640721236 -0.0624571494307
absolute error = 1.002e-15
relative error = 4.873e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4403
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4403
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2725.9MB, alloc=44.3MB, time=35.65
x[1] = 0.1669 0.38
h = 0.0001 0.005
y2[1] (numeric) = 0.821734429972 -0.383803298756
y2[1] (closed_form) = 0.821734429972 -0.383803298756
absolute error = 4.243e-16
relative error = 4.678e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.05816210876 -0.0646582534612
y1[1] (closed_form) = 2.05816210876 -0.0646582534612
absolute error = 1.003e-15
relative error = 4.872e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4486
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4486
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.167 0.385
h = 0.0001 0.003
y2[1] (numeric) = 0.82130290049 -0.389092371911
y2[1] (closed_form) = 0.82130290049 -0.389092371911
absolute error = 4.243e-16
relative error = 4.668e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.0600764959 -0.0655893028202
y1[1] (closed_form) = 2.0600764959 -0.0655893028202
absolute error = 8e-17
relative error = 3.881e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4548
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4548
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2773.5MB, alloc=44.3MB, time=36.27
x[1] = 0.1671 0.388
h = 0.001 0.001
y2[1] (numeric) = 0.820999204189 -0.392267742556
y2[1] (closed_form) = 0.820999204189 -0.392267742556
absolute error = 4.243e-16
relative error = 4.663e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.06123065034 -0.0661649171799
y1[1] (closed_form) = 2.06123065034 -0.0661649171799
absolute error = 1.003e-15
relative error = 4.864e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4585
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4585
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2821.4MB, alloc=44.3MB, time=36.89
x[1] = 0.1681 0.389
h = 0.001 0.003
y2[1] (numeric) = 0.819871416022 -0.393262628912
y2[1] (closed_form) = 0.819871416022 -0.393262628912
absolute error = 4.472e-16
relative error = 4.918e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.06144385093 -0.06673724702
y1[1] (closed_form) = 2.06144385093 -0.06673724702
absolute error = 1.003e-15
relative error = 4.864e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.46
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.46
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2869.2MB, alloc=44.3MB, time=37.51
x[1] = 0.1691 0.392
h = 0.0001 0.004
y2[1] (numeric) = 0.818607855327 -0.396381258778
y2[1] (closed_form) = 0.818607855327 -0.396381258778
absolute error = 3.606e-16
relative error = 3.964e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.06244755619 -0.0676743489303
y1[1] (closed_form) = 2.06244755619 -0.0676743489303
absolute error = 1.003e-15
relative error = 4.861e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4641
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4641
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1692 0.396
h = 0.003 0.006
y2[1] (numeric) = 0.81822930282 -0.400627389341
y2[1] (closed_form) = 0.81822930282 -0.400627389341
absolute error = 4.472e-16
relative error = 4.909e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.0640234133 -0.0684405239204
y1[1] (closed_form) = 2.0640234133 -0.0684405239204
absolute error = 9e-17
relative error = 4.358e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4691
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4691
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2916.9MB, alloc=44.3MB, time=38.13
x[1] = 0.1722 0.402
h = 0.0001 0.005
y2[1] (numeric) = 0.814616870926 -0.40680835101
y2[1] (closed_form) = 0.814616870926 -0.40680835101
absolute error = 4.472e-16
relative error = 4.911e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.06589499251 -0.0707531281916
y1[1] (closed_form) = 2.06589499251 -0.0707531281916
absolute error = 1.004e-15
relative error = 4.857e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4776
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4776
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2964.7MB, alloc=44.3MB, time=38.76
x[1] = 0.1723 0.407
h = 0.0001 0.003
y2[1] (numeric) = 0.814153993209 -0.41213576314
y2[1] (closed_form) = 0.814153993209 -0.41213576314
absolute error = 4.472e-16
relative error = 4.901e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.06792378719 -0.0717221460499
y1[1] (closed_form) = 2.06792378719 -0.0717221460499
absolute error = 1.005e-15
relative error = 4.857e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4839
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4839
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3012.6MB, alloc=44.3MB, time=39.38
x[1] = 0.1724 0.41
h = 0.001 0.001
y2[1] (numeric) = 0.813831074571 -0.415334163842
y2[1] (closed_form) = 0.813831074571 -0.415334163842
absolute error = 4.472e-16
relative error = 4.895e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.06914639045 -0.0723215414344
y1[1] (closed_form) = 2.06914639045 -0.0723215414344
absolute error = 1.0e-16
relative error = 4.830e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4877
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4877
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1734 0.411
h = 0.0001 0.004
y2[1] (numeric) = 0.812689190973 -0.416330802141
y2[1] (closed_form) = 0.812689190973 -0.416330802141
absolute error = 4.472e-16
relative error = 4.898e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.06937548317 -0.0729241137464
y1[1] (closed_form) = 2.06937548317 -0.0729241137464
absolute error = 1.0e-16
relative error = 4.829e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4893
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4893
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3060.3MB, alloc=44.3MB, time=40.00
x[1] = 0.1735 0.415
h = 0.003 0.006
y2[1] (numeric) = 0.812288891253 -0.420604276634
y2[1] (closed_form) = 0.812288891253 -0.420604276634
absolute error = 4.123e-16
relative error = 4.507e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.07103060008 -0.0737160031704
y1[1] (closed_form) = 2.07103060008 -0.0737160031704
absolute error = 1.1e-16
relative error = 5.308e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4945
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4945
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3108.0MB, alloc=44.3MB, time=40.62
x[1] = 0.1765 0.421
h = 0.0001 0.005
y2[1] (numeric) = 0.808623344747 -0.426811617548
y2[1] (closed_form) = 0.808623344747 -0.426811617548
absolute error = 4.123e-16
relative error = 4.509e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.0730042189 -0.076124378964
y1[1] (closed_form) = 2.0730042189 -0.076124378964
absolute error = 1.1e-16
relative error = 5.303e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5032
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5032
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3155.6MB, alloc=44.3MB, time=41.24
x[1] = 0.1766 0.426
h = 0.0001 0.003
y2[1] (numeric) = 0.808132814843 -0.43217428577
y2[1] (closed_form) = 0.808132814843 -0.43217428577
absolute error = 5.099e-16
relative error = 5.564e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.07513251711 -0.0771254355981
y1[1] (closed_form) = 2.07513251711 -0.0771254355981
absolute error = 1.1e-16
relative error = 5.297e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5097
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5097
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1767 0.429
h = 0.001 0.001
y2[1] (numeric) = 0.807792932359 -0.43539386063
y2[1] (closed_form) = 0.807792932359 -0.43539386063
absolute error = 5.099e-16
relative error = 5.557e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.07641466469 -0.0777449248564
y1[1] (closed_form) = 2.07641466469 -0.0777449248564
absolute error = 1.006e-15
relative error = 4.842e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5136
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5136
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3203.2MB, alloc=44.3MB, time=41.86
x[1] = 0.1777 0.43
h = 0.001 0.003
y2[1] (numeric) = 0.806638337042 -0.436392337778
y2[1] (closed_form) = 0.806638337042 -0.436392337778
absolute error = 5.099e-16
relative error = 5.560e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.07665777353 -0.0783736022804
y1[1] (closed_form) = 2.07665777353 -0.0783736022804
absolute error = 1.006e-15
relative error = 4.841e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5153
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5153
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3251.0MB, alloc=44.3MB, time=42.48
x[1] = 0.1787 0.433
h = 0.0001 0.004
y2[1] (numeric) = 0.805324470936 -0.439545105871
y2[1] (closed_form) = 0.805324470936 -0.439545105871
absolute error = 5.099e-16
relative error = 5.558e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.07777766086 -0.0793936255503
y1[1] (closed_form) = 2.07777766086 -0.0793936255503
absolute error = 1.1e-16
relative error = 5.290e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5195
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5195
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3298.7MB, alloc=44.3MB, time=43.11
x[1] = 0.1788 0.437
h = 0.003 0.006
y2[1] (numeric) = 0.804897384709 -0.44385172486
y2[1] (closed_form) = 0.804897384709 -0.44385172486
absolute error = 5.099e-16
relative error = 5.547e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.07952496334 -0.0802173504665
y1[1] (closed_form) = 2.07952496334 -0.0802173504665
absolute error = 1.2e-16
relative error = 5.766e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5248
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5248
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1818 0.443
h = 0.0001 0.005
y2[1] (numeric) = 0.80116682831 -0.450090708459
y2[1] (closed_form) = 0.80116682831 -0.450090708459
absolute error = 5.099e-16
relative error = 5.549e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.08161588983 -0.0827400595285
y1[1] (closed_form) = 2.08161588983 -0.0827400595285
absolute error = 1.008e-15
relative error = 4.841e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5338
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5338
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3346.3MB, alloc=44.3MB, time=43.73
x[1] = 0.1819 0.448
h = 0.0001 0.003
y2[1] (numeric) = 0.800642253877 -0.455496060783
y2[1] (closed_form) = 0.800642253877 -0.455496060783
absolute error = 5.099e-16
relative error = 5.536e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.08385994262 -0.0837808138071
y1[1] (closed_form) = 2.08385994262 -0.0837808138071
absolute error = 1.3e-16
relative error = 6.233e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5405
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5405
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3394.1MB, alloc=44.3MB, time=44.35
x[1] = 0.182 0.451
h = 0.001 0.001
y2[1] (numeric) = 0.800281491816 -0.458741255002
y2[1] (closed_form) = 0.800281491816 -0.458741255002
absolute error = 5e-16
relative error = 5.420e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.0852113438 -0.0844251395041
y1[1] (closed_form) = 2.0852113438 -0.0844251395041
absolute error = 1.3e-16
relative error = 6.229e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5446
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5446
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3442.0MB, alloc=44.3MB, time=44.98
x[1] = 0.183 0.452
h = 0.001 0.003
y2[1] (numeric) = 0.799111396258 -0.459741841098
y2[1] (closed_form) = 0.799111396258 -0.459741841098
absolute error = 5e-16
relative error = 5.423e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.0854702819 -0.085084684565
y1[1] (closed_form) = 2.0854702819 -0.085084684565
absolute error = 1.3e-16
relative error = 6.228e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5463
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5463
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.184 0.455
h = 0.0001 0.004
y2[1] (numeric) = 0.797768484181 -0.462914406448
y2[1] (closed_form) = 0.797768484181 -0.462914406448
absolute error = 5e-16
relative error = 5.421e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.08665270596 -0.0861506915662
y1[1] (closed_form) = 2.08665270596 -0.0861506915662
absolute error = 1.3e-16
relative error = 6.225e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5507
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5507
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3489.6MB, alloc=44.3MB, time=45.60
x[1] = 0.1841 0.459
h = 0.003 0.006
y2[1] (numeric) = 0.797313412348 -0.467256033816
y2[1] (closed_form) = 0.797313412348 -0.467256033816
absolute error = 5e-16
relative error = 5.410e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.08849279854 -0.0870070350314
y1[1] (closed_form) = 2.08849279854 -0.0870070350314
absolute error = 1.4e-16
relative error = 6.698e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5562
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5562
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3537.3MB, alloc=44.3MB, time=46.22
x[1] = 0.1871 0.465
h = 0.0001 0.005
y2[1] (numeric) = 0.793514690168 -0.473528634562
y2[1] (closed_form) = 0.793514690168 -0.473528634562
absolute error = 5.099e-16
relative error = 5.518e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.09070139764 -0.0896457151636
y1[1] (closed_form) = 2.09070139764 -0.0896457151636
absolute error = 1.4e-16
relative error = 6.690e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5653
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5653
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3585.0MB, alloc=44.3MB, time=46.84
x[1] = 0.1872 0.47
h = 0.0001 0.003
y2[1] (numeric) = 0.79295457142 -0.478979013072
y2[1] (closed_form) = 0.79295457142 -0.478979013072
absolute error = 5.099e-16
relative error = 5.504e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.0930619854 -0.0907271649432
y1[1] (closed_form) = 2.0930619854 -0.0907271649432
absolute error = 1.4e-16
relative error = 6.682e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5723
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5723
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1873 0.473
h = 0.001 0.001
y2[1] (numeric) = 0.792572008464 -0.482251222072
y2[1] (closed_form) = 0.792572008464 -0.482251222072
absolute error = 5.385e-16
relative error = 5.804e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.09448310605 -0.0913969360123
y1[1] (closed_form) = 2.09448310605 -0.0913969360123
absolute error = 1.5e-16
relative error = 7.155e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5766
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5766
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3632.7MB, alloc=44.3MB, time=47.46
x[1] = 0.1883 0.474
h = 0.001 0.003
y2[1] (numeric) = 0.791385645836 -0.483254100418
y2[1] (closed_form) = 0.791385645836 -0.483254100418
absolute error = 5.099e-16
relative error = 5.499e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.09475783765 -0.0920877098006
y1[1] (closed_form) = 2.09475783765 -0.0920877098006
absolute error = 1.5e-16
relative error = 7.154e-15 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5783
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5783
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3680.4MB, alloc=44.3MB, time=48.08
x[1] = 0.1893 0.477
h = 0.0001 0.004
y2[1] (numeric) = 0.790012335627 -0.48644759628
y2[1] (closed_form) = 0.790012335627 -0.48644759628
absolute error = 6.083e-16
relative error = 6.556e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.09600308892 -0.0932004623123
y1[1] (closed_form) = 2.09600308892 -0.0932004623123
absolute error = 1.011e-15
relative error = 4.820e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5828
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5828
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1894 0.481
h = 0.003 0.006
y2[1] (numeric) = 0.789528058167 -0.490826105342
y2[1] (closed_form) = 0.789528058167 -0.490826105342
absolute error = 5.099e-16
relative error = 5.485e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.09793661082 -0.0940902438952
y1[1] (closed_form) = 2.09793661082 -0.0940902438952
absolute error = 1.013e-15
relative error = 4.822e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5885
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5885
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3728.2MB, alloc=44.3MB, time=48.70
x[1] = 0.1924 0.487
h = 0.0001 0.005
y2[1] (numeric) = 0.7856579754 -0.497134297128
y2[1] (closed_form) = 0.7856579754 -0.497134297128
absolute error = 5.099e-16
relative error = 5.484e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.10026327411 -0.0968466132164
y1[1] (closed_form) = 2.10026327411 -0.0968466132164
absolute error = 1.013e-15
relative error = 4.817e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.598
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.598
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3775.8MB, alloc=44.3MB, time=49.33
x[1] = 0.1925 0.492
h = 0.0001 0.003
y2[1] (numeric) = 0.785060785839 -0.502632056145
y2[1] (closed_form) = 0.785060785839 -0.502632056145
absolute error = 5.099e-16
relative error = 5.470e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.10274122087 -0.0979698020854
y1[1] (closed_form) = 2.10274122087 -0.0979698020854
absolute error = 1.013e-15
relative error = 4.811e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6052
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6052
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3823.7MB, alloc=44.3MB, time=49.96
x[1] = 0.1926 0.495
h = 0.001 0.001
y2[1] (numeric) = 0.784655484433 -0.50593268258
y2[1] (closed_form) = 0.784655484433 -0.50593268258
absolute error = 5.385e-16
relative error = 5.768e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.10423255271 -0.0986656553211
y1[1] (closed_form) = 2.10423255271 -0.0986656553211
absolute error = 2.006e-15
relative error = 9.525e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6096
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6096
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1936 0.496
h = 0.001 0.003
y2[1] (numeric) = 0.783452079957 -0.506938033732
y2[1] (closed_form) = 0.783452079957 -0.506938033732
absolute error = 5.385e-16
relative error = 5.771e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.10452304197 -0.0993880368486
y1[1] (closed_form) = 2.10452304197 -0.0993880368486
absolute error = 1.013e-15
relative error = 4.807e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6113
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6113
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3871.4MB, alloc=44.3MB, time=50.58
x[1] = 0.1946 0.499
h = 0.0001 0.004
y2[1] (numeric) = 0.782047000712 -0.510153595812
y2[1] (closed_form) = 0.782047000712 -0.510153595812
absolute error = 5.831e-16
relative error = 6.245e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.10583142866 -0.100548332615
y1[1] (closed_form) = 2.10583142866 -0.100548332615
absolute error = 1.020e-15
relative error = 4.837e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.616
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.616
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3919.2MB, alloc=44.3MB, time=51.20
x[1] = 0.1947 0.503
h = 0.003 0.006
y2[1] (numeric) = 0.781532275685 -0.514570869889
y2[1] (closed_form) = 0.781532275685 -0.514570869889
absolute error = 5.831e-16
relative error = 6.231e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.10785905392 -0.101472408919
y1[1] (closed_form) = 2.10785905392 -0.101472408919
absolute error = 1.020e-15
relative error = 4.833e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6219
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6219
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3967.1MB, alloc=44.3MB, time=51.82
x[1] = 0.1977 0.509
h = 0.0001 0.005
y2[1] (numeric) = 0.777587596691 -0.520916626191
y2[1] (closed_form) = 0.777587596691 -0.520916626191
absolute error = 5.000e-16
relative error = 5.342e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.11030419934 -0.10434826674
y1[1] (closed_form) = 2.11030419934 -0.10434826674
absolute error = 1.044e-15
relative error = 4.941e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6317
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6317
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.1978 0.514
h = 0.0001 0.003
y2[1] (numeric) = 0.77695178187 -0.526464132994
y2[1] (closed_form) = 0.77695178187 -0.526464132994
absolute error = 5.000e-16
relative error = 5.328e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.1129003729 -0.105514284687
y1[1] (closed_form) = 2.1129003729 -0.105514284687
absolute error = 2.010e-15
relative error = 9.501e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6392
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6392
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4014.7MB, alloc=44.3MB, time=52.44
x[1] = 0.1979 0.517
h = 0.001 0.001
y2[1] (numeric) = 0.776522787463 -0.529794587172
y2[1] (closed_form) = 0.776522787463 -0.529794587172
absolute error = 5.000e-16
relative error = 5.319e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.11446243357 -0.106236885149
y1[1] (closed_form) = 2.11446243357 -0.106236885149
absolute error = 2.010e-15
relative error = 9.494e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6437
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6437
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4062.6MB, alloc=44.3MB, time=53.07
x[1] = 0.1989 0.518
h = 0.0001 0.004
y2[1] (numeric) = 0.775301558014 -0.530802588836
y2[1] (closed_form) = 0.775301558014 -0.530802588836
absolute error = 5.000e-16
relative error = 5.321e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.11476864446 -0.106991271513
y1[1] (closed_form) = 2.11476864446 -0.106991271513
absolute error = 2.010e-15
relative error = 9.492e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6455
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6455
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4110.4MB, alloc=44.3MB, time=53.69
x[1] = 0.199 0.522
h = 0.003 0.006
y2[1] (numeric) = 0.774760105245 -0.535255129962
y2[1] (closed_form) = 0.774760105245 -0.535255129962
absolute error = 5.000e-16
relative error = 5.310e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.11687826023 -0.107944449662
y1[1] (closed_form) = 2.11687826023 -0.107944449662
absolute error = 2.022e-15
relative error = 9.541e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6516
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6516
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.202 0.528
h = 0.0001 0.005
y2[1] (numeric) = 0.77074907214 -0.541635742479
y2[1] (closed_form) = 0.77074907214 -0.541635742479
absolute error = 5.000e-16
relative error = 5.308e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.11942719981 -0.110923244089
y1[1] (closed_form) = 2.11942719981 -0.110923244089
absolute error = 2.022e-15
relative error = 9.529e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6616
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6616
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4158.0MB, alloc=44.3MB, time=54.31
x[1] = 0.2021 0.533
h = 0.0001 0.003
y2[1] (numeric) = 0.770079374177 -0.547228462435
y2[1] (closed_form) = 0.770079374177 -0.547228462435
absolute error = 5.000e-16
relative error = 5.293e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.12212639623 -0.112125613455
y1[1] (closed_form) = 2.12212639623 -0.112125613455
absolute error = 3.015e-15
relative error = 1.419e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6694
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6694
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4205.7MB, alloc=44.3MB, time=54.93
x[1] = 0.2022 0.536
h = 0.001 0.001
y2[1] (numeric) = 0.769629586027 -0.550586024862
y2[1] (closed_form) = 0.769629586027 -0.550586024862
absolute error = 5.000e-16
relative error = 5.284e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.12375010223 -0.112870940099
y1[1] (closed_form) = 2.12375010223 -0.112870940099
absolute error = 2.010e-15
relative error = 9.451e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6741
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6741
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4253.6MB, alloc=44.3MB, time=55.55
x[1] = 0.2032 0.537
h = 0.001 0.003
y2[1] (numeric) = 0.768392414061 -0.551596673241
y2[1] (closed_form) = 0.768392414061 -0.551596673241
absolute error = 4.243e-16
relative error = 4.485e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.12407020471 -0.113653020395
y1[1] (closed_form) = 2.12407020471 -0.113653020395
absolute error = 2.010e-15
relative error = 9.449e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6759
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6759
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2042 0.54
h = 0.0001 0.004
y2[1] (numeric) = 0.766924798361 -0.554856745278
y2[1] (closed_form) = 0.766924798361 -0.554856745278
absolute error = 4.243e-16
relative error = 4.482e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.12549754312 -0.114903269739
y1[1] (closed_form) = 2.12549754312 -0.114903269739
absolute error = 1.020e-15
relative error = 4.791e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6809
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6809
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4301.1MB, alloc=44.3MB, time=56.17
x[1] = 0.2043 0.544
h = 0.003 0.006
y2[1] (numeric) = 0.766350548022 -0.55935159987
y2[1] (closed_form) = 0.766350548022 -0.55935159987
absolute error = 5.000e-16
relative error = 5.270e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.1277026207 -0.115892427998
y1[1] (closed_form) = 2.1277026207 -0.115892427998
absolute error = 1.044e-15
relative error = 4.900e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6872
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6872
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4348.9MB, alloc=44.3MB, time=56.80
x[1] = 0.2073 0.55
h = 0.0001 0.005
y2[1] (numeric) = 0.762258806091 -0.565773488247
y2[1] (closed_form) = 0.762258806091 -0.565773488247
absolute error = 4.243e-16
relative error = 4.469e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.1303709133 -0.118994272584
y1[1] (closed_form) = 2.1303709133 -0.118994272584
absolute error = 1.044e-15
relative error = 4.893e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6975
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6975
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4396.7MB, alloc=44.3MB, time=57.42
x[1] = 0.2074 0.555
h = 0.0001 0.003
y2[1] (numeric) = 0.761547540278 -0.571420417242
y2[1] (closed_form) = 0.761547540278 -0.571420417242
absolute error = 4.243e-16
relative error = 4.456e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.13319008261 -0.120241613581
y1[1] (closed_form) = 2.13319008261 -0.120241613581
absolute error = 1.044e-15
relative error = 4.886e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7056
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7056
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2075 0.558
h = 0.001 0.001
y2[1] (numeric) = 0.761072252109 -0.574810465358
y2[1] (closed_form) = 0.761072252109 -0.574810465358
absolute error = 5.000e-16
relative error = 5.242e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.13488555869 -0.121014994772
y1[1] (closed_form) = 2.13488555869 -0.121014994772
absolute error = 3e-16
relative error = 1.403e-14 %
Correct digits = 16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7105
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7105
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4444.4MB, alloc=44.3MB, time=58.04
x[1] = 0.2085 0.559
h = 0.001 0.003
y2[1] (numeric) = 0.759815776407 -0.575824096575
y2[1] (closed_form) = 0.759815776407 -0.575824096575
absolute error = 4.243e-16
relative error = 4.450e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.13522132013 -0.121829867983
y1[1] (closed_form) = 2.13522132013 -0.121829867983
absolute error = 1.044e-15
relative error = 4.882e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7123
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7123
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4492.3MB, alloc=44.3MB, time=58.66
x[1] = 0.2095 0.562
h = 0.0001 0.004
y2[1] (numeric) = 0.758312371986 -0.579109516289
y2[1] (closed_form) = 0.758312371986 -0.579109516289
absolute error = 4.243e-16
relative error = 4.447e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.13671278427 -0.123130140954
y1[1] (closed_form) = 2.13671278427 -0.123130140954
absolute error = 1.044e-15
relative error = 4.878e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7175
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7175
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4540.2MB, alloc=44.3MB, time=59.29
x[1] = 0.2096 0.566
h = 0.003 0.006
y2[1] (numeric) = 0.757704013984 -0.583648599727
y2[1] (closed_form) = 0.757704013984 -0.583648599727
absolute error = 5.000e-16
relative error = 5.228e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.13901409833 -0.124156244567
y1[1] (closed_form) = 2.13901409833 -0.124156244567
absolute error = 2.022e-15
relative error = 9.439e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7241
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7241
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2126 0.572
h = 0.0001 0.005
y2[1] (numeric) = 0.753528200011 -0.590113737583
y2[1] (closed_form) = 0.753528200011 -0.590113737583
absolute error = 5.000e-16
relative error = 5.224e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.14180223707 -0.127383175806
y1[1] (closed_form) = 2.14180223707 -0.127383175806
absolute error = 2.022e-15
relative error = 9.426e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7347
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7347
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4587.7MB, alloc=44.3MB, time=59.91
x[1] = 0.2127 0.577
h = 0.0001 0.003
y2[1] (numeric) = 0.752773725101 -0.595817284301
y2[1] (closed_form) = 0.752773725101 -0.595817284301
absolute error = 5.000e-16
relative error = 5.208e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.1447423737 -0.128676714606
y1[1] (closed_form) = 2.1447423737 -0.128676714606
absolute error = 2.040e-15
relative error = 9.493e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7431
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7431
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4635.6MB, alloc=44.3MB, time=60.53
x[1] = 0.2128 0.58
h = 0.001 0.001
y2[1] (numeric) = 0.752271929599 -0.59924125286
y2[1] (closed_form) = 0.752271929599 -0.59924125286
absolute error = 4.472e-16
relative error = 4.650e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.14651021251 -0.129478898361
y1[1] (closed_form) = 2.14651021251 -0.129478898361
absolute error = 2.040e-15
relative error = 9.485e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7482
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7482
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2138 0.581
h = 0.001 0.003
y2[1] (numeric) = 0.750995340908 -0.60025803602
y2[1] (closed_form) = 0.750995340908 -0.60025803602
absolute error = 4.472e-16
relative error = 4.652e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.14686159593 -0.130327014312
y1[1] (closed_form) = 2.14686159593 -0.130327014312
absolute error = 3.027e-15
relative error = 1.407e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7501
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7501
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4683.4MB, alloc=44.3MB, time=61.15
x[1] = 0.2148 0.584
h = 0.0001 0.004
y2[1] (numeric) = 0.749454696113 -0.603569950688
y2[1] (closed_form) = 0.749454696113 -0.603569950688
absolute error = 5.000e-16
relative error = 5.196e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.14841756257 -0.131678251571
y1[1] (closed_form) = 2.14841756257 -0.131678251571
absolute error = 2.040e-15
relative error = 9.476e-14 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7554
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7554
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4731.1MB, alloc=44.3MB, time=61.78
x[1] = 0.2149 0.588
h = 0.003 0.006
y2[1] (numeric) = 0.748810894489 -0.608155190564
y2[1] (closed_form) = 0.748810894489 -0.608155190564
absolute error = 5.000e-16
relative error = 5.183e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.150815923 -0.132742305069
y1[1] (closed_form) = 2.150815923 -0.132742305069
absolute error = 3.041e-15
relative error = 1.411e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7622
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7622
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4778.9MB, alloc=44.3MB, time=62.40
x[1] = 0.2179 0.594
h = 0.0001 0.005
y2[1] (numeric) = 0.74454759684 -0.61466555163
y2[1] (closed_form) = 0.74454759684 -0.61466555163
absolute error = 4.472e-16
relative error = 4.632e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.15372442649 -0.136096444436
y1[1] (closed_form) = 2.15372442649 -0.136096444436
absolute error = 3.041e-15
relative error = 1.409e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7733
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7733
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.218 0.599
h = 0.0001 0.003
y2[1] (numeric) = 0.743748238683 -0.62042814049
y2[1] (closed_form) = 0.743748238683 -0.62042814049
absolute error = 4.472e-16
relative error = 4.617e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.15678656924 -0.137437456484
y1[1] (closed_form) = 2.15678656924 -0.137437456484
absolute error = 3.041e-15
relative error = 1.407e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.782
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.782
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4826.5MB, alloc=44.3MB, time=63.02
x[1] = 0.2181 0.602
h = 0.001 0.001
y2[1] (numeric) = 0.743218908538 -0.623887473529
y2[1] (closed_form) = 0.743218908538 -0.623887473529
absolute error = 3.162e-16
relative error = 3.259e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.15862738968 -0.138269220829
y1[1] (closed_form) = 2.15862738968 -0.138269220829
absolute error = 3.041e-15
relative error = 1.406e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7872
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7872
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4874.3MB, alloc=44.3MB, time=63.64
x[1] = 0.2191 0.603
h = 0.001 0.003
y2[1] (numeric) = 0.7419213877 -0.624907574485
y2[1] (closed_form) = 0.7419213877 -0.624907574485
absolute error = 4.472e-16
relative error = 4.610e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.1589943575 -0.139151048143
y1[1] (closed_form) = 2.1589943575 -0.139151048143
absolute error = 3.041e-15
relative error = 1.406e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7892
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7892
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4922.2MB, alloc=44.3MB, time=64.26
x[1] = 0.2201 0.606
h = 0.0001 0.004
y2[1] (numeric) = 0.740342027719 -0.628247134777
y2[1] (closed_form) = 0.740342027719 -0.628247134777
absolute error = 3.606e-16
relative error = 3.713e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.16061522089 -0.140554228629
y1[1] (closed_form) = 2.16061522089 -0.140554228629
absolute error = 3.041e-15
relative error = 1.405e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7947
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7947
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2202 0.61
h = 0.003 0.006
y2[1] (numeric) = 0.73966141959 -0.632880471461
y2[1] (closed_form) = 0.73966141959 -0.632880471461
absolute error = 4.123e-16
relative error = 4.235e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.16311147303 -0.141657276478
y1[1] (closed_form) = 2.16311147303 -0.141657276478
absolute error = 3.041e-15
relative error = 1.403e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8018
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8018
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4969.8MB, alloc=44.3MB, time=64.88
x[1] = 0.2232 0.616
h = 0.0001 0.005
y2[1] (numeric) = 0.735307176198 -0.639438029682
y2[1] (closed_form) = 0.735307176198 -0.639438029682
absolute error = 4.123e-16
relative error = 4.231e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.16614088506 -0.145140831516
y1[1] (closed_form) = 2.16614088506 -0.145140831516
absolute error = 3.041e-15
relative error = 1.401e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8133
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8133
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5017.6MB, alloc=44.3MB, time=65.50
x[1] = 0.2233 0.621
h = 0.0001 0.003
y2[1] (numeric) = 0.73446122641 -0.645262101556
y2[1] (closed_form) = 0.73446122641 -0.645262101556
absolute error = 4.123e-16
relative error = 4.217e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.16932611729 -0.146530642357
y1[1] (closed_form) = 2.16932611729 -0.146530642357
absolute error = 3.059e-15
relative error = 1.407e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8223
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8223
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5065.6MB, alloc=44.3MB, time=66.13
x[1] = 0.2234 0.624
h = 0.001 0.001
y2[1] (numeric) = 0.733903313512 -0.648758252816
y2[1] (closed_form) = 0.733903313512 -0.648758252816
absolute error = 4.123e-16
relative error = 4.209e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.17124056466 -0.147392795823
y1[1] (closed_form) = 2.17124056466 -0.147392795823
absolute error = 3.059e-15
relative error = 1.406e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8278
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8278
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2244 0.625
h = 0.0001 0.004
y2[1] (numeric) = 0.732584031052 -0.649781834048
y2[1] (closed_form) = 0.732584031052 -0.649781834048
absolute error = 4e-16
relative error = 4.085e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.17162307852 -0.14830882213
y1[1] (closed_form) = 2.17162307852 -0.14830882213
absolute error = 3.059e-15
relative error = 1.406e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8298
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8298
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5113.2MB, alloc=44.3MB, time=66.75
x[1] = 0.2245 0.629
h = 0.003 0.006
y2[1] (numeric) = 0.731871233032 -0.654458595881
y2[1] (closed_form) = 0.731871233032 -0.654458595881
absolute error = 5e-16
relative error = 5.093e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.17420477878 -0.149445121938
y1[1] (closed_form) = 2.17420477878 -0.149445121938
absolute error = 3.059e-15
relative error = 1.404e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8372
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8372
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5160.9MB, alloc=44.3MB, time=67.37
x[1] = 0.2275 0.635
h = 0.0001 0.005
y2[1] (numeric) = 0.727436488457 -0.661059501194
y2[1] (closed_form) = 0.727436488457 -0.661059501194
absolute error = 4e-16
relative error = 4.069e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.17734029839 -0.153040458423
y1[1] (closed_form) = 2.17734029839 -0.153040458423
absolute error = 3.059e-15
relative error = 1.402e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8489
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8489
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5208.6MB, alloc=44.3MB, time=67.99
x[1] = 0.2276 0.64
h = 0.0001 0.003
y2[1] (numeric) = 0.726549811259 -0.666939046621
y2[1] (closed_form) = 0.726549811259 -0.666939046621
absolute error = 5.099e-16
relative error = 5.170e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.18063298733 -0.154471889345
y1[1] (closed_form) = 2.18063298733 -0.154471889345
absolute error = 3.059e-15
relative error = 1.399e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8583
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8583
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2277 0.643
h = 0.001 0.001
y2[1] (numeric) = 0.725966901827 -0.670468419478
y2[1] (closed_form) = 0.725966901827 -0.670468419478
absolute error = 4.123e-16
relative error = 4.172e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.18261172293 -0.155359983885
y1[1] (closed_form) = 2.18261172293 -0.155359983885
absolute error = 3.059e-15
relative error = 1.398e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8639
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8639
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5256.3MB, alloc=44.3MB, time=68.61
x[1] = 0.2287 0.644
h = 0.001 0.003
y2[1] (numeric) = 0.724628259309 -0.671495396738
y2[1] (closed_form) = 0.724628259309 -0.671495396738
absolute error = 4.123e-16
relative error = 4.174e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.18300800258 -0.156305668146
y1[1] (closed_form) = 2.18300800258 -0.156305668146
absolute error = 3.059e-15
relative error = 1.398e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.866
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.866
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5304.1MB, alloc=44.3MB, time=69.23
x[1] = 0.2297 0.647
h = 0.0001 0.004
y2[1] (numeric) = 0.722973212731 -0.674889977815
y2[1] (closed_form) = 0.722973212731 -0.674889977815
absolute error = 3.162e-16
relative error = 3.197e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.18475138096 -0.157807456753
y1[1] (closed_form) = 2.18475138096 -0.157807456753
absolute error = 3.059e-15
relative error = 1.397e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.872
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.872
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5351.9MB, alloc=44.3MB, time=69.86
x[1] = 0.2298 0.651
h = 0.003 0.006
y2[1] (numeric) = 0.722221020349 -0.679618500022
y2[1] (closed_form) = 0.722221020349 -0.679618500022
absolute error = 3.162e-16
relative error = 3.189e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.18743265414 -0.158984791963
y1[1] (closed_form) = 2.18743265414 -0.158984791963
absolute error = 4.061e-15
relative error = 1.852e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8796
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8796
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2328 0.657
h = 0.0001 0.005
y2[1] (numeric) = 0.717688770229 -0.686270319178
y2[1] (closed_form) = 0.717688770229 -0.686270319178
absolute error = 3.162e-16
relative error = 3.185e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.19069018914 -0.162713877657
y1[1] (closed_form) = 2.19069018914 -0.162713877657
absolute error = 4.045e-15
relative error = 1.841e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8918
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8918
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5399.4MB, alloc=44.3MB, time=70.48
x[1] = 0.2329 0.662
h = 0.0001 0.003
y2[1] (numeric) = 0.716752256325 -0.692215957118
y2[1] (closed_form) = 0.716752256325 -0.692215957118
absolute error = 3.162e-16
relative error = 3.174e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.19410811989 -0.164196696031
y1[1] (closed_form) = 2.19410811989 -0.164196696031
absolute error = 4.061e-15
relative error = 1.846e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9015
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9015
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5447.3MB, alloc=44.3MB, time=71.10
x[1] = 0.233 0.665
h = 0.001 0.001
y2[1] (numeric) = 0.716138773286 -0.695784893628
y2[1] (closed_form) = 0.716138773286 -0.695784893628
absolute error = 3.162e-16
relative error = 3.167e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.19616176422 -0.165116758738
y1[1] (closed_form) = 2.19616176422 -0.165116758738
absolute error = 4.045e-15
relative error = 1.837e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9074
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9074
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5495.3MB, alloc=44.3MB, time=71.72
x[1] = 0.234 0.666
h = 0.001 0.003
y2[1] (numeric) = 0.714776798635 -0.696815654319
y2[1] (closed_form) = 0.714776798635 -0.696815654319
absolute error = 3.162e-16
relative error = 3.168e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.19657352245 -0.166097601157
y1[1] (closed_form) = 2.19657352245 -0.166097601157
absolute error = 5.036e-15
relative error = 2.286e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9096
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9096
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.235 0.669
h = 0.0001 0.004
y2[1] (numeric) = 0.713078695283 -0.700241211747
y2[1] (closed_form) = 0.713078695283 -0.700241211747
absolute error = 2.236e-16
relative error = 2.237e-14 %
Correct digits = 16
h = 0.0001 0.004
y1[1] (numeric) = 2.19838303506 -0.167654344407
y1[1] (closed_form) = 2.19838303506 -0.167654344407
absolute error = 4.045e-15
relative error = 1.835e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9157
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9157
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5543.0MB, alloc=44.3MB, time=72.34
x[1] = 0.2351 0.673
h = 0.003 0.006
y2[1] (numeric) = 0.712285662822 -0.705023474745
y2[1] (closed_form) = 0.712285662822 -0.705023474745
absolute error = 2.828e-16
relative error = 2.822e-14 %
Correct digits = 16
h = 0.003 0.006
y1[1] (numeric) = 2.20116482903 -0.168873877114
y1[1] (closed_form) = 2.20116482903 -0.168873877114
absolute error = 5.036e-15
relative error = 2.281e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9236
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9236
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5590.8MB, alloc=44.3MB, time=72.96
x[1] = 0.2381 0.679
h = 0.0001 0.005
y2[1] (numeric) = 0.707652289478 -0.711728183458
y2[1] (closed_form) = 0.707652289478 -0.711728183458
absolute error = 3.606e-16
relative error = 3.592e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.20454499492 -0.172739171907
y1[1] (closed_form) = 2.20454499492 -0.172739171907
absolute error = 4.045e-15
relative error = 1.829e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9363
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9363
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2382 0.684
h = 0.0001 0.003
y2[1] (numeric) = 0.706664125261 -0.717742406252
y2[1] (closed_form) = 0.706664125261 -0.717742406252
absolute error = 3.606e-16
relative error = 3.580e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.20808937996 -0.174274850906
y1[1] (closed_form) = 2.20808937996 -0.174274850906
absolute error = 5.036e-15
relative error = 2.274e-13 %
Correct digits = 15
memory used=5638.5MB, alloc=44.3MB, time=73.58
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9464
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9464
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2383 0.687
h = 0.001 0.001
y2[1] (numeric) = 0.706018956577 -0.7213523905
y2[1] (closed_form) = 0.706018956577 -0.7213523905
absolute error = 4.243e-16
relative error = 4.203e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.21021865477 -0.175227780203
y1[1] (closed_form) = 2.21021865477 -0.175227780203
absolute error = 4.061e-15
relative error = 1.832e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9525
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9525
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5686.2MB, alloc=44.3MB, time=74.20
x[1] = 0.2393 0.688
h = 0.001 0.003
y2[1] (numeric) = 0.704632788445 -0.722387086932
y2[1] (closed_form) = 0.704632788445 -0.722387086932
absolute error = 3.606e-16
relative error = 3.573e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.21064585055 -0.176244323998
y1[1] (closed_form) = 2.21064585055 -0.176244323998
absolute error = 4.045e-15
relative error = 1.824e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9548
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9548
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5734.0MB, alloc=44.3MB, time=74.82
x[1] = 0.2403 0.691
h = 0.0001 0.004
y2[1] (numeric) = 0.702890055214 -0.725844786474
y2[1] (closed_form) = 0.702890055214 -0.725844786474
absolute error = 3.606e-16
relative error = 3.568e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.21252195933 -0.177857153656
y1[1] (closed_form) = 2.21252195933 -0.177857153656
absolute error = 4.045e-15
relative error = 1.822e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9612
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9612
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2404 0.695
h = 0.003 0.006
y2[1] (numeric) = 0.702054705804 -0.730682785655
y2[1] (closed_form) = 0.702054705804 -0.730682785655
absolute error = 3.606e-16
relative error = 3.558e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.21540525796 -0.179120088638
y1[1] (closed_form) = 2.21540525796 -0.179120088638
absolute error = 4.045e-15
relative error = 1.820e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9694
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9694
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5781.7MB, alloc=44.3MB, time=75.44
x[1] = 0.2434 0.701
h = 0.0001 0.005
y2[1] (numeric) = 0.69731653312 -0.73744236017
y2[1] (closed_form) = 0.69731653312 -0.73744236017
absolute error = 4.243e-16
relative error = 4.180e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.21890869438 -0.18312414312
y1[1] (closed_form) = 2.21890869438 -0.18312414312
absolute error = 5.036e-15
relative error = 2.262e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9825
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9825
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5829.4MB, alloc=44.3MB, time=76.07
x[1] = 0.2435 0.706
h = 0.0001 0.003
y2[1] (numeric) = 0.69627486544 -0.743527679381
y2[1] (closed_form) = 0.69627486544 -0.743527679381
absolute error = 4.243e-16
relative error = 4.165e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.22258079154 -0.184714209508
y1[1] (closed_form) = 2.22258079154 -0.184714209508
absolute error = 5.036e-15
relative error = 2.258e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9931
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9931
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5877.3MB, alloc=44.3MB, time=76.69
x[1] = 0.2436 0.709
h = 0.001 0.001
y2[1] (numeric) = 0.69559687505 -0.747180206777
y2[1] (closed_form) = 0.69559687505 -0.747180206777
absolute error = 3.606e-16
relative error = 3.532e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.22478644535 -0.185700936442
y1[1] (closed_form) = 2.22478644535 -0.185700936442
absolute error = 4.045e-15
relative error = 1.812e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9995
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9995
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2446 0.71
h = 0.001 0.003
y2[1] (numeric) = 0.694185640142 -0.748218987413
y2[1] (closed_form) = 0.694185640142 -0.748218987413
absolute error = 3.606e-16
relative error = 3.533e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.22522903638 -0.186753744708
y1[1] (closed_form) = 2.22522903638 -0.186753744708
absolute error = 5.036e-15
relative error = 2.255e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.002
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.002
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5924.9MB, alloc=44.3MB, time=77.31
x[1] = 0.2456 0.713
h = 0.0001 0.004
y2[1] (numeric) = 0.692396676084 -0.751709999076
y2[1] (closed_form) = 0.692396676084 -0.751709999076
absolute error = 3.606e-16
relative error = 3.528e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.22717222056 -0.188423833642
y1[1] (closed_form) = 2.22717222056 -0.188423833642
absolute error = 5.025e-15
relative error = 2.248e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.008
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5972.7MB, alloc=44.3MB, time=77.94
x[1] = 0.2457 0.717
h = 0.003 0.006
y2[1] (numeric) = 0.691517500563 -0.756605745377
y2[1] (closed_form) = 0.691517500563 -0.756605745377
absolute error = 3.606e-16
relative error = 3.518e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.23015804386 -0.189731419135
y1[1] (closed_form) = 2.23015804386 -0.189731419135
absolute error = 5.025e-15
relative error = 2.245e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.017
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.017
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6020.5MB, alloc=44.3MB, time=78.56
x[1] = 0.2487 0.723
h = 0.0001 0.005
y2[1] (numeric) = 0.686670791845 -0.763422162512
y2[1] (closed_form) = 0.686670791845 -0.763422162512
absolute error = 4.243e-16
relative error = 4.132e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.2337854143 -0.19387687591
y1[1] (closed_form) = 2.2337854143 -0.19387687591
absolute error = 5.036e-15
relative error = 2.246e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.031
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.031
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2488 0.728
h = 0.0001 0.003
y2[1] (numeric) = 0.685573726578 -0.769581109641
y2[1] (closed_form) = 0.685573726578 -0.769581109641
absolute error = 3.606e-16
relative error = 3.498e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.23758652693 -0.195522911033
y1[1] (closed_form) = 2.23758652693 -0.195522911033
absolute error = 5.036e-15
relative error = 2.242e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.042
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.042
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6068.1MB, alloc=44.3MB, time=79.18
x[1] = 0.2489 0.731
h = 0.001 0.001
y2[1] (numeric) = 0.684861753537 -0.773277687335
y2[1] (closed_form) = 0.684861753537 -0.773277687335
absolute error = 3.606e-16
relative error = 3.491e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.23986933524 -0.196544399873
y1[1] (closed_form) = 2.23986933524 -0.196544399873
absolute error = 6.030e-15
relative error = 2.682e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.048
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.048
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6116.0MB, alloc=44.3MB, time=79.80
x[1] = 0.2499 0.732
h = 0.0001 0.004
y2[1] (numeric) = 0.683424566177 -0.774320696654
y2[1] (closed_form) = 0.683424566177 -0.774320696654
absolute error = 4.243e-16
relative error = 4.108e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.24032727777 -0.197634055829
y1[1] (closed_form) = 2.24032727777 -0.197634055829
absolute error = 6.030e-15
relative error = 2.681e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.051
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6163.9MB, alloc=44.3MB, time=80.42
x[1] = 0.25 0.736
h = 0.003 0.006
y2[1] (numeric) = 0.682507153376 -0.779268319478
y2[1] (closed_form) = 0.682507153376 -0.779268319478
absolute error = 4.243e-16
relative error = 4.096e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.24340274838 -0.198979869842
y1[1] (closed_form) = 2.24340274838 -0.198979869842
absolute error = 6.030e-15
relative error = 2.677e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.06
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.253 0.742
h = 0.0001 0.005
y2[1] (numeric) = 0.677564689534 -0.786136602907
y2[1] (closed_form) = 0.677564689534 -0.786136602907
absolute error = 4.243e-16
relative error = 4.088e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.24713907531 -0.203247740885
y1[1] (closed_form) = 2.24713907531 -0.203247740885
absolute error = 6.030e-15
relative error = 2.672e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.074
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6211.5MB, alloc=44.3MB, time=81.04
x[1] = 0.2531 0.747
h = 0.0001 0.003
y2[1] (numeric) = 0.676419309226 -0.792361660785
y2[1] (closed_form) = 0.676419309226 -0.792361660785
absolute error = 4.243e-16
relative error = 4.072e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.25105301216 -0.204941701948
y1[1] (closed_form) = 2.25105301216 -0.204941701948
absolute error = 7.026e-15
relative error = 3.108e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.085
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.085
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6259.2MB, alloc=44.3MB, time=81.66
x[1] = 0.2532 0.75
h = 0.001 0.001
y2[1] (numeric) = 0.675677685132 -0.796097795764
y2[1] (closed_form) = 0.675677685132 -0.796097795764
absolute error = 4.243e-16
relative error = 4.063e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.25340330449 -0.205992978524
y1[1] (closed_form) = 2.25340330449 -0.205992978524
absolute error = 7.018e-15
relative error = 3.101e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.092
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6307.2MB, alloc=44.3MB, time=82.29
x[1] = 0.2542 0.751
h = 0.001 0.003
y2[1] (numeric) = 0.674217492402 -0.797144881281
y2[1] (closed_form) = 0.674217492402 -0.797144881281
absolute error = 4.243e-16
relative error = 4.064e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.2538748736 -0.207114652195
y1[1] (closed_form) = 2.2538748736 -0.207114652195
absolute error = 7.026e-15
relative error = 3.104e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.094
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.094
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2552 0.754
h = 0.0001 0.004
y2[1] (numeric) = 0.672338572949 -0.800701605346
y2[1] (closed_form) = 0.672338572949 -0.800701605346
absolute error = 5.000e-16
relative error = 4.782e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.25594492087 -0.208893739119
y1[1] (closed_form) = 2.25594492087 -0.208893739119
absolute error = 7.026e-15
relative error = 3.101e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.102
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.102
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6354.6MB, alloc=44.3MB, time=82.90
x[1] = 0.2553 0.758
h = 0.0001 0.004
y2[1] (numeric) = 0.671374460334 -0.805710779413
y2[1] (closed_form) = 0.671374460334 -0.805710779413
absolute error = 5.000e-16
relative error = 4.768e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.25912492715 -0.210286631604
y1[1] (closed_form) = 2.25912492715 -0.210286631604
absolute error = 8.022e-15
relative error = 3.536e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.111
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.111
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6402.5MB, alloc=44.3MB, time=83.53
x[1] = 0.2554 0.762
h = 0.003 0.006
y2[1] (numeric) = 0.670404448419 -0.810732573911
y2[1] (closed_form) = 0.670404448419 -0.810732573911
absolute error = 5.831e-16
relative error = 5.543e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.26232489863 -0.211683893879
y1[1] (closed_form) = 2.26232489863 -0.211683893879
absolute error = 8.022e-15
relative error = 3.531e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.12
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.12
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6450.3MB, alloc=44.3MB, time=84.16
x[1] = 0.2584 0.768
h = 0.0001 0.005
y2[1] (numeric) = 0.665328263185 -0.817676484628
y2[1] (closed_form) = 0.665328263185 -0.817676484628
absolute error = 6.708e-16
relative error = 6.364e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.26621372943 -0.216119287686
y1[1] (closed_form) = 2.26621372943 -0.216119287686
absolute error = 8.022e-15
relative error = 3.524e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.135
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.135
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2585 0.773
h = 0.0001 0.003
y2[1] (numeric) = 0.664116448722 -0.823996016976
y2[1] (closed_form) = 0.664116448722 -0.823996016976
absolute error = 6.708e-16
relative error = 6.339e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.27028437459 -0.21787775553
y1[1] (closed_form) = 2.27028437459 -0.21787775553
absolute error = 8.022e-15
relative error = 3.518e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.147
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.147
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6498.0MB, alloc=44.3MB, time=84.77
x[1] = 0.2586 0.776
h = 0.001 0.001
y2[1] (numeric) = 0.663334028473 -0.827788691023
y2[1] (closed_form) = 0.663334028473 -0.827788691023
absolute error = 6.708e-16
relative error = 6.324e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.2727284224 -0.21896916811
y1[1] (closed_form) = 2.2727284224 -0.21896916811
absolute error = 7.035e-15
relative error = 3.081e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.154
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.154
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6545.9MB, alloc=44.3MB, time=85.40
x[1] = 0.2596 0.777
h = 0.001 0.003
y2[1] (numeric) = 0.661841502742 -0.828842113114
y2[1] (closed_form) = 0.661841502742 -0.828842113114
absolute error = 6.708e-16
relative error = 6.325e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.27321932576 -0.220134895664
y1[1] (closed_form) = 2.27321932576 -0.220134895664
absolute error = 7.035e-15
relative error = 3.080e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.157
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.157
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2606 0.78
h = 0.0001 0.004
y2[1] (numeric) = 0.659904033388 -0.832443939954
y2[1] (closed_form) = 0.659904033388 -0.832443939954
absolute error = 7.616e-16
relative error = 7.169e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.2753721271 -0.221982918078
y1[1] (closed_form) = 2.2753721271 -0.221982918078
memory used=6593.9MB, alloc=44.3MB, time=86.02
absolute error = 7.035e-15
relative error = 3.077e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.164
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.164
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2607 0.784
h = 0.003 0.006
y2[1] (numeric) = 0.65888550907 -0.837529762931
y2[1] (closed_form) = 0.65888550907 -0.837529762931
absolute error = 7.616e-16
relative error = 7.147e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.27867800967 -0.223428835531
y1[1] (closed_form) = 2.27867800967 -0.223428835531
absolute error = 7.035e-15
relative error = 3.073e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.174
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.174
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6641.6MB, alloc=44.3MB, time=86.64
x[1] = 0.2637 0.79
h = 0.0001 0.005
y2[1] (numeric) = 0.653689156081 -0.844536711474
y2[1] (closed_form) = 0.653689156081 -0.844536711474
absolute error = 8.544e-16
relative error = 8.000e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.28269307582 -0.228014188885
y1[1] (closed_form) = 2.28269307582 -0.228014188885
absolute error = 7.035e-15
relative error = 3.067e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.189
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6689.4MB, alloc=44.3MB, time=87.26
x[1] = 0.2638 0.795
h = 0.0001 0.003
y2[1] (numeric) = 0.652416060048 -0.850937781192
y2[1] (closed_form) = 0.652416060048 -0.850937781192
absolute error = 8.544e-16
relative error = 7.968e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.2868970587 -0.22983369543
y1[1] (closed_form) = 2.2868970587 -0.22983369543
absolute error = 7.035e-15
relative error = 3.061e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.202
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.202
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2639 0.798
h = 0.001 0.001
y2[1] (numeric) = 0.651596049974 -0.85477921536
y2[1] (closed_form) = 0.651596049974 -0.85477921536
absolute error = 8.544e-16
relative error = 7.949e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.28942083297 -0.230962962143
y1[1] (closed_form) = 2.28942083297 -0.230962962143
absolute error = 7.026e-15
relative error = 3.053e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.209
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.209
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6737.2MB, alloc=44.3MB, time=87.88
x[1] = 0.2649 0.799
h = 0.001 0.003
y2[1] (numeric) = 0.650074811047 -0.85583732432
y2[1] (closed_form) = 0.650074811047 -0.85583732432
absolute error = 8.246e-16
relative error = 7.673e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.28992697687 -0.232167434898
y1[1] (closed_form) = 2.28992697687 -0.232167434898
absolute error = 8.031e-15
relative error = 3.489e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.212
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6785.0MB, alloc=44.3MB, time=88.50
x[1] = 0.2659 0.802
h = 0.0001 0.004
y2[1] (numeric) = 0.648084408263 -0.859477314253
y2[1] (closed_form) = 0.648084408263 -0.859477314253
absolute error = 8.246e-16
relative error = 7.661e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.29214902791 -0.234077851003
y1[1] (closed_form) = 2.29214902791 -0.234077851003
absolute error = 8.022e-15
relative error = 3.482e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.22
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.22
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6832.9MB, alloc=44.3MB, time=89.13
x[1] = 0.266 0.806
h = 0.003 0.006
y2[1] (numeric) = 0.647015721069 -0.864629246913
y2[1] (closed_form) = 0.647015721069 -0.864629246913
absolute error = 8.544e-16
relative error = 7.912e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.29556199159 -0.235573853852
y1[1] (closed_form) = 2.29556199159 -0.235573853852
absolute error = 8.031e-15
relative error = 3.480e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.23
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.23
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.269 0.812
h = 0.0001 0.005
y2[1] (numeric) = 0.641695197045 -0.871701216028
y2[1] (closed_form) = 0.641695197045 -0.871701216028
absolute error = 9.220e-16
relative error = 8.518e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.29970405426 -0.240312193705
y1[1] (closed_form) = 2.29970405426 -0.240312193705
absolute error = 8.022e-15
relative error = 3.470e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.246
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6880.5MB, alloc=44.3MB, time=89.75
x[1] = 0.2691 0.817
h = 0.0001 0.003
y2[1] (numeric) = 0.640358746166 -0.878186444601
y2[1] (closed_form) = 0.640358746166 -0.878186444601
absolute error = 9.220e-16
relative error = 8.483e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.30404286723 -0.242194548948
y1[1] (closed_form) = 2.30404286723 -0.242194548948
absolute error = 9.027e-15
relative error = 3.897e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.259
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.259
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6928.3MB, alloc=44.3MB, time=90.37
x[1] = 0.2692 0.82
h = 0.001 0.001
y2[1] (numeric) = 0.639499876514 -0.882078199046
y2[1] (closed_form) = 0.639499876514 -0.882078199046
absolute error = 1.020e-15
relative error = 9.360e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.30664725523 -0.243362773241
y1[1] (closed_form) = 2.30664725523 -0.243362773241
absolute error = 9.020e-15
relative error = 3.889e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.267
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.267
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6976.2MB, alloc=44.3MB, time=91.00
x[1] = 0.2702 0.821
h = 0.001 0.003
y2[1] (numeric) = 0.637948984053 -0.883141122511
y2[1] (closed_form) = 0.637948984053 -0.883141122511
absolute error = 1.020e-15
relative error = 9.361e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.30716858953 -0.244606658384
y1[1] (closed_form) = 2.30716858953 -0.244606658384
absolute error = 9.020e-15
relative error = 3.888e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.269
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.269
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2712 0.824
h = 0.0001 0.004
y2[1] (numeric) = 0.635903891459 -0.886820470894
y2[1] (closed_form) = 0.635903891459 -0.886820470894
absolute error = 1.020e-15
relative error = 9.345e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.30946045781 -0.246580857406
y1[1] (closed_form) = 2.30946045781 -0.246580857406
absolute error = 9.027e-15
relative error = 3.887e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.277
Order of pole (three term test) = 31.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7023.9MB, alloc=44.3MB, time=91.62
x[1] = 0.2713 0.828
h = 0.003 0.006
y2[1] (numeric) = 0.63478335263 -0.892040612884
y2[1] (closed_form) = 0.63478335263 -0.892040612884
absolute error = 1.020e-15
relative error = 9.315e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.31298170976 -0.248128423675
y1[1] (closed_form) = 2.31298170976 -0.248128423675
absolute error = 9.027e-15
relative error = 3.881e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.288
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.288
Order of pole (three term test) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7071.7MB, alloc=44.3MB, time=92.23
x[1] = 0.2743 0.834
h = 0.0001 0.005
y2[1] (numeric) = 0.629334582513 -0.899179586003
y2[1] (closed_form) = 0.629334582513 -0.899179586003
absolute error = 1.118e-15
relative error = 1.019e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.31725155233 -0.253022876346
y1[1] (closed_form) = 2.31725155233 -0.253022876346
absolute error = 8.022e-15
relative error = 3.442e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.305
Order of pole (three term test) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7119.4MB, alloc=44.3MB, time=92.86
x[1] = 0.2744 0.839
h = 0.0001 0.003
y2[1] (numeric) = 0.627932654999 -0.90575161851
y2[1] (closed_form) = 0.627932654999 -0.90575161851
absolute error = 1.105e-15
relative error = 1.002e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.32172673455 -0.254969950384
y1[1] (closed_form) = 2.32172673455 -0.254969950384
absolute error = 8.022e-15
relative error = 3.435e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.318
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.318
Order of pole (three term test) = 31.33 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2745 0.842
h = 0.001 0.001
y2[1] (numeric) = 0.627033626567 -0.909695267268
y2[1] (closed_form) = 0.627033626567 -0.909695267268
absolute error = 1.118e-15
relative error = 1.012e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.32441265124 -0.256178272267
y1[1] (closed_form) = 2.32441265124 -0.256178272267
absolute error = 8.022e-15
relative error = 3.431e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.326
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.326
Order of pole (three term test) = 31.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7167.2MB, alloc=44.3MB, time=93.48
x[1] = 0.2755 0.843
h = 0.001 0.003
y2[1] (numeric) = 0.625452125592 -0.910763128154
y2[1] (closed_form) = 0.625452125592 -0.910763128154
absolute error = 1.105e-15
relative error = 9.997e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.32494912353 -0.257462258499
y1[1] (closed_form) = 2.32494912353 -0.257462258499
absolute error = 9.020e-15
relative error = 3.856e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.329
Order of pole (three term test) = 31.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7215.0MB, alloc=44.3MB, time=94.10
x[1] = 0.2765 0.846
h = 0.0001 0.004
y2[1] (numeric) = 0.623350552694 -0.914483035533
y2[1] (closed_form) = 0.623350552694 -0.914483035533
absolute error = 1.204e-15
relative error = 1.088e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.32731139356 -0.259501675023
y1[1] (closed_form) = 2.32731139356 -0.259501675023
absolute error = 8.022e-15
relative error = 3.426e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.338
Order of pole (three term test) = 31.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7262.8MB, alloc=44.3MB, time=94.72
x[1] = 0.2766 0.85
h = 0.003 0.006
y2[1] (numeric) = 0.62217643392 -0.919773505505
y2[1] (closed_form) = 0.62217643392 -0.919773505505
absolute error = 1.217e-15
relative error = 1.096e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.33094217826 -0.261102331502
y1[1] (closed_form) = 2.33094217826 -0.261102331502
absolute error = 9.020e-15
relative error = 3.846e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.349
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.349
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2796 0.856
h = 0.0001 0.005
y2[1] (numeric) = 0.616595268557 -0.9269814667
y2[1] (closed_form) = 0.616595268557 -0.9269814667
absolute error = 1.217e-15
relative error = 1.093e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.33534060599 -0.266156124286
y1[1] (closed_form) = 2.33534060599 -0.266156124286
absolute error = 9.020e-15
relative error = 3.838e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.366
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.366
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7310.3MB, alloc=44.3MB, time=95.34
x[1] = 0.2797 0.861
h = 0.0001 0.003
y2[1] (numeric) = 0.615125692523 -0.933642972525
y2[1] (closed_form) = 0.615125692523 -0.933642972525
absolute error = 1.315e-15
relative error = 1.176e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.3399537437 -0.268169848527
y1[1] (closed_form) = 2.3399537437 -0.268169848527
absolute error = 9.020e-15
relative error = 3.830e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.38
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.38
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7358.0MB, alloc=44.3MB, time=95.96
x[1] = 0.2798 0.864
h = 0.001 0.001
y2[1] (numeric) = 0.614185175693 -0.937640103926
y2[1] (closed_form) = 0.614185175693 -0.937640103926
absolute error = 1.315e-15
relative error = 1.173e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.34272213184 -0.269419445304
y1[1] (closed_form) = 2.34272213184 -0.269419445304
absolute error = 1.002e-14
relative error = 4.248e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.389
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.389
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7405.8MB, alloc=44.3MB, time=96.59
x[1] = 0.2808 0.865
h = 0.0001 0.004
y2[1] (numeric) = 0.612572096118 -0.938713020261
y2[1] (closed_form) = 0.612572096118 -0.938713020261
absolute error = 1.315e-15
relative error = 1.173e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.34327368726 -0.270744243139
y1[1] (closed_form) = 2.34327368726 -0.270744243139
absolute error = 1.002e-14
relative error = 4.247e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.392
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.392
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2809 0.869
h = 0.003 0.006
y2[1] (numeric) = 0.611351314844 -0.944066404719
y2[1] (closed_form) = 0.611351314844 -0.944066404719
absolute error = 1.315e-15
relative error = 1.169e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.34700043743 -0.272390532846
y1[1] (closed_form) = 2.34700043743 -0.272390532846
absolute error = 9.020e-15
relative error = 3.818e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.403
Order of pole (three term test) = 33.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.403
Order of pole (three term test) = 31.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7453.5MB, alloc=44.3MB, time=97.21
x[1] = 0.2839 0.875
h = 0.0001 0.005
y2[1] (numeric) = 0.605653661186 -0.951336983551
y2[1] (closed_form) = 0.605653661186 -0.951336983551
absolute error = 1.404e-15
relative error = 1.245e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.35151216048 -0.277582597783
y1[1] (closed_form) = 2.35151216048 -0.277582597783
absolute error = 1.002e-14
relative error = 4.231e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.421
Order of pole (three term test) = 33.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.421
Order of pole (three term test) = 31.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7501.2MB, alloc=44.3MB, time=97.83
x[1] = 0.284 0.88
h = 0.0001 0.003
y2[1] (numeric) = 0.604125186478 -0.958078503676
y2[1] (closed_form) = 0.604125186478 -0.958078503676
absolute error = 1.404e-15
relative error = 1.239e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.35624617846 -0.279653616731
y1[1] (closed_form) = 2.35624617846 -0.279653616731
absolute error = 9.020e-15
relative error = 3.801e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.436
Order of pole (three term test) = 33.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.436
Order of pole (three term test) = 31.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7549.1MB, alloc=44.3MB, time=98.46
x[1] = 0.2841 0.883
h = 0.001 0.001
y2[1] (numeric) = 0.603148532263 -0.96212347061
y2[1] (closed_form) = 0.603148532263 -0.96212347061
absolute error = 1.404e-15
relative error = 1.236e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.35908684304 -0.280938715146
y1[1] (closed_form) = 2.35908684304 -0.280938715146
absolute error = 9.020e-15
relative error = 3.797e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.444
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.444
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2851 0.884
h = 0.001 0.003
y2[1] (numeric) = 0.601507544222 -0.96320122134
y2[1] (closed_form) = 0.601507544222 -0.96320122134
absolute error = 1.404e-15
relative error = 1.236e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.35965183365 -0.28229904936
y1[1] (closed_form) = 2.35965183365 -0.28229904936
absolute error = 1.002e-14
relative error = 4.215e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.447
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.447
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7596.8MB, alloc=44.3MB, time=99.08
x[1] = 0.2861 0.887
h = 0.0001 0.004
y2[1] (numeric) = 0.599296504924 -0.967000537974
y2[1] (closed_form) = 0.599296504924 -0.967000537974
absolute error = 1.503e-15
relative error = 1.321e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.36214753773 -0.284462941475
y1[1] (closed_form) = 2.36214753773 -0.284462941475
absolute error = 9.020e-15
relative error = 3.791e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.457
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7644.7MB, alloc=44.3MB, time=99.70
x[1] = 0.2862 0.891
h = 0.003 0.006
y2[1] (numeric) = 0.598018843856 -0.972428267003
y2[1] (closed_form) = 0.598018843856 -0.972428267003
absolute error = 1.503e-15
relative error = 1.317e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.36598625611 -0.286165279694
y1[1] (closed_form) = 2.36598625611 -0.286165279694
absolute error = 9.020e-15
relative error = 3.785e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.469
Order of pole (three term test) = 33.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.469
Order of pole (three term test) = 31.23 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2892 0.897
h = 0.0001 0.005
y2[1] (numeric) = 0.592180892694 -0.979771578895
y2[1] (closed_form) = 0.592180892694 -0.979771578895
absolute error = 1.603e-15
relative error = 1.400e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.37062816088 -0.291522954273
y1[1] (closed_form) = 2.37062816088 -0.291522954273
absolute error = 9.020e-15
relative error = 3.776e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.487
Order of pole (three term test) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.487
Order of pole (three term test) = 31.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7692.5MB, alloc=44.3MB, time=100.32
x[1] = 0.2893 0.902
h = 0.0001 0.003
y2[1] (numeric) = 0.590580621729 -0.986607633921
y2[1] (closed_form) = 0.590580621729 -0.986607633921
absolute error = 1.603e-15
relative error = 1.394e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.37550323701 -0.293664364581
y1[1] (closed_form) = 2.37550323701 -0.293664364581
absolute error = 1.002e-14
relative error = 4.185e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.502
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.502
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7740.2MB, alloc=44.3MB, time=100.94
x[1] = 0.2894 0.905
h = 0.001 0.001
y2[1] (numeric) = 0.589559940052 -0.990709095211
y2[1] (closed_form) = 0.589559940052 -0.990709095211
absolute error = 1.603e-15
relative error = 1.391e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.37842821701 -0.294993018434
y1[1] (closed_form) = 2.37842821701 -0.294993018434
absolute error = 1.001e-14
relative error = 4.178e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.512
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.512
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7788.2MB, alloc=44.3MB, time=101.57
x[1] = 0.2904 0.906
h = 0.001 0.003
y2[1] (numeric) = 0.587885527746 -0.991792119412
y2[1] (closed_form) = 0.587885527746 -0.991792119412
absolute error = 1.603e-15
relative error = 1.390e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.37900819058 -0.29639554621
y1[1] (closed_form) = 2.37900819058 -0.29639554621
absolute error = 1.001e-14
relative error = 4.176e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.515
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.515
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2914 0.909
h = 0.0001 0.004
y2[1] (numeric) = 0.585612702213 -0.995635482114
y2[1] (closed_form) = 0.585612702213 -0.995635482114
absolute error = 1.603e-15
relative error = 1.388e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.38157608051 -0.298629009893
y1[1] (closed_form) = 2.38157608051 -0.298629009893
absolute error = 1.001e-14
relative error = 4.171e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.524
Order of pole (three term test) = 33.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.524
Order of pole (three term test) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7835.7MB, alloc=44.3MB, time=102.18
x[1] = 0.2915 0.913
h = 0.003 0.006
y2[1] (numeric) = 0.584276312995 -1.00113973237
y2[1] (closed_form) = 0.584276312995 -1.00113973237
absolute error = 1.005e-15
relative error = 8.670e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.38552812024 -0.300389068015
y1[1] (closed_form) = 2.38552812024 -0.300389068015
absolute error = 1.001e-14
relative error = 4.164e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.537
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.537
Order of pole (three term test) = 31.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7883.6MB, alloc=44.3MB, time=102.81
x[1] = 0.2945 0.919
h = 0.0001 0.005
y2[1] (numeric) = 0.578293690083 -1.00855776379
y2[1] (closed_form) = 0.578293690083 -1.00855776379
absolute error = 1.005e-15
relative error = 8.644e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.39030107357 -0.305915877496
y1[1] (closed_form) = 2.39030107357 -0.305915877496
absolute error = 9.014e-15
relative error = 3.741e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 33.85 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.556
Order of pole (three term test) = 31.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7931.4MB, alloc=44.3MB, time=103.43
x[1] = 0.2946 0.924
h = 0.0001 0.003
y2[1] (numeric) = 0.576619298973 -1.01549109722
y2[1] (closed_form) = 0.576619298973 -1.01549109722
absolute error = 1.005e-15
relative error = 8.606e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.39531893111 -0.308129792437
y1[1] (closed_form) = 2.39531893111 -0.308129792437
absolute error = 9.014e-15
relative error = 3.732e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 33.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.572
Order of pole (three term test) = 31.16 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2947 0.927
h = 0.001 0.001
y2[1] (numeric) = 0.575553167947 -1.01965068477
y2[1] (closed_form) = 0.575553167947 -1.01965068477
absolute error = 1.020e-15
relative error = 8.710e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.39832925022 -0.309503289647
y1[1] (closed_form) = 2.39832925022 -0.309503289647
absolute error = 9.014e-15
relative error = 3.727e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.582
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.582
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7979.2MB, alloc=44.3MB, time=104.05
x[1] = 0.2957 0.928
h = 0.001 0.003
y2[1] (numeric) = 0.573844315394 -1.02073908572
y2[1] (closed_form) = 0.573844315394 -1.02073908572
absolute error = 1.020e-15
relative error = 8.709e-14 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.39892414409 -0.310948785691
y1[1] (closed_form) = 2.39892414409 -0.310948785691
absolute error = 9.014e-15
relative error = 3.726e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.585
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8027.1MB, alloc=44.3MB, time=104.67
x[1] = 0.2967 0.931
h = 0.0001 0.004
y2[1] (numeric) = 0.571507771053 -1.0246277167
y2[1] (closed_form) = 0.571507771053 -1.0246277167
absolute error = 1.005e-15
relative error = 8.566e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.40156486972 -0.313253438106
y1[1] (closed_form) = 2.40156486972 -0.313253438106
absolute error = 9.020e-15
relative error = 3.724e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.595
Order of pole (three term test) = 33.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.595
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8074.9MB, alloc=44.3MB, time=105.30
x[1] = 0.2968 0.935
h = 0.003 0.006
y2[1] (numeric) = 0.570110760705 -1.03021068602
y2[1] (closed_form) = 0.570110760705 -1.03021068602
absolute error = 1.020e-15
relative error = 8.661e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.40563162216 -0.315072940267
y1[1] (closed_form) = 2.40563162216 -0.315072940267
absolute error = 9.020e-15
relative error = 3.718e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 33.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.608
Order of pole (three term test) = 31.14 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2998 0.941
h = 0.0001 0.005
y2[1] (numeric) = 0.563979008412 -1.03770542376
y2[1] (closed_form) = 0.563979008412 -1.03770542376
absolute error = 1.020e-15
relative error = 8.635e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.41053651121 -0.320772517585
y1[1] (closed_form) = 2.41053651121 -0.320772517585
absolute error = 9.014e-15
relative error = 3.707e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 33.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.628
Order of pole (three term test) = 31.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8122.4MB, alloc=44.3MB, time=105.91
x[1] = 0.2999 0.946
h = 0.0001 0.003
y2[1] (numeric) = 0.562228116787 -1.04473880616
y2[1] (closed_form) = 0.562228116787 -1.04473880616
absolute error = 1.020e-15
relative error = 8.596e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.41569892158 -0.323061116788
y1[1] (closed_form) = 2.41569892158 -0.323061116788
absolute error = 8.016e-15
relative error = 3.289e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.645
Order of pole (three term test) = 33.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.645
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8170.1MB, alloc=44.3MB, time=106.53
x[1] = 0.3 0.949
h = 0.001 0.001
y2[1] (numeric) = 0.561115080251 -1.04895816779
y2[1] (closed_form) = 0.561115080251 -1.04895816779
absolute error = 1.020e-15
relative error = 8.573e-14 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.41879563195 -0.324480785622
y1[1] (closed_form) = 2.41879563195 -0.324480785622
absolute error = 8.016e-15
relative error = 3.284e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.655
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.655
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8218.0MB, alloc=44.3MB, time=107.16
x[1] = 0.301 0.95
h = 0.001 0.003
y2[1] (numeric) = 0.55937075451 -1.05005204317
y2[1] (closed_form) = 0.55937075451 -1.05005204317
absolute error = 2.010e-15
relative error = 1.689e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.41940538022 -0.325970047709
y1[1] (closed_form) = 2.41940538022 -0.325970047709
absolute error = 8.016e-15
relative error = 3.283e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.658
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.658
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.302 0.953
h = 0.0001 0.004
y2[1] (numeric) = 0.55696851918 -1.05398717043
y2[1] (closed_form) = 0.55696851918 -1.05398717043
absolute error = 1.020e-15
relative error = 8.555e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.42211960806 -0.328347555463
y1[1] (closed_form) = 2.42211960806 -0.328347555463
absolute error = 8.016e-15
relative error = 3.279e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.669
Order of pole (three term test) = 33.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.669
Order of pole (three term test) = 31.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8265.5MB, alloc=44.3MB, time=107.78
x[1] = 0.3021 0.957
h = 0.003 0.006
y2[1] (numeric) = 0.555508948727 -1.05965107841
y2[1] (closed_form) = 0.555508948727 -1.05965107841
absolute error = 1.020e-15
relative error = 8.524e-14 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.42630250298 -0.330228279655
y1[1] (closed_form) = 2.42630250298 -0.330228279655
absolute error = 9.014e-15
relative error = 3.681e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.682
Order of pole (three term test) = 33.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.682
Order of pole (three term test) = 31.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8313.3MB, alloc=44.3MB, time=108.40
x[1] = 0.3051 0.963
h = 0.0001 0.005
y2[1] (numeric) = 0.549223523542 -1.06722450947
y2[1] (closed_form) = 0.549223523542 -1.06722450947
absolute error = 1.020e-15
relative error = 8.497e-14 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.43134023474 -0.336104367285
y1[1] (closed_form) = 2.43134023474 -0.336104367285
absolute error = 9.020e-15
relative error = 3.675e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.703
Order of pole (three term test) = 31.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8361.2MB, alloc=44.3MB, time=109.04
x[1] = 0.3052 0.968
h = 0.0001 0.003
y2[1] (numeric) = 0.547393692821 -1.07436073918
y2[1] (closed_form) = 0.547393692821 -1.07436073918
absolute error = 1.020e-15
relative error = 8.458e-14 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.43664901787 -0.338469898138
y1[1] (closed_form) = 2.43664901787 -0.338469898138
absolute error = 9.020e-15
relative error = 3.667e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.721
Order of pole (three term test) = 33.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.721
Order of pole (three term test) = 31.07 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3053 0.971
h = 0.001 0.001
y2[1] (numeric) = 0.546232259285 -1.07864153901
y2[1] (closed_form) = 0.546232259285 -1.07864153901
absolute error = 2.010e-15
relative error = 1.662e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.43983320027 -0.339937108066
y1[1] (closed_form) = 2.43983320027 -0.339937108066
absolute error = 9.020e-15
relative error = 3.662e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.731
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.731
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8409.0MB, alloc=44.3MB, time=109.67
x[1] = 0.3063 0.972
h = 0.0001 0.004
y2[1] (numeric) = 0.544451409969 -1.07974098074
y2[1] (closed_form) = 0.544451409969 -1.07974098074
absolute error = 1.020e-15
relative error = 8.433e-14 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.44045773362 -0.341470957387
y1[1] (closed_form) = 2.44045773362 -0.341470957387
absolute error = 1.002e-14
relative error = 4.065e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.735
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8456.9MB, alloc=44.3MB, time=110.29
x[1] = 0.3064 0.976
h = 0.003 0.006
y2[1] (numeric) = 0.542937401565 -1.08547712996
y2[1] (closed_form) = 0.542937401565 -1.08547712996
absolute error = 2.010e-15
relative error = 1.656e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.4447425337 -0.343404437807
y1[1] (closed_form) = 2.4447425337 -0.343404437807
absolute error = 9.020e-15
relative error = 3.654e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.749
Order of pole (three term test) = 33.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.749
Order of pole (three term test) = 31.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8504.8MB, alloc=44.3MB, time=110.92
x[1] = 0.3094 0.982
h = 0.0001 0.005
y2[1] (numeric) = 0.536516963721 -1.09312179461
y2[1] (closed_form) = 0.536516963721 -1.09312179461
absolute error = 2.010e-15
relative error = 1.651e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.44989751851 -0.349433944067
y1[1] (closed_form) = 2.44989751851 -0.349433944067
absolute error = 9.020e-15
relative error = 3.645e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.771
Order of pole (three term test) = 31.04 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3095 0.987
h = 0.0001 0.003
y2[1] (numeric) = 0.53461845737 -1.10034979538
y2[1] (closed_form) = 0.53461845737 -1.10034979538
absolute error = 3.007e-15
relative error = 2.458e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.45533474314 -0.351865773576
y1[1] (closed_form) = 2.45533474314 -0.351865773576
absolute error = 9.020e-15
relative error = 3.636e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.789
Order of pole (three term test) = 34.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.789
Order of pole (three term test) = 31.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8552.5MB, alloc=44.3MB, time=111.54
x[1] = 0.3096 0.99
h = 0.001 0.001
y2[1] (numeric) = 0.533414902345 -1.10468542586
y2[1] (closed_form) = 0.533414902345 -1.10468542586
absolute error = 3.007e-15
relative error = 2.451e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.45859569527 -0.353373974005
y1[1] (closed_form) = 2.45859569527 -0.353373974005
absolute error = 9.027e-15
relative error = 3.634e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.8
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8600.5MB, alloc=44.3MB, time=112.16
x[1] = 0.3106 0.991
h = 0.001 0.003
y2[1] (numeric) = 0.531601827622 -1.10579018039
y2[1] (closed_form) = 0.531601827622 -1.10579018039
absolute error = 3.007e-15
relative error = 2.451e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.4592334417 -0.354946703337
y1[1] (closed_form) = 2.4592334417 -0.354946703337
absolute error = 1.002e-14
relative error = 4.034e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.803
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3116 0.994
h = 0.0001 0.004
y2[1] (numeric) = 0.529072555714 -1.10981595482
y2[1] (closed_form) = 0.529072555714 -1.10981595482
absolute error = 3.007e-15
relative error = 2.445e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.46208718745 -0.357463491725
y1[1] (closed_form) = 2.46208718745 -0.357463491725
absolute error = 1.002e-14
relative error = 4.029e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.815
Order of pole (three term test) = 34.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.815
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8648.2MB, alloc=44.3MB, time=112.78
x[1] = 0.3117 0.998
h = 0.003 0.006
y2[1] (numeric) = 0.527492279055 -1.11563725712
y2[1] (closed_form) = 0.527492279055 -1.11563725712
absolute error = 3.007e-15
relative error = 2.436e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.46649091638 -0.35946163176
y1[1] (closed_form) = 2.46649091638 -0.35946163176
absolute error = 1.002e-14
relative error = 4.022e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.829
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.829
Order of pole (three term test) = 31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8696.0MB, alloc=44.3MB, time=113.41
x[1] = 0.3147 1.004
h = 0.0001 0.005
y2[1] (numeric) = 0.520909500285 -1.12336436903
y2[1] (closed_form) = 0.520909500285 -1.12336436903
absolute error = 3.007e-15
relative error = 2.428e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.47178053067 -0.365674899012
y1[1] (closed_form) = 2.47178053067 -0.365674899012
absolute error = 9.027e-15
relative error = 3.613e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.852
Order of pole (three term test) = 34.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.852
Order of pole (three term test) = 30.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8743.9MB, alloc=44.3MB, time=114.03
x[1] = 0.3148 1.009
h = 0.0001 0.003
y2[1] (numeric) = 0.518927390356 -1.13070053128
y2[1] (closed_form) = 0.518927390356 -1.13070053128
absolute error = 3.007e-15
relative error = 2.417e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.47736767334 -0.368188004331
y1[1] (closed_form) = 2.47736767334 -0.368188004331
absolute error = 1.002e-14
relative error = 4.002e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.871
Order of pole (three term test) = 34.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.871
Order of pole (three term test) = 30.97 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3149 1.012
h = 0.001 0.001
y2[1] (numeric) = 0.517672585626 -1.13510076014
y2[1] (closed_form) = 0.517672585626 -1.13510076014
absolute error = 3.007e-15
relative error = 2.410e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.48071820284 -0.369746393097
y1[1] (closed_form) = 2.48071820284 -0.369746393097
absolute error = 1.002e-14
relative error = 3.997e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.882
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.882
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8791.6MB, alloc=44.3MB, time=114.65
x[1] = 0.3159 1.013
h = 0.001 0.003
y2[1] (numeric) = 0.515820985559 -1.13621124901
y2[1] (closed_form) = 0.515820985559 -1.13621124901
absolute error = 4.011e-15
relative error = 3.215e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.4813706059 -0.371365302207
y1[1] (closed_form) = 2.4813706059 -0.371365302207
absolute error = 1.002e-14
relative error = 3.995e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.886
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.886
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8839.3MB, alloc=44.3MB, time=115.27
x[1] = 0.3169 1.016
h = 0.0001 0.004
y2[1] (numeric) = 0.513220166158 -1.14028709067
y2[1] (closed_form) = 0.513220166158 -1.14028709067
absolute error = 4.005e-15
relative error = 3.203e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.48429987333 -0.373959986455
y1[1] (closed_form) = 2.48429987333 -0.373959986455
absolute error = 1.002e-14
relative error = 3.990e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.898
Order of pole (three term test) = 34.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.898
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8887.0MB, alloc=44.3MB, time=115.89
x[1] = 0.317 1.02
h = 0.003 0.006
y2[1] (numeric) = 0.51157154313 -1.14619583156
y2[1] (closed_form) = 0.51157154313 -1.14619583156
absolute error = 4.005e-15
relative error = 3.191e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.48882407287 -0.37602472413
y1[1] (closed_form) = 2.48882407287 -0.37602472413
absolute error = 1.002e-14
relative error = 3.983e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.913
Order of pole (three term test) = 34.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.913
Order of pole (three term test) = 30.95 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.32 1.026
h = 0.0001 0.005
y2[1] (numeric) = 0.504821620095 -1.15400737847
y2[1] (closed_form) = 0.504821620095 -1.15400737847
absolute error = 4.005e-15
relative error = 3.180e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.49424927924 -0.382425818777
y1[1] (closed_form) = 2.49424927924 -0.382425818777
absolute error = 1.002e-14
relative error = 3.973e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.937
Order of pole (three term test) = 34.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.937
Order of pole (three term test) = 30.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8934.6MB, alloc=44.3MB, time=116.51
x[1] = 0.3201 1.031
h = 0.0001 0.003
y2[1] (numeric) = 0.502753291975 -1.16145458467
y2[1] (closed_form) = 0.502753291975 -1.16145458467
absolute error = 3.007e-15
relative error = 2.376e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.49998830116 -0.385022648709
y1[1] (closed_form) = 2.49998830116 -0.385022648709
absolute error = 1.103e-14
relative error = 4.360e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.957
Order of pole (three term test) = 34.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.957
Order of pole (three term test) = 30.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8982.5MB, alloc=44.3MB, time=117.14
x[1] = 0.3202 1.034
h = 0.001 0.001
y2[1] (numeric) = 0.501445639235 -1.16592112543
y2[1] (closed_form) = 0.501445639235 -1.16592112543
absolute error = 4.005e-15
relative error = 3.156e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.50342957217 -0.386632717719
y1[1] (closed_form) = 2.50342957217 -0.386632717719
absolute error = 1.103e-14
relative error = 4.354e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.968
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.968
Order of pole (three term test) = 30.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9030.5MB, alloc=44.3MB, time=117.76
x[1] = 0.3212 1.035
h = 0.001 0.003
y2[1] (numeric) = 0.499554410652 -1.1670374231
y2[1] (closed_form) = 0.499554410652 -1.1670374231
absolute error = 3.007e-15
relative error = 2.368e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.50409655175 -0.388298696857
y1[1] (closed_form) = 2.50409655175 -0.388298696857
absolute error = 1.104e-14
relative error = 4.355e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.973
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.973
Order of pole (three term test) = 30.91 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3222 1.038
h = 0.0001 0.004
y2[1] (numeric) = 0.496879907427 -1.1711645837
y2[1] (closed_form) = 0.496879907427 -1.1711645837
absolute error = 3.002e-15
relative error = 2.359e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.50710207125 -0.390973143098
y1[1] (closed_form) = 2.50710207125 -0.390973143098
absolute error = 1.004e-14
relative error = 3.957e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.985
Order of pole (three term test) = 34.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.985
Order of pole (three term test) = 30.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9078.1MB, alloc=44.3MB, time=118.38
x[1] = 0.3223 1.042
h = 0.003 0.006
y2[1] (numeric) = 0.495160808362 -1.17716307263
y2[1] (closed_form) = 0.495160808362 -1.17716307263
absolute error = 3.007e-15
relative error = 2.354e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.51174832255 -0.393106474897
y1[1] (closed_form) = 2.51174832255 -0.393106474897
absolute error = 1.004e-14
relative error = 3.949e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.001
Order of pole (three term test) = 34.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.001
Order of pole (three term test) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9126.0MB, alloc=44.3MB, time=119.00
x[1] = 0.3253 1.048
h = 0.0001 0.005
y2[1] (numeric) = 0.488238841827 -1.18506104181
y2[1] (closed_form) = 0.488238841827 -1.18506104181
absolute error = 3.007e-15
relative error = 2.346e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.51731010164 -0.399699580598
y1[1] (closed_form) = 2.51731010164 -0.399699580598
absolute error = 1.104e-14
relative error = 4.330e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.025
Order of pole (three term test) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.025
Order of pole (three term test) = 30.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9173.8MB, alloc=44.3MB, time=119.63
x[1] = 0.3254 1.053
h = 0.0001 0.003
y2[1] (numeric) = 0.486081615699 -1.19262220492
y2[1] (closed_form) = 0.486081615699 -1.19262220492
absolute error = 3.007e-15
relative error = 2.335e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.52320301373 -0.402382657538
y1[1] (closed_form) = 2.52320301373 -0.402382657538
absolute error = 1.004e-14
relative error = 3.930e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.046
Order of pole (three term test) = 34.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.046
Order of pole (three term test) = 30.87 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3255 1.056
h = 0.001 0.001
y2[1] (numeric) = 0.484719477083 -1.19715678901
y2[1] (closed_form) = 0.484719477083 -1.19715678901
absolute error = 3.007e-15
relative error = 2.328e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.52673621971 -0.404045943426
y1[1] (closed_form) = 2.52673621971 -0.404045943426
absolute error = 1.004e-14
relative error = 3.924e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.058
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.058
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9221.4MB, alloc=44.3MB, time=120.24
x[1] = 0.3265 1.057
h = 0.001 0.003
y2[1] (numeric) = 0.482787497389 -1.19827896336
y2[1] (closed_form) = 0.482787497389 -1.19827896336
absolute error = 3.007e-15
relative error = 2.327e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.52741769136 -0.405759907701
y1[1] (closed_form) = 2.52741769136 -0.405759907701
absolute error = 1.104e-14
relative error = 4.312e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.063
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.063
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9269.3MB, alloc=44.3MB, time=120.87
x[1] = 0.3275 1.06
h = 0.0001 0.004
y2[1] (numeric) = 0.480037128446 -1.20245870083
y2[1] (closed_form) = 0.480037128446 -1.20245870083
absolute error = 3.007e-15
relative error = 2.322e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.53050020949 -0.408516036216
y1[1] (closed_form) = 2.53050020949 -0.408516036216
absolute error = 1.004e-14
relative error = 3.917e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.075
Order of pole (three term test) = 34.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.075
Order of pole (three term test) = 30.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9317.2MB, alloc=44.3MB, time=121.50
x[1] = 0.3276 1.064
h = 0.003 0.006
y2[1] (numeric) = 0.478245370613 -1.20854927172
y2[1] (closed_form) = 0.478245370613 -1.20854927172
absolute error = 3.007e-15
relative error = 2.313e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.53527013335 -0.410720018362
y1[1] (closed_form) = 2.53527013335 -0.410720018362
absolute error = 1.004e-14
relative error = 3.909e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.092
Order of pole (three term test) = 34.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.092
Order of pole (three term test) = 30.84 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3306 1.07
h = 0.0001 0.005
y2[1] (numeric) = 0.471146362751 -1.21653564971
y2[1] (closed_form) = 0.471146362751 -1.21653564971
absolute error = 3.015e-15
relative error = 2.311e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.54096948326 -0.417509438169
y1[1] (closed_form) = 2.54096948326 -0.417509438169
absolute error = 1.004e-14
relative error = 3.899e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.118
Order of pole (three term test) = 34.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.118
Order of pole (three term test) = 30.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9364.8MB, alloc=44.3MB, time=122.12
x[1] = 0.3307 1.075
h = 0.0001 0.003
y2[1] (numeric) = 0.468897491688 -1.22421371394
y2[1] (closed_form) = 0.468897491688 -1.22421371394
absolute error = 3.007e-15
relative error = 2.294e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.5470183465 -0.420281359725
y1[1] (closed_form) = 2.5470183465 -0.420281359725
absolute error = 1.004e-14
relative error = 3.889e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.139
Order of pole (three term test) = 34.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.139
Order of pole (three term test) = 30.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9412.7MB, alloc=44.3MB, time=122.74
x[1] = 0.3308 1.078
h = 0.001 0.001
y2[1] (numeric) = 0.467479188621 -1.22881809111
y2[1] (closed_form) = 0.467479188621 -1.22881809111
absolute error = 3.007e-15
relative error = 2.287e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.55064471041 -0.421999444826
y1[1] (closed_form) = 2.55064471041 -0.421999444826
absolute error = 1.004e-14
relative error = 3.884e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.152
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.152
Order of pole (three term test) = 30.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9460.5MB, alloc=44.3MB, time=123.36
x[1] = 0.3318 1.079
h = 0.0001 0.004
y2[1] (numeric) = 0.465505315271 -1.2299462032
y2[1] (closed_form) = 0.465505315271 -1.2299462032
absolute error = 3.015e-15
relative error = 2.293e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.5513405851 -0.423762334605
y1[1] (closed_form) = 2.5513405851 -0.423762334605
absolute error = 1.004e-14
relative error = 3.882e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.157
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.157
Order of pole (three term test) = 30.8 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3319 1.083
h = 0.003 0.006
y2[1] (numeric) = 0.463650360851 -1.23611882512
y2[1] (closed_form) = 0.463650360851 -1.23611882512
absolute error = 3.007e-15
relative error = 2.277e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.55621916659 -0.426027323161
y1[1] (closed_form) = 2.55621916659 -0.426027323161
absolute error = 1.003e-14
relative error = 3.871e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.174
Order of pole (three term test) = 34.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.174
Order of pole (three term test) = 30.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9508.2MB, alloc=44.3MB, time=123.98
x[1] = 0.3349 1.089
h = 0.0001 0.005
y2[1] (numeric) = 0.456395967599 -1.2441850843
y2[1] (closed_form) = 0.456395967599 -1.2441850843
absolute error = 3.007e-15
relative error = 2.269e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.5620401556 -0.432987606916
y1[1] (closed_form) = 2.5620401556 -0.432987606916
absolute error = 1.003e-14
relative error = 3.861e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.201
Order of pole (three term test) = 34.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.201
Order of pole (three term test) = 30.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9555.9MB, alloc=44.3MB, time=124.60
x[1] = 0.335 1.094
h = 0.0001 0.003
y2[1] (numeric) = 0.454067400145 -1.2519672926
y2[1] (closed_form) = 0.454067400145 -1.2519672926
absolute error = 3.007e-15
relative error = 2.258e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.56822604706 -0.435836249668
y1[1] (closed_form) = 2.56822604706 -0.435836249668
absolute error = 1.003e-14
relative error = 3.851e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.223
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.223
Order of pole (three term test) = 30.76 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3351 1.097
h = 0.001 0.001
y2[1] (numeric) = 0.452600236572 -1.25663385777
y2[1] (closed_form) = 0.452600236572 -1.25663385777
absolute error = 3.007e-15
relative error = 2.251e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.57193427948 -0.437601676763
y1[1] (closed_form) = 2.57193427948 -0.437601676763
absolute error = 9.045e-15
relative error = 3.467e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.237
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.237
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9603.6MB, alloc=44.3MB, time=125.22
x[1] = 0.3361 1.098
h = 0.001 0.003
y2[1] (numeric) = 0.450589443603 -1.25776764231
y2[1] (closed_form) = 0.450589443603 -1.25776764231
absolute error = 3.007e-15
relative error = 2.250e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.57264307537 -0.439407282554
y1[1] (closed_form) = 2.57264307537 -0.439407282554
absolute error = 1.004e-14
relative error = 3.847e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.241
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.241
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9651.5MB, alloc=44.3MB, time=125.84
x[1] = 0.3371 1.101
h = 0.0001 0.004
y2[1] (numeric) = 0.447692599597 -1.2620495499
y2[1] (closed_form) = 0.447692599597 -1.2620495499
absolute error = 3.007e-15
relative error = 2.245e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.57587194149 -0.44231976453
y1[1] (closed_form) = 2.57587194149 -0.44231976453
absolute error = 9.045e-15
relative error = 3.461e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.255
Order of pole (three term test) = 34.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.255
Order of pole (three term test) = 30.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9699.4MB, alloc=44.3MB, time=126.47
x[1] = 0.3372 1.105
h = 0.003 0.006
y2[1] (numeric) = 0.44576080685 -1.26831869129
y2[1] (closed_form) = 0.44576080685 -1.26831869129
absolute error = 3.007e-15
relative error = 2.236e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.58087734412 -0.444659372678
y1[1] (closed_form) = 2.58087734412 -0.444659372678
absolute error = 9.055e-15
relative error = 3.458e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.273
Order of pole (three term test) = 34.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.273
Order of pole (three term test) = 30.73 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3402 1.111
h = 0.0001 0.005
y2[1] (numeric) = 0.438319824271 -1.27647711538
y2[1] (closed_form) = 0.438319824271 -1.27647711538
absolute error = 3.007e-15
relative error = 2.228e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.58683786057 -0.451824290492
y1[1] (closed_form) = 2.58683786057 -0.451824290492
absolute error = 9.055e-15
relative error = 3.448e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.301
Order of pole (three term test) = 34.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.301
Order of pole (three term test) = 30.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9747.0MB, alloc=44.3MB, time=127.09
x[1] = 0.3403 1.116
h = 0.0001 0.003
y2[1] (numeric) = 0.435894351198 -1.28438182348
y2[1] (closed_form) = 0.435894351198 -1.28438182348
absolute error = 3.007e-15
relative error = 2.217e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.59318370566 -0.454766791343
y1[1] (closed_form) = 2.59318370566 -0.454766791343
absolute error = 9.055e-15
relative error = 3.440e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.324
Order of pole (three term test) = 34.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.324
Order of pole (three term test) = 30.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9794.7MB, alloc=44.3MB, time=127.71
x[1] = 0.3404 1.119
h = 0.001 0.001
y2[1] (numeric) = 0.434367808725 -1.28912150893
y2[1] (closed_form) = 0.434367808725 -1.28912150893
absolute error = 3.015e-15
relative error = 2.216e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.59698747101 -0.456590071714
y1[1] (closed_form) = 2.59698747101 -0.456590071714
absolute error = 9.055e-15
relative error = 3.434e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.338
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.338
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9842.7MB, alloc=44.3MB, time=128.33
x[1] = 0.3414 1.12
h = 0.001 0.003
y2[1] (numeric) = 0.432312941681 -1.29026134001
y2[1] (closed_form) = 0.432312941681 -1.29026134001
absolute error = 4.005e-15
relative error = 2.943e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.59771050312 -0.458446422643
y1[1] (closed_form) = 2.59771050312 -0.458446422643
absolute error = 9.055e-15
relative error = 3.433e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.343
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.343
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3424 1.123
h = 0.0001 0.004
y2[1] (numeric) = 0.429333742073 -1.29459948589
y2[1] (closed_form) = 0.429333742073 -1.29459948589
absolute error = 4.005e-15
relative error = 2.936e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.60101861699 -0.461446379376
y1[1] (closed_form) = 2.60101861699 -0.461446379376
absolute error = 9.055e-15
relative error = 3.428e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.357
Order of pole (three term test) = 34.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.357
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9890.3MB, alloc=44.3MB, time=128.95
x[1] = 0.3425 1.127
h = 0.003 0.006
y2[1] (numeric) = 0.427322768176 -1.30096755446
y2[1] (closed_form) = 0.427322768176 -1.30096755446
absolute error = 4.005e-15
relative error = 2.925e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.60615257722 -0.463862841145
y1[1] (closed_form) = 2.60615257722 -0.463862841145
absolute error = 9.055e-15
relative error = 3.421e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.376
Order of pole (three term test) = 34.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.376
Order of pole (three term test) = 30.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9938.2MB, alloc=44.3MB, time=129.57
x[1] = 0.3455 1.133
h = 0.0001 0.005
y2[1] (numeric) = 0.419689901068 -1.30922012769
y2[1] (closed_form) = 0.419689901068 -1.30922012769
absolute error = 4.005e-15
relative error = 2.913e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.61225366766 -0.471237049766
y1[1] (closed_form) = 2.61225366766 -0.471237049766
absolute error = 9.055e-15
relative error = 3.411e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.405
Order of pole (three term test) = 34.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.405
Order of pole (three term test) = 30.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9985.9MB, alloc=44.3MB, time=130.19
x[1] = 0.3456 1.138
h = 0.0001 0.003
y2[1] (numeric) = 0.417164573029 -1.31725037387
y2[1] (closed_form) = 0.417164573029 -1.31725037387
absolute error = 4.005e-15
relative error = 2.899e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.61876167334 -0.474276230234
y1[1] (closed_form) = 2.61876167334 -0.474276230234
absolute error = 8.075e-15
relative error = 3.034e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.43
Order of pole (three term test) = 34.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.43
Order of pole (three term test) = 30.64 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3457 1.141
h = 0.001 0.001
y2[1] (numeric) = 0.415576850293 -1.3220649845
y2[1] (closed_form) = 0.415576850293 -1.3220649845
absolute error = 4.005e-15
relative error = 2.890e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.62266228062 -0.476159082261
y1[1] (closed_form) = 2.62266228062 -0.476159082261
absolute error = 8.062e-15
relative error = 3.025e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.444
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.444
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10033.7MB, alloc=44.3MB, time=130.81
x[1] = 0.3467 1.142
h = 0.001 0.003
y2[1] (numeric) = 0.413476706483 -1.32321090258
y2[1] (closed_form) = 0.413476706483 -1.32321090258
absolute error = 5.004e-15
relative error = 3.610e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.62339944566 -0.478067193304
y1[1] (closed_form) = 2.62339944566 -0.478067193304
absolute error = 8.062e-15
relative error = 3.023e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.449
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.449
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10081.5MB, alloc=44.3MB, time=131.44
x[1] = 0.3477 1.145
h = 0.0001 0.004
y2[1] (numeric) = 0.410412781256 -1.32760656979
y2[1] (closed_form) = 0.410412781256 -1.32760656979
absolute error = 5.001e-15
relative error = 3.599e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.6267876159 -0.481156764054
y1[1] (closed_form) = 2.6267876159 -0.481156764054
absolute error = 8.062e-15
relative error = 3.019e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.464
Order of pole (three term test) = 34.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.464
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10129.5MB, alloc=44.3MB, time=132.06
x[1] = 0.3478 1.149
h = 0.003 0.006
y2[1] (numeric) = 0.408320224215 -1.33407599991
y2[1] (closed_form) = 0.408320224215 -1.33407599991
absolute error = 5.001e-15
relative error = 3.585e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.63205191084 -0.483652378496
y1[1] (closed_form) = 2.63205191084 -0.483652378496
absolute error = 8.062e-15
relative error = 3.013e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.484
Order of pole (three term test) = 34.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.484
Order of pole (three term test) = 30.61 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3508 1.155
h = 0.0001 0.005
y2[1] (numeric) = 0.400490067932 -1.3424247047
y2[1] (closed_form) = 0.400490067932 -1.3424247047
absolute error = 5.001e-15
relative error = 3.570e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.63829463711 -0.491240662874
y1[1] (closed_form) = 2.63829463711 -0.491240662874
absolute error = 7.058e-15
relative error = 2.630e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.515
Order of pole (three term test) = 34.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.515
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10177.0MB, alloc=44.3MB, time=132.68
x[1] = 0.3509 1.16
h = 0.0001 0.003
y2[1] (numeric) = 0.397861860778 -1.35058356117
y2[1] (closed_form) = 0.397861860778 -1.35058356117
absolute error = 4.001e-15
relative error = 2.842e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.64496706174 -0.494379426373
y1[1] (closed_form) = 2.64496706174 -0.494379426373
absolute error = 7.058e-15
relative error = 2.623e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.54
Order of pole (three term test) = 34.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.54
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10224.9MB, alloc=44.3MB, time=133.30
x[1] = 0.351 1.163
h = 0.001 0.001
y2[1] (numeric) = 0.396211111046 -1.3554749218
y2[1] (closed_form) = 0.396211111046 -1.3554749218
absolute error = 4.005e-15
relative error = 2.836e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.64896585022 -0.496323618183
y1[1] (closed_form) = 2.64896585022 -0.496323618183
absolute error = 7.071e-15
relative error = 2.624e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.555
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.555
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10272.8MB, alloc=44.3MB, time=133.92
x[1] = 0.352 1.164
h = 0.001 0.003
y2[1] (numeric) = 0.394064465719 -1.35662695953
y2[1] (closed_form) = 0.394064465719 -1.35662695953
absolute error = 4.005e-15
relative error = 2.835e-13 %
Correct digits = 15
h = 0.001 0.003
y1[1] (numeric) = 2.64971703927 -0.49828453121
y1[1] (closed_form) = 2.64971703927 -0.49828453121
absolute error = 7.071e-15
relative error = 2.623e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.561
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.561
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.353 1.167
h = 0.0001 0.004
y2[1] (numeric) = 0.390913392813 -1.36108143761
y2[1] (closed_form) = 0.390913392813 -1.36108143761
absolute error = 4.005e-15
relative error = 2.828e-13 %
Correct digits = 15
h = 0.0001 0.004
y1[1] (numeric) = 2.65318609007 -0.501465914766
y1[1] (closed_form) = 2.65318609007 -0.501465914766
absolute error = 7.071e-15
relative error = 2.619e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.576
Order of pole (three term test) = 34.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.576
Order of pole (three term test) = 30.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10320.6MB, alloc=44.3MB, time=134.55
x[1] = 0.3531 1.171
h = 0.003 0.006
y2[1] (numeric) = 0.388736789796 -1.3676546908
y2[1] (closed_form) = 0.388736789796 -1.3676546908
absolute error = 4.001e-15
relative error = 2.814e-13 %
Correct digits = 15
h = 0.003 0.006
y1[1] (numeric) = 2.65858253782 -0.504043047413
y1[1] (closed_form) = 2.65858253782 -0.504043047413
absolute error = 7.071e-15
relative error = 2.613e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.597
Order of pole (three term test) = 34.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.597
Order of pole (three term test) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10368.4MB, alloc=44.3MB, time=135.17
x[1] = 0.3561 1.177
h = 0.0001 0.005
y2[1] (numeric) = 0.380703827328 -1.37610150738
y2[1] (closed_form) = 0.380703827328 -1.37610150738
absolute error = 4.001e-15
relative error = 2.802e-13 %
Correct digits = 15
h = 0.0001 0.005
y1[1] (numeric) = 2.6649679764 -0.511850323136
y1[1] (closed_form) = 2.6649679764 -0.511850323136
absolute error = 7.071e-15
relative error = 2.606e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.629
Order of pole (three term test) = 34.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.629
Order of pole (three term test) = 30.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10416.3MB, alloc=44.3MB, time=135.80
x[1] = 0.3562 1.182
h = 0.0001 0.003
y2[1] (numeric) = 0.377969640007 -1.38439208101
y2[1] (closed_form) = 0.377969640007 -1.38439208101
absolute error = 4.001e-15
relative error = 2.788e-13 %
Correct digits = 15
h = 0.0001 0.003
y1[1] (numeric) = 2.67180713007 -0.515091656827
y1[1] (closed_form) = 2.67180713007 -0.515091656827
absolute error = 7.071e-15
relative error = 2.599e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.655
Order of pole (three term test) = 34.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.655
Order of pole (three term test) = 30.52 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3563 1.185
h = 0.001 0.001
y2[1] (numeric) = 0.376253969915 -1.38936203674
y2[1] (closed_form) = 0.376253969915 -1.38936203674
absolute error = 4.005e-15
relative error = 2.782e-13 %
Correct digits = 15
h = 0.001 0.001
y1[1] (numeric) = 2.67590546946 -0.51709900741
y1[1] (closed_form) = 2.67590546946 -0.51709900741
absolute error = 7.071e-15
relative error = 2.594e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.671
Order of pole (three term test) = 34.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.671
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10464.1MB, alloc=44.3MB, time=136.41
x[1] = 0.3573 1.186
h = 0.0001 0.004
y2[1] (numeric) = 0.37405957569 -1.39052021872
y2[1] (closed_form) = 0.37405957569 -1.39052021872
absolute error = 5.001e-15
relative error = 3.473e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.67667056769 -0.519113791637
y1[1] (closed_form) = 2.67667056769 -0.519113791637
absolute error = 7.071e-15
relative error = 2.593e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.677
Order of pole (three term test) = 34.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.677
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10512.0MB, alloc=44.3MB, time=137.04
x[1] = 0.3574 1.19
h = 0.003 0.006
y2[1] (numeric) = 0.371809885989 -1.3971858739
y2[1] (closed_form) = 0.371809885989 -1.3971858739
absolute error = 5.004e-15
relative error = 3.461e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.68218326618 -0.521761434123
y1[1] (closed_form) = 2.68218326618 -0.521761434123
absolute error = 7.071e-15
relative error = 2.588e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.698
Order of pole (three term test) = 34.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.698
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3604 1.196
h = 0.0001 0.005
y2[1] (numeric) = 0.363599049611 -1.40572123301
y2[1] (closed_form) = 0.363599049611 -1.40572123301
absolute error = 5.004e-15
relative error = 3.446e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.68869511025 -0.529759530445
y1[1] (closed_form) = 2.68869511025 -0.529759530445
absolute error = 7.071e-15
relative error = 2.580e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.731
Order of pole (three term test) = 34.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.731
Order of pole (three term test) = 30.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10559.7MB, alloc=44.3MB, time=137.66
x[1] = 0.3605 1.201
h = 0.0001 0.003
y2[1] (numeric) = 0.360772714603 -1.41412901341
y2[1] (closed_form) = 0.360772714603 -1.41412901341
absolute error = 5.004e-15
relative error = 3.429e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.69568094018 -0.53308958603
y1[1] (closed_form) = 2.69568094018 -0.53308958603
absolute error = 7.071e-15
relative error = 2.573e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.758
Order of pole (three term test) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.758
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10607.5MB, alloc=44.3MB, time=138.28
x[1] = 0.3606 1.204
h = 0.001 0.001
y2[1] (numeric) = 0.35900057703 -1.41916891938
y2[1] (closed_form) = 0.35900057703 -1.41916891938
absolute error = 6.003e-15
relative error = 4.101e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.69986687271 -0.535151589235
y1[1] (closed_form) = 2.69986687271 -0.535151589235
absolute error = 7.071e-15
relative error = 2.569e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.775
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.775
Order of pole (three term test) = 30.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10655.4MB, alloc=44.3MB, time=138.91
x[1] = 0.3616 1.205
h = 0.001 0.003
y2[1] (numeric) = 0.356764139011 -1.42033299292
y2[1] (closed_form) = 0.356764139011 -1.42033299292
absolute error = 6.003e-15
relative error = 4.099e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.70064450637 -0.537213457703
y1[1] (closed_form) = 2.70064450637 -0.537213457703
absolute error = 7.058e-15
relative error = 2.563e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.781
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.781
Order of pole (three term test) = 30.45 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3626 1.208
h = 0.0001 0.004
y2[1] (numeric) = 0.353445011201 -1.42490146738
y2[1] (closed_form) = 0.353445011201 -1.42490146738
absolute error = 6.001e-15
relative error = 4.088e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.7042674619 -0.540570757159
y1[1] (closed_form) = 2.7042674619 -0.540570757159
absolute error = 7.058e-15
relative error = 2.559e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.798
Order of pole (three term test) = 34.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.798
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10703.1MB, alloc=44.3MB, time=139.52
x[1] = 0.3627 1.212
h = 0.003 0.006
y2[1] (numeric) = 0.351106555132 -1.43167563134
y2[1] (closed_form) = 0.351106555132 -1.43167563134
absolute error = 6.001e-15
relative error = 4.071e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.70991583633 -0.543304478862
y1[1] (closed_form) = 2.70991583633 -0.543304478862
absolute error = 7.071e-15
relative error = 2.558e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 34.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.82
Order of pole (three term test) = 30.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10751.0MB, alloc=44.3MB, time=140.16
x[1] = 0.3657 1.218
h = 0.0001 0.005
y2[1] (numeric) = 0.342682360895 -1.44031284887
y2[1] (closed_form) = 0.342682360895 -1.44031284887
absolute error = 6.001e-15
relative error = 4.053e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.71657249485 -0.551531056354
y1[1] (closed_form) = 2.71657249485 -0.551531056354
absolute error = 7.071e-15
relative error = 2.551e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.855
Order of pole (three term test) = 34.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.855
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10798.9MB, alloc=44.3MB, time=140.79
x[1] = 0.3658 1.223
h = 0.0001 0.003
y2[1] (numeric) = 0.339744101382 -1.44885826136
y2[1] (closed_form) = 0.339744101382 -1.44885826136
absolute error = 6.003e-15
relative error = 4.034e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.72372952933 -0.554969440997
y1[1] (closed_form) = 2.72372952933 -0.554969440997
absolute error = 7.071e-15
relative error = 2.544e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.883
Order of pole (three term test) = 34.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.883
Order of pole (three term test) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3659 1.226
h = 0.001 0.001
y2[1] (numeric) = 0.337903414331 -1.45398027503
y2[1] (closed_form) = 0.337903414331 -1.45398027503
absolute error = 7.003e-15
relative error = 4.691e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.7280176664 -0.557098109841
y1[1] (closed_form) = 2.7280176664 -0.557098109841
absolute error = 7.071e-15
relative error = 2.540e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.901
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.901
Order of pole (three term test) = 30.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10846.7MB, alloc=44.3MB, time=141.42
x[1] = 0.3669 1.227
h = 0.001 0.003
y2[1] (numeric) = 0.335616844184 -1.45515053172
y2[1] (closed_form) = 0.335616844184 -1.45515053172
absolute error = 7.003e-15
relative error = 4.689e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.72880899229 -0.559215914983
y1[1] (closed_form) = 2.72880899229 -0.559215914983
absolute error = 7.071e-15
relative error = 2.539e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.907
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.907
Order of pole (three term test) = 30.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10894.5MB, alloc=44.3MB, time=142.04
x[1] = 0.3679 1.23
h = 0.0001 0.004
y2[1] (numeric) = 0.332203355287 -1.459781573
y2[1] (closed_form) = 0.332203355287 -1.459781573
absolute error = 7.003e-15
relative error = 4.678e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.7325152998 -0.56267164658
y1[1] (closed_form) = 2.7325152998 -0.56267164658
absolute error = 7.071e-15
relative error = 2.535e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.924
Order of pole (three term test) = 34.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.924
Order of pole (three term test) = 30.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10942.4MB, alloc=44.3MB, time=142.66
x[1] = 0.368 1.234
h = 0.003 0.006
y2[1] (numeric) = 0.329773486839 -1.46666678888
y2[1] (closed_form) = 0.329773486839 -1.46666678888
absolute error = 6.003e-15
relative error = 3.993e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.73830128785 -0.565494011167
y1[1] (closed_form) = 2.73830128785 -0.565494011167
absolute error = 7.071e-15
relative error = 2.529e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.948
Order of pole (three term test) = 34.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.948
Order of pole (three term test) = 30.36 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.371 1.24
h = 0.0001 0.005
y2[1] (numeric) = 0.32113007961 -1.47540783806
y2[1] (closed_form) = 0.32113007961 -1.47540783806
absolute error = 6.003e-15
relative error = 3.976e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.74510387715 -0.573954372964
y1[1] (closed_form) = 2.74510387715 -0.573954372964
absolute error = 7.058e-15
relative error = 2.517e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.984
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.984
Order of pole (three term test) = 30.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10989.9MB, alloc=44.3MB, time=143.28
x[1] = 0.3711 1.245
h = 0.0001 0.003
y2[1] (numeric) = 0.318076563029 -1.48409409343
y2[1] (closed_form) = 0.318076563029 -1.48409409343
absolute error = 6.003e-15
relative error = 3.955e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.75243457734 -0.577504323451
y1[1] (closed_form) = 2.75243457734 -0.577504323451
absolute error = 7.058e-15
relative error = 2.509e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.014
Order of pole (three term test) = 34.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.014
Order of pole (three term test) = 30.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11037.8MB, alloc=44.3MB, time=143.90
x[1] = 0.3712 1.248
h = 0.001 0.001
y2[1] (numeric) = 0.316165292745 -1.48930012076
y2[1] (closed_form) = 0.316165292745 -1.48930012076
absolute error = 6.003e-15
relative error = 3.943e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.75682637758 -0.579701628512
y1[1] (closed_form) = 2.75682637758 -0.579701628512
absolute error = 7.058e-15
relative error = 2.505e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.032
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.032
Order of pole (three term test) = 30.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11085.8MB, alloc=44.3MB, time=144.53
x[1] = 0.3722 1.249
h = 0.001 0.003
y2[1] (numeric) = 0.313827275047 -1.49047656089
y2[1] (closed_form) = 0.313827275047 -1.49047656089
absolute error = 6.003e-15
relative error = 3.941e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.75763126256 -0.581876520435
y1[1] (closed_form) = 2.75763126256 -0.581876520435
absolute error = 7.058e-15
relative error = 2.504e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.038
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.038
Order of pole (three term test) = 30.32 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3732 1.252
h = 0.0001 0.004
y2[1] (numeric) = 0.310316788734 -1.4951714843
y2[1] (closed_form) = 0.310316788734 -1.4951714843
absolute error = 7.001e-15
relative error = 4.585e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.76142180591 -0.585433124095
y1[1] (closed_form) = 2.76142180591 -0.585433124095
absolute error = 8.050e-15
relative error = 2.852e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.056
Order of pole (three term test) = 34.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.056
Order of pole (three term test) = 30.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11133.5MB, alloc=44.3MB, time=145.14
x[1] = 0.3733 1.256
h = 0.003 0.006
y2[1] (numeric) = 0.30779279432 -1.50217032453
y2[1] (closed_form) = 0.30779279432 -1.50217032453
absolute error = 7.001e-15
relative error = 4.566e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.76734738731 -0.588346767742
y1[1] (closed_form) = 2.76734738731 -0.588346767742
absolute error = 8.050e-15
relative error = 2.845e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.081
Order of pole (three term test) = 34.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.081
Order of pole (three term test) = 30.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11181.3MB, alloc=44.3MB, time=145.77
x[1] = 0.3763 1.262
h = 0.0001 0.005
y2[1] (numeric) = 0.298924194804 -1.51101717482
y2[1] (closed_form) = 0.298924194804 -1.51101717482
absolute error = 7.001e-15
relative error = 4.545e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.77429703575 -0.597046357601
y1[1] (closed_form) = 2.77429703575 -0.597046357601
absolute error = 7.058e-15
relative error = 2.487e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.118
Order of pole (three term test) = 34.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.118
Order of pole (three term test) = 30.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11229.2MB, alloc=44.3MB, time=146.40
x[1] = 0.3764 1.267
h = 0.0001 0.003
y2[1] (numeric) = 0.295752003199 -1.51984752119
y2[1] (closed_form) = 0.295752003199 -1.51984752119
absolute error = 7.001e-15
relative error = 4.521e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.78180391598 -0.600711202083
y1[1] (closed_form) = 2.78180391598 -0.600711202083
absolute error = 7.046e-15
relative error = 2.476e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.15
Order of pole (three term test) = 34.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.15
Order of pole (three term test) = 30.26 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3765 1.27
h = 0.001 0.001
y2[1] (numeric) = 0.293768064154 -1.52513948999
y2[1] (closed_form) = 0.293768064154 -1.52513948999
absolute error = 7.001e-15
relative error = 4.507e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.78630086924 -0.602979169409
y1[1] (closed_form) = 2.78630086924 -0.602979169409
absolute error = 7.046e-15
relative error = 2.471e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.169
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.169
Order of pole (three term test) = 30.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11277.0MB, alloc=44.3MB, time=147.02
x[1] = 0.3775 1.271
h = 0.001 0.003
y2[1] (numeric) = 0.291377258581 -1.52632210466
y2[1] (closed_form) = 0.291377258581 -1.52632210466
absolute error = 7.001e-15
relative error = 4.505e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.78711917307 -0.605212327408
y1[1] (closed_form) = 2.78711917307 -0.605212327408
absolute error = 7.046e-15
relative error = 2.470e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.175
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.175
Order of pole (three term test) = 30.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11324.7MB, alloc=44.3MB, time=147.65
x[1] = 0.3785 1.274
h = 0.0001 0.004
y2[1] (numeric) = 0.287767079402 -1.53108223201
y2[1] (closed_form) = 0.287767079402 -1.53108223201
absolute error = 7.001e-15
relative error = 4.494e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.79099485099 -0.608872308692
y1[1] (closed_form) = 2.79099485099 -0.608872308692
absolute error = 7.046e-15
relative error = 2.466e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.194
Order of pole (three term test) = 34.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.194
Order of pole (three term test) = 30.24 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3786 1.278
h = 0.003 0.006
y2[1] (numeric) = 0.285146176023 -1.53819729889
y2[1] (closed_form) = 0.285146176023 -1.53819729889
absolute error = 7.001e-15
relative error = 4.475e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.79706204783 -0.611879941745
y1[1] (closed_form) = 2.79706204783 -0.611879941745
absolute error = 7.046e-15
relative error = 2.461e-13 %
Correct digits = 15
memory used=11372.7MB, alloc=44.3MB, time=148.27
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.22
Order of pole (three term test) = 34.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.22
Order of pole (three term test) = 30.23 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3816 1.284
h = 0.0001 0.005
y2[1] (numeric) = 0.276046277582 -1.54715191543
y2[1] (closed_form) = 0.276046277582 -1.54715191543
absolute error = 7.001e-15
relative error = 4.455e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.80415989502 -0.620824346788
y1[1] (closed_form) = 2.80415989502 -0.620824346788
absolute error = 8.040e-15
relative error = 2.799e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.259
Order of pole (three term test) = 34.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.259
Order of pole (three term test) = 30.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11420.4MB, alloc=44.3MB, time=148.89
x[1] = 0.3817 1.289
h = 0.0001 0.003
y2[1] (numeric) = 0.272751905285 -1.55612963896
y2[1] (closed_form) = 0.272751905285 -1.55612963896
absolute error = 8.001e-15
relative error = 5.064e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.81184552312 -0.624607506889
y1[1] (closed_form) = 2.81184552312 -0.624607506889
absolute error = 8.040e-15
relative error = 2.791e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.292
Order of pole (three term test) = 34.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.292
Order of pole (three term test) = 30.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11468.3MB, alloc=44.3MB, time=149.52
x[1] = 0.3818 1.292
h = 0.001 0.001
y2[1] (numeric) = 0.270693158774 -1.56150949926
y2[1] (closed_form) = 0.270693158774 -1.56150949926
absolute error = 8.001e-15
relative error = 5.048e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.81644915075 -0.626948219266
y1[1] (closed_form) = 2.81644915075 -0.626948219266
absolute error = 9.045e-15
relative error = 3.135e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.312
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.312
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3828 1.293
h = 0.0001 0.004
y2[1] (numeric) = 0.268248199498 -1.56269827007
y2[1] (closed_form) = 0.268248199498 -1.56269827007
absolute error = 7.001e-15
relative error = 4.415e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.8172807257 -0.629240852333
y1[1] (closed_form) = 2.8172807257 -0.629240852333
absolute error = 9.045e-15
relative error = 3.133e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.318
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.318
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11516.1MB, alloc=44.3MB, time=150.14
x[1] = 0.3829 1.297
h = 0.003 0.006
y2[1] (numeric) = 0.265543024419 -1.56991668882
y2[1] (closed_form) = 0.265543024419 -1.56991668882
absolute error = 7.001e-15
relative error = 4.397e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.82347263713 -0.632329896104
y1[1] (closed_form) = 2.82347263713 -0.632329896104
absolute error = 9.045e-15
relative error = 3.126e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.345
Order of pole (three term test) = 35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.345
Order of pole (three term test) = 30.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11563.9MB, alloc=44.3MB, time=150.76
x[1] = 0.3859 1.303
h = 0.0001 0.005
y2[1] (numeric) = 0.256240357398 -1.57896849362
y2[1] (closed_form) = 0.256240357398 -1.57896849362
absolute error = 8e-15
relative error = 5.001e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.83070197896 -0.641487831439
y1[1] (closed_form) = 2.83070197896 -0.641487831439
absolute error = 8.050e-15
relative error = 2.774e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.386
Order of pole (three term test) = 35.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.386
Order of pole (three term test) = 30.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11611.7MB, alloc=44.3MB, time=151.38
x[1] = 0.386 1.308
h = 0.0001 0.003
y2[1] (numeric) = 0.252839749623 -1.58807724939
y2[1] (closed_form) = 0.252839749623 -1.58807724939
absolute error = 8e-15
relative error = 4.975e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.83854503131 -0.645373474713
y1[1] (closed_form) = 2.83854503131 -0.645373474713
absolute error = 8.050e-15
relative error = 2.766e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.42
Order of pole (three term test) = 35.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.42
Order of pole (three term test) = 30.13 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3861 1.311
h = 0.001 0.001
y2[1] (numeric) = 0.250715936063 -1.59353526936
y2[1] (closed_form) = 0.250715936063 -1.59353526936
absolute error = 8e-15
relative error = 4.959e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.84324262448 -0.647777219775
y1[1] (closed_form) = 2.84324262448 -0.647777219775
absolute error = 9.035e-15
relative error = 3.098e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.44
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.44
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11659.5MB, alloc=44.3MB, time=152.00
x[1] = 0.3871 1.312
h = 0.001 0.003
y2[1] (numeric) = 0.248223322285 -1.59472998465
y2[1] (closed_form) = 0.248223322285 -1.59472998465
absolute error = 8e-15
relative error = 4.957e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.84408622712 -0.650121882632
y1[1] (closed_form) = 2.84408622712 -0.650121882632
absolute error = 9.035e-15
relative error = 3.097e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.447
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.447
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11707.2MB, alloc=44.3MB, time=152.63
x[1] = 0.3881 1.315
h = 0.0001 0.004
y2[1] (numeric) = 0.244421069164 -1.59961624775
y2[1] (closed_form) = 0.244421069164 -1.59961624775
absolute error = 9.001e-15
relative error = 5.562e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.8481240679 -0.65398008457
y1[1] (closed_form) = 2.8481240679 -0.65398008457
absolute error = 9.035e-15
relative error = 3.092e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 35.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.468
Order of pole (three term test) = 30.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11755.3MB, alloc=44.3MB, time=153.26
x[1] = 0.3882 1.319
h = 0.003 0.006
y2[1] (numeric) = 0.241613647269 -1.60695585189
y2[1] (closed_form) = 0.241613647269 -1.60695585189
absolute error = 9e-15
relative error = 5.538e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.85446150561 -0.657168339072
y1[1] (closed_form) = 2.85446150561 -0.657168339072
absolute error = 9.035e-15
relative error = 3.085e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.496
Order of pole (three term test) = 35.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.496
Order of pole (three term test) = 30.09 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3912 1.325
h = 0.0001 0.005
y2[1] (numeric) = 0.232067991474 -1.61611914291
y2[1] (closed_form) = 0.232067991474 -1.61611914291
absolute error = 9e-15
relative error = 5.512e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.86184126469 -0.666581863328
y1[1] (closed_form) = 2.86184126469 -0.666581863328
absolute error = 9.035e-15
relative error = 3.075e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.538
Order of pole (three term test) = 35.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.538
Order of pole (three term test) = 30.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11802.9MB, alloc=44.3MB, time=153.88
x[1] = 0.3913 1.33
h = 0.0001 0.003
y2[1] (numeric) = 0.22853847844 -1.62538153844
y2[1] (closed_form) = 0.22853847844 -1.62538153844
absolute error = 9e-15
relative error = 5.483e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.86986803033 -0.670592413166
y1[1] (closed_form) = 2.86986803033 -0.670592413166
absolute error = 9.045e-15
relative error = 3.069e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.574
Order of pole (three term test) = 35.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.574
Order of pole (three term test) = 30.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11850.7MB, alloc=44.3MB, time=154.50
x[1] = 0.3914 1.333
h = 0.001 0.001
y2[1] (numeric) = 0.226335755211 -1.63093116603
y2[1] (closed_form) = 0.226335755211 -1.63093116603
absolute error = 9e-15
relative error = 5.466e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.87467523962 -0.673072915352
y1[1] (closed_form) = 2.87467523962 -0.673072915352
absolute error = 9.045e-15
relative error = 3.064e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.596
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.596
Order of pole (three term test) = 30.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11898.8MB, alloc=44.3MB, time=155.13
x[1] = 0.3924 1.334
h = 0.001 0.003
y2[1] (numeric) = 0.223786375725 -1.63213199384
y2[1] (closed_form) = 0.223786375725 -1.63213199384
absolute error = 9e-15
relative error = 5.463e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.87553183267 -0.675479385724
y1[1] (closed_form) = 2.87553183267 -0.675479385724
absolute error = 9.035e-15
relative error = 3.059e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.603
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.603
Order of pole (three term test) = 30.05 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3934 1.337
h = 0.0001 0.004
y2[1] (numeric) = 0.219876394323 -1.63708731254
y2[1] (closed_form) = 0.219876394323 -1.63708731254
absolute error = 9e-15
relative error = 5.449e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.87965749225 -0.679448496513
y1[1] (closed_form) = 2.87965749225 -0.679448496513
absolute error = 8.040e-15
relative error = 2.717e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.625
Order of pole (three term test) = 35.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.625
Order of pole (three term test) = 30.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11946.6MB, alloc=44.3MB, time=155.75
x[1] = 0.3935 1.341
h = 0.003 0.006
y2[1] (numeric) = 0.216963733917 -1.64455079361
y2[1] (closed_form) = 0.216963733917 -1.64455079361
absolute error = 9e-15
relative error = 5.426e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.88614260204 -0.682738893345
y1[1] (closed_form) = 2.88614260204 -0.682738893345
absolute error = 8.040e-15
relative error = 2.711e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.654
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.654
Order of pole (three term test) = 30.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11994.4MB, alloc=44.3MB, time=156.38
x[1] = 0.3965 1.347
h = 0.0001 0.005
y2[1] (numeric) = 0.207168600224 -1.6538275224
y2[1] (closed_form) = 0.207168600224 -1.6538275224
absolute error = 9e-15
relative error = 5.400e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.89367394757 -0.692414019454
y1[1] (closed_form) = 2.89367394757 -0.692414019454
absolute error = 8.040e-15
relative error = 2.702e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.698
Order of pole (three term test) = 35.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.698
Order of pole (three term test) = 30.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12042.2MB, alloc=44.3MB, time=157.00
x[1] = 0.3966 1.352
h = 0.0001 0.003
y2[1] (numeric) = 0.203506412591 -1.66324695748
y2[1] (closed_form) = 0.203506412591 -1.66324695748
absolute error = 1.0e-14
relative error = 5.968e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.90188715077 -0.696553176342
y1[1] (closed_form) = 2.90188715077 -0.696553176342
absolute error = 8.040e-15
relative error = 2.694e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.735
Order of pole (three term test) = 35.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.735
Order of pole (three term test) = 29.99 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3967 1.355
h = 0.001 0.001
y2[1] (numeric) = 0.201222481151 -1.66889020918
y2[1] (closed_form) = 0.201222481151 -1.66889020918
absolute error = 1.0e-14
relative error = 5.949e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.9068055894 -0.699112687696
y1[1] (closed_form) = 2.9068055894 -0.699112687696
absolute error = 9.027e-15
relative error = 3.019e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.758
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.758
Order of pole (three term test) = 29.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12090.0MB, alloc=44.3MB, time=157.62
x[1] = 0.3977 1.356
h = 0.001 0.003
y2[1] (numeric) = 0.198614893581 -1.67009710244
y2[1] (closed_form) = 0.198614893581 -1.67009710244
absolute error = 1.0e-14
relative error = 5.946e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.90767500216 -0.701582262519
y1[1] (closed_form) = 2.90767500216 -0.701582262519
absolute error = 8.031e-15
relative error = 2.685e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.765
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.765
Order of pole (three term test) = 29.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12137.8MB, alloc=44.3MB, time=158.25
x[1] = 0.3987 1.359
h = 0.0001 0.004
y2[1] (numeric) = 0.194594245581 -1.67512282409
y2[1] (closed_form) = 0.194594245581 -1.67512282409
absolute error = 1.1e-14
relative error = 6.523e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.91188943585 -0.705665053945
y1[1] (closed_form) = 2.91188943585 -0.705665053945
absolute error = 9.027e-15
relative error = 3.013e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.788
Order of pole (three term test) = 35.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.788
Order of pole (three term test) = 29.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12185.8MB, alloc=44.3MB, time=158.87
x[1] = 0.3988 1.363
h = 0.003 0.006
y2[1] (numeric) = 0.191573278101 -1.68271290559
y2[1] (closed_form) = 0.191573278101 -1.68271290559
absolute error = 1.000e-14
relative error = 5.905e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.91852440707 -0.709060605717
y1[1] (closed_form) = 2.91852440707 -0.709060605717
absolute error = 9.027e-15
relative error = 3.006e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.818
Order of pole (three term test) = 35.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.818
Order of pole (three term test) = 29.95 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4018 1.369
h = 0.0001 0.005
y2[1] (numeric) = 0.181522037186 -1.69210501722
y2[1] (closed_form) = 0.181522037186 -1.69210501722
absolute error = 1.000e-14
relative error = 5.876e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.92620851635 -0.719003501232
y1[1] (closed_form) = 2.92620851635 -0.719003501232
absolute error = 9.027e-15
relative error = 2.996e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.865
Order of pole (three term test) = 35.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.865
Order of pole (three term test) = 29.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12233.4MB, alloc=44.3MB, time=159.49
x[1] = 0.4019 1.374
h = 0.0001 0.003
y2[1] (numeric) = 0.1777233085 -1.70168493229
y2[1] (closed_form) = 0.1777233085 -1.70168493229
absolute error = 1.000e-14
relative error = 5.845e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.93461093635 -0.723275067769
y1[1] (closed_form) = 2.93461093635 -0.723275067769
absolute error = 9.027e-15
relative error = 2.987e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.903
Order of pole (three term test) = 35.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.903
Order of pole (three term test) = 29.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12281.3MB, alloc=44.3MB, time=160.12
x[1] = 0.402 1.377
h = 0.001 0.001
y2[1] (numeric) = 0.175355811447 -1.70742384834
y2[1] (closed_form) = 0.175355811447 -1.70742384834
absolute error = 1.100e-14
relative error = 6.409e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.93964224984 -0.725915902298
y1[1] (closed_form) = 2.93964224984 -0.725915902298
absolute error = 9.027e-15
relative error = 2.981e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.927
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.927
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.403 1.378
h = 0.001 0.003
y2[1] (numeric) = 0.172688545466 -1.70863674915
y2[1] (closed_form) = 0.172688545466 -1.70863674915
absolute error = 1.000e-14
relative error = 5.823e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.94052430274 -0.728449910272
y1[1] (closed_form) = 2.94052430274 -0.728449910272
absolute error = 8.031e-15
relative error = 2.651e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.935
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.935
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12329.2MB, alloc=44.3MB, time=160.74
x[1] = 0.404 1.381
h = 0.0001 0.004
y2[1] (numeric) = 0.168554225674 -1.71373422742
y2[1] (closed_form) = 0.168554225674 -1.71373422742
absolute error = 1.000e-14
relative error = 5.807e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 2.94482847982 -0.732649226652
y1[1] (closed_form) = 2.94482847982 -0.732649226652
absolute error = 9.027e-15
relative error = 2.975e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.959
Order of pole (three term test) = 35.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.959
Order of pole (three term test) = 29.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12376.9MB, alloc=44.3MB, time=161.36
x[1] = 0.4041 1.385
h = 0.003 0.006
y2[1] (numeric) = 0.165421803651 -1.72145366529
y2[1] (closed_form) = 0.165421803651 -1.72145366529
absolute error = 1.000e-14
relative error = 5.784e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.9516155456 -0.736153028866
y1[1] (closed_form) = 2.9516155456 -0.736153028866
absolute error = 8.031e-15
relative error = 2.640e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.99
Order of pole (three term test) = 35.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.99
Order of pole (three term test) = 29.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12424.9MB, alloc=44.3MB, time=161.98
x[1] = 0.4071 1.391
h = 0.0001 0.005
y2[1] (numeric) = 0.155107682519 -1.73096309771
y2[1] (closed_form) = 0.155107682519 -1.73096309771
absolute error = 1.000e-14
relative error = 5.755e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.95945360313 -0.74637001905
y1[1] (closed_form) = 2.95945360313 -0.74637001905
absolute error = 8.022e-15
relative error = 2.628e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.039
Order of pole (three term test) = 35.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.039
Order of pole (three term test) = 29.86 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4072 1.396
h = 0.0001 0.003
y2[1] (numeric) = 0.151168446647 -1.74070697454
y2[1] (closed_form) = 0.151168446647 -1.74070697454
absolute error = 1.000e-14
relative error = 5.724e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.96804807459 -0.750777902335
y1[1] (closed_form) = 2.96804807459 -0.750777902335
absolute error = 8.022e-15
relative error = 2.620e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.079
Order of pole (three term test) = 35.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.079
Order of pole (three term test) = 29.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12472.6MB, alloc=44.3MB, time=162.60
x[1] = 0.4073 1.399
h = 0.001 0.001
y2[1] (numeric) = 0.148714966166 -1.7465436193
y2[1] (closed_form) = 0.148714966166 -1.7465436193
absolute error = 1.000e-14
relative error = 5.706e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.97319394093 -0.753502437447
y1[1] (closed_form) = 2.97319394093 -0.753502437447
absolute error = 8.022e-15
relative error = 2.616e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.104
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.104
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12520.6MB, alloc=44.3MB, time=163.22
x[1] = 0.4083 1.4
h = 0.003 0.006
y2[1] (numeric) = 0.145986522838 -1.74776245861
y2[1] (closed_form) = 0.145986522838 -1.74776245861
absolute error = 1.000e-14
relative error = 5.703e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 2.97408844515 -0.756102239592
y1[1] (closed_form) = 2.97408844515 -0.756102239592
absolute error = 8.031e-15
relative error = 2.617e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.112
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.112
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12568.6MB, alloc=44.3MB, time=163.85
x[1] = 0.4113 1.406
h = 0.0001 0.005
y2[1] (numeric) = 0.135484550515 -1.75734688534
y2[1] (closed_form) = 0.135484550515 -1.75734688534
absolute error = 1.000e-14
relative error = 5.675e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 2.98202599317 -0.766515443146
y1[1] (closed_form) = 2.98202599317 -0.766515443146
absolute error = 8.031e-15
relative error = 2.608e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.162
Order of pole (three term test) = 35.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.162
Order of pole (three term test) = 29.81 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4114 1.411
h = 0.0001 0.003
y2[1] (numeric) = 0.131442071453 -1.76720192988
y2[1] (closed_form) = 0.131442071453 -1.76720192988
absolute error = 1.000e-14
relative error = 5.644e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 2.99075069374 -0.771024343915
y1[1] (closed_form) = 2.99075069374 -0.771024343915
absolute error = 8.031e-15
relative error = 2.600e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.204
Order of pole (three term test) = 35.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.204
Order of pole (three term test) = 29.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12616.3MB, alloc=44.3MB, time=164.47
x[1] = 0.4115 1.414
h = 0.001 0.001
y2[1] (numeric) = 0.128925484666 -1.77310477112
y2[1] (closed_form) = 0.128925484666 -1.77310477112
absolute error = 1.000e-14
relative error = 5.626e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 2.9959741684 -0.773810805567
y1[1] (closed_form) = 2.9959741684 -0.773810805567
absolute error = 8.031e-15
relative error = 2.595e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.229
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.229
Order of pole (three term test) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12664.3MB, alloc=44.3MB, time=165.10
x[1] = 0.4125 1.415
h = 0.001 0.003
y2[1] (numeric) = 0.12615392618 -1.77432606248
y2[1] (closed_form) = 0.12615392618 -1.77432606248
absolute error = 1.100e-14
relative error = 6.185e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 2.99687542396 -0.776456981128
y1[1] (closed_form) = 2.99687542396 -0.776456981128
absolute error = 8.031e-15
relative error = 2.594e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.238
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.238
Order of pole (three term test) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12712.2MB, alloc=44.3MB, time=165.72
x[1] = 0.4135 1.418
h = 0.0001 0.004
y2[1] (numeric) = 0.121818850459 -1.77954471017
y2[1] (closed_form) = 0.121818850459 -1.77954471017
absolute error = 1.100e-14
relative error = 6.168e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.00133021574 -0.780861952185
y1[1] (closed_form) = 3.00133021574 -0.780861952185
absolute error = 9.027e-15
relative error = 2.911e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.263
Order of pole (three term test) = 35.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.263
Order of pole (three term test) = 29.77 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4136 1.422
h = 0.003 0.006
y2[1] (numeric) = 0.118487526827 -1.78748584172
y2[1] (closed_form) = 0.118487526827 -1.78748584172
absolute error = 1.100e-14
relative error = 6.141e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.00837628302 -0.784559685562
y1[1] (closed_form) = 3.00837628302 -0.784559685562
absolute error = 8.031e-15
relative error = 2.583e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.297
Order of pole (three term test) = 35.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.297
Order of pole (three term test) = 29.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12759.9MB, alloc=44.3MB, time=166.34
x[1] = 0.4166 1.428
h = 0.0001 0.005
y2[1] (numeric) = 0.107710858102 -1.79719066332
y2[1] (closed_form) = 0.107710858102 -1.79719066332
absolute error = 1.100e-14
relative error = 6.111e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.016469624 -0.795258056813
y1[1] (closed_form) = 3.016469624 -0.795258056813
absolute error = 8.031e-15
relative error = 2.574e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.349
Order of pole (three term test) = 35.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.349
Order of pole (three term test) = 29.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12807.7MB, alloc=44.3MB, time=166.96
x[1] = 0.4167 1.433
h = 0.0001 0.003
y2[1] (numeric) = 0.103520854012 -1.8072155364
y2[1] (closed_form) = 0.103520854012 -1.8072155364
absolute error = 1.200e-14
relative error = 6.630e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.02539118289 -0.799910187411
y1[1] (closed_form) = 3.02539118289 -0.799910187411
absolute error = 8.031e-15
relative error = 2.566e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.393
Order of pole (three term test) = 35.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.393
Order of pole (three term test) = 29.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12855.7MB, alloc=44.3MB, time=167.58
x[1] = 0.4168 1.436
h = 0.001 0.001
y2[1] (numeric) = 0.10091400799 -1.81321958215
y2[1] (closed_form) = 0.10091400799 -1.81321958215
absolute error = 1.100e-14
relative error = 6.058e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.03073205346 -0.802784554454
y1[1] (closed_form) = 3.03073205346 -0.802784554454
absolute error = 8.031e-15
relative error = 2.561e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.419
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.419
Order of pole (three term test) = 29.7 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4178 1.437
h = 0.001 0.003
y2[1] (numeric) = 0.0980786777538 -1.81444662962
y2[1] (closed_form) = 0.0980786777538 -1.81444662962
absolute error = 1.100e-14
relative error = 6.055e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.03164538336 -0.805498891064
y1[1] (closed_form) = 3.03164538336 -0.805498891064
absolute error = 8.022e-15
relative error = 2.558e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.428
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.428
Order of pole (three term test) = 29.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12903.4MB, alloc=44.3MB, time=168.20
x[1] = 0.4188 1.44
h = 0.0001 0.004
y2[1] (numeric) = 0.0936214734435 -1.8197406215
y2[1] (closed_form) = 0.0936214734435 -1.8197406215
absolute error = 1.100e-14
relative error = 6.038e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.03619251354 -0.81002842917
y1[1] (closed_form) = 3.03619251354 -0.81002842917
absolute error = 8.022e-15
relative error = 2.553e-13 %
Correct digits = 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) = 29.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12951.4MB, alloc=44.3MB, time=168.83
x[1] = 0.4189 1.444
h = 0.003 0.006
y2[1] (numeric) = 0.0901697558186 -1.82781859604
y2[1] (closed_form) = 0.0901697558186 -1.82781859604
absolute error = 1.100e-14
relative error = 6.012e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.04339681219 -0.813843219109
y1[1] (closed_form) = 3.04339681219 -0.813843219109
absolute error = 7.035e-15
relative error = 2.233e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.491
Order of pole (three term test) = 35.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.491
Order of pole (three term test) = 29.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12999.3MB, alloc=44.3MB, time=169.46
x[1] = 0.4219 1.45
h = 0.0001 0.005
y2[1] (numeric) = 0.0791112140249 -1.83764572385
y2[1] (closed_form) = 0.0791112140249 -1.83764572385
absolute error = 1.200e-14
relative error = 6.525e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.05164714102 -0.8248335232
y1[1] (closed_form) = 3.05164714102 -0.8248335232
absolute error = 7.026e-15
relative error = 2.223e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.545
Order of pole (three term test) = 35.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.545
Order of pole (three term test) = 29.66 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.422 1.455
h = 0.0001 0.003
y2[1] (numeric) = 0.0747694366112 -1.84784401885
y2[1] (closed_form) = 0.0747694366112 -1.84784401885
absolute error = 1.200e-14
relative error = 6.490e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.06076854081 -0.829633085305
y1[1] (closed_form) = 3.06076854081 -0.829633085305
absolute error = 7.026e-15
relative error = 2.215e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.591
Order of pole (three term test) = 35.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.591
Order of pole (three term test) = 29.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13047.0MB, alloc=44.3MB, time=170.09
x[1] = 0.4221 1.458
h = 0.001 0.001
y2[1] (numeric) = 0.0720697425848 -1.85395139853
y2[1] (closed_form) = 0.0720697425848 -1.85395139853
absolute error = 1.200e-14
relative error = 6.469e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.06622857195 -0.832597913813
y1[1] (closed_form) = 3.06622857195 -0.832597913813
absolute error = 8.022e-15
relative error = 2.525e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.618
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.618
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13094.9MB, alloc=44.3MB, time=170.71
x[1] = 0.4231 1.459
h = 0.001 0.003
y2[1] (numeric) = 0.0691690617365 -1.85518410029
y2[1] (closed_form) = 0.0691690617365 -1.85518410029
absolute error = 1.200e-14
relative error = 6.465e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.06715375957 -0.835381862006
y1[1] (closed_form) = 3.06715375957 -0.835381862006
absolute error = 7.018e-15
relative error = 2.208e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.628
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.628
Order of pole (three term test) = 29.63 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4241 1.462
h = 0.0001 0.004
y2[1] (numeric) = 0.0645864620426 -1.86055481053
y2[1] (closed_form) = 0.0645864620426 -1.86055481053
absolute error = 1.300e-14
relative error = 6.984e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.07179424493 -0.840039092751
y1[1] (closed_form) = 3.07179424493 -0.840039092751
absolute error = 8.016e-15
relative error = 2.517e-13 %
Correct digits = 15
memory used=13142.7MB, alloc=44.3MB, time=171.33
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.656
Order of pole (three term test) = 35.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.656
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4242 1.466
h = 0.003 0.006
y2[1] (numeric) = 0.0610108927813 -1.86877250597
y2[1] (closed_form) = 0.0610108927813 -1.86877250597
absolute error = 1.300e-14
relative error = 6.953e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.07915916988 -0.843974358672
y1[1] (closed_form) = 3.07915916988 -0.843974358672
absolute error = 8.016e-15
relative error = 2.511e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.693
Order of pole (three term test) = 35.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.693
Order of pole (three term test) = 29.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13190.6MB, alloc=44.3MB, time=171.96
x[1] = 0.4272 1.472
h = 0.0001 0.005
y2[1] (numeric) = 0.0496631442181 -1.87872384136
y2[1] (closed_form) = 0.0496631442181 -1.87872384136
absolute error = 1.300e-14
relative error = 6.918e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.08756768493 -0.855263530456
y1[1] (closed_form) = 3.08756768493 -0.855263530456
absolute error = 8.016e-15
relative error = 2.502e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.75
Order of pole (three term test) = 35.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.75
Order of pole (three term test) = 29.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13238.4MB, alloc=44.3MB, time=172.59
x[1] = 0.4273 1.477
h = 0.0001 0.003
y2[1] (numeric) = 0.045165235542 -1.88909919533
y2[1] (closed_form) = 0.045165235542 -1.88909919533
absolute error = 1.300e-14
relative error = 6.880e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.09689196493 -0.860214839571
y1[1] (closed_form) = 3.09689196493 -0.860214839571
absolute error = 8.022e-15
relative error = 2.496e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.797
Order of pole (three term test) = 35.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.797
Order of pole (three term test) = 29.56 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4274 1.48
h = 0.001 0.001
y2[1] (numeric) = 0.0423700383094 -1.89531206382
y2[1] (closed_form) = 0.0423700383094 -1.89531206382
absolute error = 1.300e-14
relative error = 6.859e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.10247295456 -0.863272754653
y1[1] (closed_form) = 3.10247295456 -0.863272754653
absolute error = 9.020e-15
relative error = 2.801e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.826
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.826
Order of pole (three term test) = 29.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13286.2MB, alloc=44.3MB, time=173.21
x[1] = 0.4284 1.481
h = 0.0001 0.004
y2[1] (numeric) = 0.0394023968753 -1.8965503054
y2[1] (closed_form) = 0.0394023968753 -1.8965503054
absolute error = 1.200e-14
relative error = 6.327e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.10340977243 -0.866127799464
y1[1] (closed_form) = 3.10340977243 -0.866127799464
absolute error = 9.020e-15
relative error = 2.799e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.836
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.836
Order of pole (three term test) = 29.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13334.1MB, alloc=44.3MB, time=173.84
x[1] = 0.4285 1.485
h = 0.003 0.006
y2[1] (numeric) = 0.0357190951862 -1.90489213211
y2[1] (closed_form) = 0.0357190951862 -1.90489213211
absolute error = 1.300e-14
relative error = 6.824e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.11091640365 -0.870167622718
y1[1] (closed_form) = 3.11091640365 -0.870167622718
absolute error = 9.020e-15
relative error = 2.792e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.875
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.875
Order of pole (three term test) = 29.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13382.1MB, alloc=44.3MB, time=174.46
x[1] = 0.4315 1.491
h = 0.0001 0.005
y2[1] (numeric) = 0.0241179219349 -1.91495546245
y2[1] (closed_form) = 0.0241179219349 -1.91495546245
absolute error = 1.300e-14
relative error = 6.790e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.11946571737 -0.881717831422
y1[1] (closed_form) = 3.11946571737 -0.881717831422
absolute error = 9.014e-15
relative error = 2.781e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.934
Order of pole (three term test) = 35.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.934
Order of pole (three term test) = 29.52 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4316 1.496
h = 0.0001 0.003
y2[1] (numeric) = 0.0194842140563 -1.92548810173
y2[1] (closed_form) = 0.0194842140563 -1.92548810173
absolute error = 1.200e-14
relative error = 6.233e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.12896898703 -0.886800836883
y1[1] (closed_form) = 3.12896898703 -0.886800836883
absolute error = 9.020e-15
relative error = 2.773e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.983
Order of pole (three term test) = 35.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.983
Order of pole (three term test) = 29.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13429.6MB, alloc=44.3MB, time=175.08
x[1] = 0.4317 1.499
h = 0.001 0.001
y2[1] (numeric) = 0.0166059246429 -1.93179469868
y2[1] (closed_form) = 0.0166059246429 -1.93179469868
absolute error = 1.200e-14
relative error = 6.213e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.13465671163 -0.88993956318
y1[1] (closed_form) = 3.13465671163 -0.88993956318
absolute error = 9.014e-15
relative error = 2.766e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.013
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.013
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13477.5MB, alloc=44.3MB, time=175.70
x[1] = 0.4327 1.5
h = 0.001 0.003
y2[1] (numeric) = 0.0135793961587 -1.93303843142
y2[1] (closed_form) = 0.0135793961587 -1.93303843142
absolute error = 1.200e-14
relative error = 6.209e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.13560422134 -0.892856886926
y1[1] (closed_form) = 3.13560422134 -0.892856886926
absolute error = 9.014e-15
relative error = 2.765e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.023
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.023
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13525.5MB, alloc=44.3MB, time=176.33
x[1] = 0.4337 1.503
h = 0.0001 0.004
y2[1] (numeric) = 0.0087554645371 -1.93855716263
y2[1] (closed_form) = 0.0087554645371 -1.93855716263
absolute error = 1.300e-14
relative error = 6.707e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.1404227814 -0.897759176755
y1[1] (closed_form) = 3.1404227814 -0.897759176755
absolute error = 9.014e-15
relative error = 2.760e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.054
Order of pole (three term test) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.054
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4338 1.507
h = 0.003 0.006
y2[1] (numeric) = 0.00494167384628 -1.94704420219
y2[1] (closed_form) = 0.00494167384628 -1.94704420219
absolute error = 1.200e-14
relative error = 6.164e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.14809465904 -0.901926056482
y1[1] (closed_form) = 3.14809465904 -0.901926056482
absolute error = 9.014e-15
relative error = 2.753e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.094
Order of pole (three term test) = 36.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.094
Order of pole (three term test) = 29.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13573.2MB, alloc=44.3MB, time=176.95
x[1] = 0.4368 1.513
h = 0.0001 0.005
y2[1] (numeric) = -0.00696276113512 -1.95723534058
y2[1] (closed_form) = -0.00696276113512 -1.95723534058
absolute error = 1.300e-14
relative error = 6.642e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.15680448203 -0.913788486239
y1[1] (closed_form) = 3.15680448203 -0.913788486239
absolute error = 9.009e-15
relative error = 2.741e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.156
Order of pole (three term test) = 36.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.156
Order of pole (three term test) = 29.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13621.1MB, alloc=44.3MB, time=177.58
x[1] = 0.4369 1.518
h = 0.0001 0.003
y2[1] (numeric) = -0.0117609663722 -1.96795198011
y2[1] (closed_form) = -0.0117609663722 -1.96795198011
absolute error = 1.301e-14
relative error = 6.609e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.16651649436 -0.919031543195
y1[1] (closed_form) = 3.16651649436 -0.919031543195
absolute error = 9.014e-15
relative error = 2.734e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.208
Order of pole (three term test) = 36.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.208
Order of pole (three term test) = 29.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13669.0MB, alloc=44.3MB, time=178.20
x[1] = 0.437 1.521
h = 0.001 0.001
y2[1] (numeric) = -0.0147398560031 -1.97436817816
y2[1] (closed_form) = -0.0147398560031 -1.97436817816
absolute error = 1.300e-14
relative error = 6.584e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.17232864536 -0.922268407721
y1[1] (closed_form) = 3.17232864536 -0.922268407721
absolute error = 8.016e-15
relative error = 2.426e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.239
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.239
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.438 1.522
h = 0.001 0.003
y2[1] (numeric) = -0.0178364278409 -1.97561722263
y2[1] (closed_form) = -0.0178364278409 -1.97561722263
absolute error = 1.301e-14
relative error = 6.583e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.17328735042 -0.925259688404
y1[1] (closed_form) = 3.17328735042 -0.925259688404
absolute error = 9.014e-15
relative error = 2.727e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.249
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.249
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13716.8MB, alloc=44.3MB, time=178.82
x[1] = 0.439 1.525
h = 0.0001 0.004
y2[1] (numeric) = -0.0227955046563 -1.98121667646
y2[1] (closed_form) = -0.0227955046563 -1.98121667646
absolute error = 1.302e-14
relative error = 6.570e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.17820228454 -0.930299047435
y1[1] (closed_form) = 3.17820228454 -0.930299047435
absolute error = 8.010e-15
relative error = 2.419e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.281
Order of pole (three term test) = 36.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.281
Order of pole (three term test) = 29.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13764.7MB, alloc=44.3MB, time=179.45
x[1] = 0.4391 1.529
h = 0.003 0.006
y2[1] (numeric) = -0.026743502471 -1.98985190887
y2[1] (closed_form) = -0.026743502471 -1.98985190887
absolute error = 1.300e-14
relative error = 6.535e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.1860419346 -0.934596672629
y1[1] (closed_form) = 3.1860419346 -0.934596672629
absolute error = 8.010e-15
relative error = 2.412e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.323
Order of pole (three term test) = 36.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.323
Order of pole (three term test) = 29.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13812.5MB, alloc=44.3MB, time=180.08
x[1] = 0.4421 1.535
h = 0.0001 0.005
y2[1] (numeric) = -0.0389590034397 -2.00017272536
y2[1] (closed_form) = -0.0389590034397 -2.00017272536
absolute error = 1.400e-14
relative error = 6.998e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.19491347133 -0.946778763074
y1[1] (closed_form) = 3.19491347133 -0.946778763074
absolute error = 8.010e-15
relative error = 2.404e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.388
Order of pole (three term test) = 36.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.388
Order of pole (three term test) = 29.37 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4422 1.54
h = 0.0001 0.003
y2[1] (numeric) = -0.0439263929567 -2.01107713205
y2[1] (closed_form) = -0.0439263929567 -2.01107713205
absolute error = 1.302e-14
relative error = 6.472e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.20483743149 -0.952186526969
y1[1] (closed_form) = 3.20483743149 -0.952186526969
absolute error = 8.010e-15
relative error = 2.396e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.442
Order of pole (three term test) = 36.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.442
Order of pole (three term test) = 29.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13860.2MB, alloc=44.3MB, time=180.70
x[1] = 0.4423 1.543
h = 0.001 0.001
y2[1] (numeric) = -0.0470087373198 -2.01760516178
y2[1] (closed_form) = -0.0470087373198 -2.01760516178
absolute error = 1.3e-14
relative error = 6.442e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.21077590389 -0.955524360982
y1[1] (closed_form) = 3.21077590389 -0.955524360982
absolute error = 9.009e-15
relative error = 2.689e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.475
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.475
Order of pole (three term test) = 29.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13908.2MB, alloc=44.3MB, time=181.32
x[1] = 0.4433 1.544
h = 0.001 0.003
y2[1] (numeric) = -0.0501770556081 -2.01885936525
y2[1] (closed_form) = -0.0501770556081 -2.01885936525
absolute error = 1.301e-14
relative error = 6.445e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.21174554377 -0.95859118598
y1[1] (closed_form) = 3.21174554377 -0.95859118598
absolute error = 9.005e-15
relative error = 2.687e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.486
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.486
Order of pole (three term test) = 29.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13956.0MB, alloc=44.3MB, time=181.94
x[1] = 0.4443 1.547
h = 0.0001 0.004
y2[1] (numeric) = -0.0552748444654 -2.02454093809
y2[1] (closed_form) = -0.0552748444654 -2.02454093809
absolute error = 1.300e-14
relative error = 6.419e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.21675791752 -0.963771058023
y1[1] (closed_form) = 3.21675791752 -0.963771058023
absolute error = 9.009e-15
relative error = 2.683e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.519
Order of pole (three term test) = 36.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.519
Order of pole (three term test) = 29.33 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4444 1.551
h = 0.003 0.006
y2[1] (numeric) = -0.0593608632754 -2.0333273796
y2[1] (closed_form) = -0.0593608632754 -2.0333273796
absolute error = 1.301e-14
relative error = 6.393e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.224767912 -0.968203216414
y1[1] (closed_form) = 3.224767912 -0.968203216414
absolute error = 9.009e-15
relative error = 2.676e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.563
Order of pole (three term test) = 36.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.563
Order of pole (three term test) = 29.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14003.7MB, alloc=44.3MB, time=182.57
x[1] = 0.4474 1.557
h = 0.0001 0.005
y2[1] (numeric) = -0.071895406554 -2.0437797308
y2[1] (closed_form) = -0.071895406554 -2.0437797308
absolute error = 1.400e-14
relative error = 6.846e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.23380236612 -0.98071259064
y1[1] (closed_form) = 3.23380236612 -0.98071259064
absolute error = 1.001e-14
relative error = 2.962e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.63
Order of pole (three term test) = 36.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.63
Order of pole (three term test) = 29.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14051.5MB, alloc=44.3MB, time=183.19
x[1] = 0.4475 1.562
h = 0.0001 0.003
y2[1] (numeric) = -0.0770367881978 -2.05487571776
y2[1] (closed_form) = -0.0770367881978 -2.05487571776
absolute error = 1.400e-14
relative error = 6.810e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.24394153748 -0.98628984144
y1[1] (closed_form) = 3.24394153748 -0.98628984144
absolute error = 1.001e-14
relative error = 2.952e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.687
Order of pole (three term test) = 36.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.687
Order of pole (three term test) = 29.27 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4476 1.565
h = 0.001 0.001
y2[1] (numeric) = -0.0802255150563 -2.06151783657
y2[1] (closed_form) = -0.0802255150563 -2.06151783657
absolute error = 1.401e-14
relative error = 6.792e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.25000826033 -0.98973155169
y1[1] (closed_form) = 3.25000826033 -0.98973155169
absolute error = 1.001e-14
relative error = 2.946e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.721
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.721
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14099.4MB, alloc=44.3MB, time=183.81
x[1] = 0.4486 1.566
h = 0.001 0.003
y2[1] (numeric) = -0.0834673168061 -2.06277703198
y2[1] (closed_form) = -0.0834673168061 -2.06277703198
absolute error = 1.402e-14
relative error = 6.792e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.25098856187 -0.992875545377
y1[1] (closed_form) = 3.25098856187 -0.992875545377
absolute error = 1.001e-14
relative error = 2.944e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.732
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.732
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14147.2MB, alloc=44.3MB, time=184.44
x[1] = 0.4496 1.569
h = 0.0001 0.004
y2[1] (numeric) = -0.0887074669469 -2.06854212527
y2[1] (closed_form) = -0.0887074669469 -2.06854212527
absolute error = 1.401e-14
relative error = 6.765e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.25609945247 -0.998199461027
y1[1] (closed_form) = 3.25609945247 -0.998199461027
absolute error = 1.000e-14
relative error = 2.938e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.767
Order of pole (three term test) = 36.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.767
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14195.2MB, alloc=44.3MB, time=185.06
x[1] = 0.4497 1.573
h = 0.003 0.006
y2[1] (numeric) = -0.0929354188151 -2.07748282889
y2[1] (closed_form) = -0.0929354188151 -2.07748282889
absolute error = 1.501e-14
relative error = 7.218e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.26428240963 -1.00277004141
y1[1] (closed_form) = 3.26428240963 -1.00277004141
absolute error = 1.005e-14
relative error = 2.943e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.813
Order of pole (three term test) = 36.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.813
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4527 1.579
h = 0.0001 0.005
y2[1] (numeric) = -0.105797156861 -2.08806855701
y2[1] (closed_form) = -0.105797156861 -2.08806855701
absolute error = 1.502e-14
relative error = 7.185e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.27348098276 -1.01561450972
y1[1] (closed_form) = 3.27348098276 -1.01561450972
absolute error = 1.0e-14
relative error = 2.918e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.883
Order of pole (three term test) = 36.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.883
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14242.8MB, alloc=44.3MB, time=185.68
x[1] = 0.4528 1.584
h = 0.0001 0.003
y2[1] (numeric) = -0.111117462485 -2.09935998408
y2[1] (closed_form) = -0.111117462485 -2.09935998408
absolute error = 1.500e-14
relative error = 7.136e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.2838386873 -1.02136615485
y1[1] (closed_form) = 3.2838386873 -1.02136615485
absolute error = 1.005e-14
relative error = 2.922e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.942
Order of pole (three term test) = 36.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.942
Order of pole (three term test) = 29.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14290.7MB, alloc=44.3MB, time=186.31
x[1] = 0.4529 1.587
h = 0.001 0.001
y2[1] (numeric) = -0.114415574713 -2.1061184766
y2[1] (closed_form) = -0.114415574713 -2.1061184766
absolute error = 1.502e-14
relative error = 7.119e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.29003562387 -1.02491472537
y1[1] (closed_form) = 3.29003562387 -1.02491472537
absolute error = 1.005e-14
relative error = 2.916e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.978
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.978
Order of pole (three term test) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14338.8MB, alloc=44.3MB, time=186.94
x[1] = 0.4539 1.588
h = 0.0001 0.004
y2[1] (numeric) = -0.117732631602 -2.10738248198
y2[1] (closed_form) = -0.117732631602 -2.10738248198
absolute error = 1.602e-14
relative error = 7.588e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.29102630078 -1.02813754978
y1[1] (closed_form) = 3.29102630078 -1.02813754978
absolute error = 1.005e-14
relative error = 2.915e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.99
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.99
Order of pole (three term test) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.454 1.592
h = 0.003 0.006
y2[1] (numeric) = -0.122084076449 -2.11646019845
y2[1] (closed_form) = -0.122084076449 -2.11646019845
absolute error = 1.600e-14
relative error = 7.549e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.29936198451 -1.03282836853
y1[1] (closed_form) = 3.29936198451 -1.03282836853
absolute error = 1.005e-14
relative error = 2.907e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.038
Order of pole (three term test) = 36.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.038
Order of pole (three term test) = 29.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14386.6MB, alloc=44.3MB, time=187.56
x[1] = 0.457 1.598
h = 0.0001 0.005
y2[1] (numeric) = -0.135232500291 -2.12716622938
y2[1] (closed_form) = -0.135232500291 -2.12716622938
absolute error = 1.6e-14
relative error = 7.507e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.30870690732 -1.0459657003
y1[1] (closed_form) = 3.30870690732 -1.0459657003
absolute error = 1.005e-14
relative error = 2.896e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.111
Order of pole (three term test) = 36.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.111
Order of pole (three term test) = 29.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14434.4MB, alloc=44.3MB, time=188.18
x[1] = 0.4571 1.603
h = 0.0001 0.003
y2[1] (numeric) = -0.140708472481 -2.13863122546
y2[1] (closed_form) = -0.140708472481 -2.13863122546
absolute error = 1.701e-14
relative error = 7.935e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.31925758243 -1.05186882944
y1[1] (closed_form) = 3.31925758243 -1.05186882944
absolute error = 1.105e-14
relative error = 3.172e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.173
Order of pole (three term test) = 36.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.173
Order of pole (three term test) = 29.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14482.3MB, alloc=44.3MB, time=188.80
x[1] = 0.4572 1.606
h = 0.001 0.001
y2[1] (numeric) = -0.144101779567 -2.14549309219
y2[1] (closed_form) = -0.144101779567 -2.14549309219
absolute error = 1.702e-14
relative error = 7.917e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.32556952384 -1.05551024799
y1[1] (closed_form) = 3.32556952384 -1.05551024799
absolute error = 1.105e-14
relative error = 3.166e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.21
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.21
Order of pole (three term test) = 29.12 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4582 1.607
h = 0.001 0.003
y2[1] (numeric) = -0.147485005255 -2.14676200624
y2[1] (closed_form) = -0.147485005255 -2.14676200624
absolute error = 1.603e-14
relative error = 7.447e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.32656985855 -1.05880216876
y1[1] (closed_form) = 3.32656985855 -1.05880216876
absolute error = 1.105e-14
relative error = 3.164e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.222
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.222
Order of pole (three term test) = 29.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14530.1MB, alloc=44.3MB, time=189.44
x[1] = 0.4592 1.61
h = 0.0001 0.004
y2[1] (numeric) = -0.152999025114 -2.15268806063
y2[1] (closed_form) = -0.152999025114 -2.15268806063
absolute error = 1.702e-14
relative error = 7.886e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.3318687909 -1.06440261346
y1[1] (closed_form) = 3.3318687909 -1.06440261346
absolute error = 1.1e-14
relative error = 3.145e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.26
Order of pole (three term test) = 36.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.26
Order of pole (three term test) = 29.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14578.0MB, alloc=44.3MB, time=190.06
x[1] = 0.4593 1.614
h = 0.003 0.006
y2[1] (numeric) = -0.157499914962 -2.16192586907
y2[1] (closed_form) = -0.157499914962 -2.16192586907
absolute error = 1.700e-14
relative error = 7.844e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.34038248279 -1.06923933502
y1[1] (closed_form) = 3.34038248279 -1.06923933502
absolute error = 1.1e-14
relative error = 3.136e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 36.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.31
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14626.0MB, alloc=44.3MB, time=190.68
x[1] = 0.4623 1.62
h = 0.0001 0.005
y2[1] (numeric) = -0.170991164955 -2.17276876495
y2[1] (closed_form) = -0.170991164955 -2.17276876495
absolute error = 1.702e-14
relative error = 7.809e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.34989384914 -1.08272679133
y1[1] (closed_form) = 3.34989384914 -1.08272679133
absolute error = 1.1e-14
relative error = 3.125e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.386
Order of pole (three term test) = 36.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.386
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4624 1.625
h = 0.0001 0.003
y2[1] (numeric) = -0.176655531717 -2.18443657237
y2[1] (closed_form) = -0.176655531717 -2.18443657237
absolute error = 1.701e-14
relative error = 7.760e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.36066945821 -1.08881375477
y1[1] (closed_form) = 3.36066945821 -1.08881375477
absolute error = 1.1e-14
relative error = 3.114e-13 %
Correct digits = 15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.45
Order of pole (three term test) = 36.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.45
Order of pole (three term test) = 29.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14673.7MB, alloc=44.3MB, time=191.31
x[1] = 0.4625 1.628
h = 0.001 0.001
y2[1] (numeric) = -0.180163990275 -2.19141917551
y2[1] (closed_form) = -0.180163990275 -2.19141917551
absolute error = 1.700e-14
relative error = 7.733e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.36711539622 -1.0925677737
y1[1] (closed_form) = 3.36711539622 -1.0925677737
absolute error = 1.204e-14
relative error = 3.402e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.489
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.489
Order of pole (three term test) = 29.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14721.6MB, alloc=44.3MB, time=191.93
x[1] = 0.4635 1.629
h = 0.001 0.003
y2[1] (numeric) = -0.183625865289 -2.19269254182
y2[1] (closed_form) = -0.183625865289 -2.19269254182
absolute error = 1.7e-14
relative error = 7.726e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.36812555771 -1.09594172432
y1[1] (closed_form) = 3.36812555771 -1.09594172432
absolute error = 1.204e-14
relative error = 3.400e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.502
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.502
Order of pole (three term test) = 29.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14769.5MB, alloc=44.3MB, time=192.55
x[1] = 0.4645 1.632
h = 0.0001 0.004
y2[1] (numeric) = -0.18929314216 -2.19870619901
y2[1] (closed_form) = -0.18929314216 -2.19870619901
absolute error = 1.802e-14
relative error = 8.165e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.37352619559 -1.10169679566
y1[1] (closed_form) = 3.37352619559 -1.10169679566
absolute error = 1.3e-14
relative error = 3.663e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.541
Order of pole (three term test) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.541
Order of pole (three term test) = 29.05 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4646 1.636
h = 0.003 0.006
y2[1] (numeric) = -0.193947683486 -2.20810726147
y2[1] (closed_form) = -0.193947683486 -2.20810726147
absolute error = 1.802e-14
relative error = 8.131e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.38222064922 -1.10668361076
y1[1] (closed_form) = 3.38222064922 -1.10668361076
absolute error = 1.2e-14
relative error = 3.372e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.594
Order of pole (three term test) = 36.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.594
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14817.3MB, alloc=44.3MB, time=193.18
x[1] = 0.4676 1.642
h = 0.0001 0.005
y2[1] (numeric) = -0.207790439354 -2.21908881943
y2[1] (closed_form) = -0.207790439354 -2.21908881943
absolute error = 1.802e-14
relative error = 8.084e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.39189965004 -1.12052955906
y1[1] (closed_form) = 3.39189965004 -1.12052955906
absolute error = 1.3e-14
relative error = 3.639e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.673
Order of pole (three term test) = 36.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.673
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14865.1MB, alloc=44.3MB, time=193.80
x[1] = 0.4677 1.647
h = 0.0001 0.003
y2[1] (numeric) = -0.213648504342 -2.23096343677
y2[1] (closed_form) = -0.213648504342 -2.23096343677
absolute error = 1.801e-14
relative error = 8.035e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.40290368634 -1.12680564505
y1[1] (closed_form) = 3.40290368634 -1.12680564505
absolute error = 1.304e-14
relative error = 3.637e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.74
Order of pole (three term test) = 36.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.74
Order of pole (three term test) = 29.01 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4678 1.65
h = 0.001 0.001
y2[1] (numeric) = -0.217275342425 -2.23806914163
y2[1] (closed_form) = -0.217275342425 -2.23806914163
absolute error = 1.801e-14
relative error = 8.008e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.40948568428 -1.13067547922
y1[1] (closed_form) = 3.40948568428 -1.13067547922
absolute error = 1.404e-14
relative error = 3.907e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.781
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.781
Order of pole (three term test) = 28.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14913.0MB, alloc=44.3MB, time=194.42
x[1] = 0.4688 1.651
h = 0.001 0.003
y2[1] (numeric) = -0.220817742083 -2.23934673338
y2[1] (closed_form) = -0.220817742083 -2.23934673338
absolute error = 1.800e-14
relative error = 7.999e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.41050534625 -1.13413323353
y1[1] (closed_form) = 3.41050534625 -1.13413323353
absolute error = 1.304e-14
relative error = 3.628e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.794
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.794
Order of pole (three term test) = 29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14960.9MB, alloc=44.3MB, time=195.05
x[1] = 0.4698 1.654
h = 0.0001 0.004
y2[1] (numeric) = -0.2266422623 -2.24544941343
y2[1] (closed_form) = -0.2266422623 -2.24544941343
absolute error = 1.800e-14
relative error = 7.978e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.41600880976 -1.14004681492
y1[1] (closed_form) = 3.41600880976 -1.14004681492
absolute error = 1.404e-14
relative error = 3.897e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.835
Order of pole (three term test) = 36.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.835
Order of pole (three term test) = 28.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15008.9MB, alloc=44.3MB, time=195.67
x[1] = 0.4699 1.658
h = 0.003 0.006
y2[1] (numeric) = -0.231454769711 -2.25501693053
y2[1] (closed_form) = -0.231454769711 -2.25501693053
absolute error = 1.800e-14
relative error = 7.942e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.4248868261 -1.14518802485
y1[1] (closed_form) = 3.4248868261 -1.14518802485
absolute error = 1.414e-14
relative error = 3.916e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.89
Order of pole (three term test) = 36.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.89
Order of pole (three term test) = 28.97 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4729 1.664
h = 0.0001 0.005
y2[1] (numeric) = -0.245657903774 -2.26613892894
y2[1] (closed_form) = -0.245657903774 -2.26613892894
absolute error = 1.800e-14
relative error = 7.897e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.43473464515 -1.15940103514
y1[1] (closed_form) = 3.43473464515 -1.15940103514
absolute error = 1.414e-14
relative error = 3.901e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.973
Order of pole (three term test) = 37.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.973
Order of pole (three term test) = 28.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15056.5MB, alloc=44.3MB, time=196.29
x[1] = 0.473 1.669
h = 0.0001 0.003
y2[1] (numeric) = -0.251715107185 -2.27822440391
y2[1] (closed_form) = -0.251715107185 -2.27822440391
absolute error = 1.800e-14
relative error = 7.854e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.44597066198 -1.16587167142
y1[1] (closed_form) = 3.44597066198 -1.16587167142
absolute error = 1.404e-14
relative error = 3.858e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.043
Order of pole (three term test) = 37.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.043
Order of pole (three term test) = 28.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15104.4MB, alloc=44.3MB, time=196.91
x[1] = 0.4731 1.672
h = 0.001 0.001
y2[1] (numeric) = -0.255463635527 -2.28545560429
y2[1] (closed_form) = -0.255463635527 -2.28545560429
absolute error = 1.803e-14
relative error = 7.839e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.45269081822 -1.16986062021
y1[1] (closed_form) = 3.45269081822 -1.16986062021
absolute error = 1.503e-14
relative error = 4.124e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.086
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.086
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15152.4MB, alloc=44.3MB, time=197.54
x[1] = 0.4741 1.673
h = 0.001 0.003
y2[1] (numeric) = -0.259088472848 -2.28673717781
y2[1] (closed_form) = -0.259088472848 -2.28673717781
absolute error = 1.802e-14
relative error = 7.831e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.45371963914 -1.17340399249
y1[1] (closed_form) = 3.45371963914 -1.17340399249
absolute error = 1.503e-14
relative error = 4.121e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.1
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.1
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4751 1.676
h = 0.0001 0.004
y2[1] (numeric) = -0.265074315194 -2.29293030469
y2[1] (closed_form) = -0.265074315194 -2.29293030469
absolute error = 1.802e-14
relative error = 7.806e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.45932705827 -1.17948006356
y1[1] (closed_form) = 3.45932705827 -1.17948006356
absolute error = 1.503e-14
relative error = 4.113e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.143
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.143
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15200.1MB, alloc=44.3MB, time=198.16
x[1] = 0.4752 1.68
h = 0.003 0.006
y2[1] (numeric) = -0.270049214135 -2.30266751613
y2[1] (closed_form) = -0.270049214135 -2.30266751613
absolute error = 1.800e-14
relative error = 7.764e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.46839148601 -1.18478008284
y1[1] (closed_form) = 3.46839148601 -1.18478008284
absolute error = 1.503e-14
relative error = 4.102e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.2
Order of pole (three term test) = 37.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.2
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15247.9MB, alloc=44.3MB, time=198.78
x[1] = 0.4782 1.686
h = 0.0001 0.005
y2[1] (numeric) = -0.284621795775 -2.31393171334
y2[1] (closed_form) = -0.284621795775 -2.31393171334
absolute error = 1.801e-14
relative error = 7.725e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.47840929841 -1.19936893184
y1[1] (closed_form) = 3.47840929841 -1.19936893184
absolute error = 1.503e-14
relative error = 4.086e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.287
Order of pole (three term test) = 37.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.287
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15295.8MB, alloc=44.3MB, time=199.40
x[1] = 0.4783 1.691
h = 0.0001 0.003
y2[1] (numeric) = -0.290883717772 -2.32623214333
y2[1] (closed_form) = -0.290883717772 -2.32623214333
absolute error = 1.803e-14
relative error = 7.692e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.48988090945 -1.20603968896
y1[1] (closed_form) = 3.48988090945 -1.20603968896
absolute error = 1.6e-14
relative error = 4.333e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.36
Order of pole (three term test) = 37.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.36
Order of pole (three term test) = 28.89 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4784 1.694
h = 0.001 0.001
y2[1] (numeric) = -0.294757331856 -2.33359126187
y2[1] (closed_form) = -0.294757331856 -2.33359126187
absolute error = 1.804e-14
relative error = 7.670e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.49674135757 -1.21015113829
y1[1] (closed_form) = 3.49674135757 -1.21015113829
absolute error = 1.6e-14
relative error = 4.324e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.405
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.405
Order of pole (three term test) = 28.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15343.5MB, alloc=44.3MB, time=200.04
x[1] = 0.4794 1.695
h = 0.0001 0.004
y2[1] (numeric) = -0.298466558372 -2.3348765561
y2[1] (closed_form) = -0.298466558372 -2.3348765561
absolute error = 1.802e-14
relative error = 7.657e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.49777898014 -1.21378198397
y1[1] (closed_form) = 3.49777898014 -1.21378198397
absolute error = 1.5e-14
relative error = 4.051e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.419
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.419
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15391.4MB, alloc=44.3MB, time=200.66
x[1] = 0.4795 1.699
h = 0.003 0.006
y2[1] (numeric) = -0.303582794334 -2.34476446742
y2[1] (closed_form) = -0.303582794334 -2.34476446742
absolute error = 1.801e-14
relative error = 7.619e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.50700814778 -1.21922005686
y1[1] (closed_form) = 3.50700814778 -1.21922005686
absolute error = 1.6e-14
relative error = 4.309e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.479
Order of pole (three term test) = 37.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.479
Order of pole (three term test) = 28.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15439.4MB, alloc=44.3MB, time=201.29
x[1] = 0.4825 1.705
h = 0.0001 0.005
y2[1] (numeric) = -0.318479078475 -2.35615700801
y2[1] (closed_form) = -0.318479078475 -2.35615700801
absolute error = 1.802e-14
relative error = 7.580e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.51717784127 -1.23413756062
y1[1] (closed_form) = 3.51717784127 -1.23413756062
absolute error = 1.5e-14
relative error = 4.024e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.569
Order of pole (three term test) = 37.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.569
Order of pole (three term test) = 28.86 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4826 1.71
h = 0.0001 0.003
y2[1] (numeric) = -0.324919165403 -2.3686483153
y2[1] (closed_form) = -0.324919165403 -2.3686483153
absolute error = 1.805e-14
relative error = 7.548e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.52885766091 -1.24098228127
y1[1] (closed_form) = 3.52885766091 -1.24098228127
absolute error = 1.6e-14
relative error = 4.277e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.645
Order of pole (three term test) = 37.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.645
Order of pole (three term test) = 28.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15487.2MB, alloc=44.3MB, time=201.91
x[1] = 0.4827 1.713
h = 0.001 0.001
y2[1] (numeric) = -0.328901670828 -2.37612105044
y2[1] (closed_form) = -0.328901670828 -2.37612105044
absolute error = 1.900e-14
relative error = 7.922e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.5358421189 -1.24520024748
y1[1] (closed_form) = 3.5358421189 -1.24520024748
absolute error = 1.6e-14
relative error = 4.268e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.691
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.691
Order of pole (three term test) = 28.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15535.2MB, alloc=44.3MB, time=202.53
x[1] = 0.4837 1.714
h = 0.001 0.003
y2[1] (numeric) = -0.332685089745 -2.37741036215
y2[1] (closed_form) = -0.332685089745 -2.37741036215
absolute error = 1.902e-14
relative error = 7.924e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.53688809184 -1.24890780639
y1[1] (closed_form) = 3.53688809184 -1.24890780639
absolute error = 1.603e-14
relative error = 4.274e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.707
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.707
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15583.1MB, alloc=44.3MB, time=203.16
x[1] = 0.4847 1.717
h = 0.0001 0.004
y2[1] (numeric) = -0.338981178979 -2.3837776324
y2[1] (closed_form) = -0.338981178979 -2.3837776324
absolute error = 1.904e-14
relative error = 7.910e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.54269404002 -1.25529589263
y1[1] (closed_form) = 3.54269404002 -1.25529589263
absolute error = 1.6e-14
relative error = 4.257e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.753
Order of pole (three term test) = 37.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.753
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4848 1.721
h = 0.003 0.006
y2[1] (numeric) = -0.344268306034 -2.39384142778
y2[1] (closed_form) = -0.344268306034 -2.39384142778
absolute error = 1.904e-14
relative error = 7.875e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.55211510349 -1.26090126446
y1[1] (closed_form) = 3.55211510349 -1.26090126446
absolute error = 1.6e-14
relative error = 4.245e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.815
Order of pole (three term test) = 37.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.815
Order of pole (three term test) = 28.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15631.0MB, alloc=44.3MB, time=203.78
x[1] = 0.4878 1.727
h = 0.0001 0.005
y2[1] (numeric) = -0.359551433539 -2.40537949502
y2[1] (closed_form) = -0.359551433539 -2.40537949502
absolute error = 2.001e-14
relative error = 8.228e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.56245705931 -1.27621148959
y1[1] (closed_form) = 3.56245705931 -1.27621148959
absolute error = 1.603e-14
relative error = 4.236e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.91
Order of pole (three term test) = 37.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.91
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15678.9MB, alloc=44.3MB, time=204.40
x[1] = 0.4879 1.732
h = 0.0001 0.003
y2[1] (numeric) = -0.366206956777 -2.4180935864
y2[1] (closed_form) = -0.366206956777 -2.4180935864
absolute error = 1.903e-14
relative error = 7.780e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.57437942985 -1.28326704353
y1[1] (closed_form) = 3.57437942985 -1.28326704353
absolute error = 1.7e-14
relative error = 4.476e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.989
Order of pole (three term test) = 37.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.989
Order of pole (three term test) = 28.79 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.488 1.735
h = 0.001 0.001
y2[1] (numeric) = -0.370321069298 -2.42569886843
y2[1] (closed_form) = -0.370321069298 -2.42569886843
absolute error = 1.902e-14
relative error = 7.752e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.58150828701 -1.28761402158
y1[1] (closed_form) = 3.58150828701 -1.28761402158
absolute error = 1.7e-14
relative error = 4.467e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.037
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.037
Order of pole (three term test) = 28.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15726.8MB, alloc=44.3MB, time=205.02
x[1] = 0.489 1.736
h = 0.001 0.003
y2[1] (numeric) = -0.374192617736 -2.42699139108
y2[1] (closed_form) = -0.374192617736 -2.42699139108
absolute error = 1.903e-14
relative error = 7.748e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.58256237593 -1.29141262338
y1[1] (closed_form) = 3.58256237593 -1.29141262338
absolute error = 1.7e-14
relative error = 4.464e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.053
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.053
Order of pole (three term test) = 28.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15774.6MB, alloc=44.3MB, time=205.65
x[1] = 0.49 1.739
h = 0.0001 0.004
y2[1] (numeric) = -0.380662210804 -2.43345325312
y2[1] (closed_form) = -0.380662210804 -2.43345325312
absolute error = 1.901e-14
relative error = 7.717e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.58847561482 -1.29797512061
y1[1] (closed_form) = 3.58847561482 -1.29797512061
absolute error = 1.703e-14
relative error = 4.463e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.102
Order of pole (three term test) = 37.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.102
Order of pole (three term test) = 28.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15822.5MB, alloc=44.3MB, time=206.27
x[1] = 0.4901 1.743
h = 0.003 0.006
y2[1] (numeric) = -0.38612498653 -2.44369628781
y2[1] (closed_form) = -0.38612498653 -2.44369628781
absolute error = 1.904e-14
relative error = 7.695e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.59809156211 -1.30375254414
y1[1] (closed_form) = 3.59809156211 -1.30375254414
absolute error = 1.7e-14
relative error = 4.442e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.167
Order of pole (three term test) = 37.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.167
Order of pole (three term test) = 28.76 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4931 1.749
h = 0.0001 0.005
y2[1] (numeric) = -0.401804616206 -2.45538157787
y2[1] (closed_form) = -0.401804616206 -2.45538157787
absolute error = 2.005e-14
relative error = 8.058e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.60860692478 -1.31946488285
y1[1] (closed_form) = 3.60860692478 -1.31946488285
absolute error = 1.7e-14
relative error = 4.424e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.265
Order of pole (three term test) = 37.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.265
Order of pole (three term test) = 28.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15870.2MB, alloc=44.3MB, time=206.89
x[1] = 0.4932 1.754
h = 0.0001 0.003
y2[1] (numeric) = -0.40868157531 -2.46832269779
y2[1] (closed_form) = -0.40868157531 -2.46832269779
absolute error = 2.001e-14
relative error = 7.999e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.62077563643 -1.32673726738
y1[1] (closed_form) = 3.62077563643 -1.32673726738
absolute error = 1.7e-14
relative error = 4.408e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.348
Order of pole (three term test) = 37.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.348
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15918.0MB, alloc=44.3MB, time=207.52
x[1] = 0.4933 1.757
h = 0.001 0.001
y2[1] (numeric) = -0.412930944332 -2.47606303465
y2[1] (closed_form) = -0.412930944332 -2.47606303465
absolute error = 2.005e-14
relative error = 7.987e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.62805112917 -1.33121690173
y1[1] (closed_form) = 3.62805112917 -1.33121690173
absolute error = 1.703e-14
relative error = 4.407e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.399
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.399
Order of pole (three term test) = 28.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15966.1MB, alloc=44.3MB, time=208.15
x[1] = 0.4943 1.758
h = 0.001 0.003
y2[1] (numeric) = -0.416892688858 -2.47735845462
y2[1] (closed_form) = -0.416892688858 -2.47735845462
absolute error = 2.002e-14
relative error = 7.968e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.62911292875 -1.33510852412
y1[1] (closed_form) = 3.62911292875 -1.33510852412
absolute error = 1.603e-14
relative error = 4.146e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.415
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.415
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4953 1.761
h = 0.0001 0.004
y2[1] (numeric) = -0.423540242415 -2.48391634574
y2[1] (closed_form) = -0.423540242415 -2.48391634574
absolute error = 2.005e-14
relative error = 7.957e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.63513462384 -1.34184980341
y1[1] (closed_form) = 3.63513462384 -1.34184980341
absolute error = 1.703e-14
relative error = 4.395e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.466
Order of pole (three term test) = 37.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.466
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16013.7MB, alloc=44.3MB, time=208.77
x[1] = 0.4954 1.765
h = 0.003 0.006
y2[1] (numeric) = -0.429183546273 -2.49434201576
y2[1] (closed_form) = -0.429183546273 -2.49434201576
absolute error = 2.002e-14
relative error = 7.908e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.64494849169 -1.34780415531
y1[1] (closed_form) = 3.64494849169 -1.34780415531
absolute error = 1.703e-14
relative error = 4.382e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.534
Order of pole (three term test) = 37.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.534
Order of pole (three term test) = 28.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16061.7MB, alloc=44.3MB, time=209.39
x[1] = 0.4984 1.771
h = 0.0001 0.005
y2[1] (numeric) = -0.445269552038 -2.50617619947
y2[1] (closed_form) = -0.445269552038 -2.50617619947
absolute error = 2.101e-14
relative error = 8.255e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.65563839101 -1.36392822358
y1[1] (closed_form) = 3.65563839101 -1.36392822358
absolute error = 1.703e-14
relative error = 4.365e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.637
Order of pole (three term test) = 37.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.637
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16109.5MB, alloc=44.3MB, time=210.01
x[1] = 0.4985 1.776
h = 0.0001 0.003
y2[1] (numeric) = -0.452374100469 -2.51934864425
y2[1] (closed_form) = -0.452374100469 -2.51934864425
absolute error = 2.101e-14
relative error = 8.208e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.6680572957 -1.37142359231
y1[1] (closed_form) = 3.6680572957 -1.37142359231
absolute error = 1.703e-14
relative error = 4.349e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.724
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.724
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4986 1.779
h = 0.001 0.001
y2[1] (numeric) = -0.456762468559 -2.5272265739
y2[1] (closed_form) = -0.456762468559 -2.5272265739
absolute error = 2.002e-14
relative error = 7.796e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.67548169637 -1.3760396221
y1[1] (closed_form) = 3.67548169637 -1.3760396221
absolute error = 1.703e-14
relative error = 4.339e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.776
Order of pole (three term test) = 37.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.776
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16157.3MB, alloc=44.3MB, time=210.63
x[1] = 0.4996 1.78
h = 0.001 0.003
y2[1] (numeric) = -0.460816517537 -2.52852455786
y2[1] (closed_form) = -0.460816517537 -2.52852455786
absolute error = 2.003e-14
relative error = 7.793e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.67655078311 -1.38002628698
y1[1] (closed_form) = 3.67655078311 -1.38002628698
absolute error = 1.603e-14
relative error = 4.082e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.794
Order of pole (three term test) = 37.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.794
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16205.3MB, alloc=44.3MB, time=211.26
x[1] = 0.5006 1.783
h = 0.0001 0.004
y2[1] (numeric) = -0.467646591771 -2.53517991762
y2[1] (closed_form) = -0.467646591771 -2.53517991762
absolute error = 2.001e-14
relative error = 7.762e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.68268210764 -1.3869508262
y1[1] (closed_form) = 3.68268210764 -1.3869508262
absolute error = 1.603e-14
relative error = 4.074e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.847
Order of pole (three term test) = 38.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.847
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16253.4MB, alloc=44.3MB, time=211.88
x[1] = 0.5007 1.787
h = 0.003 0.006
y2[1] (numeric) = -0.473475428123 -2.54579166015
y2[1] (closed_form) = -0.473475428123 -2.54579166015
absolute error = 2.001e-14
relative error = 7.728e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.69269698176 -1.39308710997
y1[1] (closed_form) = 3.69269698176 -1.39308710997
absolute error = 1.603e-14
relative error = 4.062e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.918
Order of pole (three term test) = 38.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.918
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5037 1.793
h = 0.0001 0.005
y2[1] (numeric) = -0.489977903894 -2.55777638144
y2[1] (closed_form) = -0.489977903894 -2.55777638144
absolute error = 2.004e-14
relative error = 7.696e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.70356253107 -1.40963275221
y1[1] (closed_form) = 3.70356253107 -1.40963275221
absolute error = 1.703e-14
relative error = 4.297e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.025
Order of pole (three term test) = 38.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.025
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16300.9MB, alloc=44.3MB, time=212.50
x[1] = 0.5038 1.798
h = 0.0001 0.003
y2[1] (numeric) = -0.497316352826 -2.5711844998
y2[1] (closed_form) = -0.497316352826 -2.5711844998
absolute error = 2.006e-14
relative error = 7.661e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.71623554282 -1.41735741875
y1[1] (closed_form) = 3.71623554282 -1.41735741875
absolute error = 1.703e-14
relative error = 4.282e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.116
Order of pole (three term test) = 38.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.116
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16348.9MB, alloc=44.3MB, time=213.13
x[1] = 0.5039 1.801
h = 0.001 0.001
y2[1] (numeric) = -0.501847558013 -2.57920259052
y2[1] (closed_form) = -0.501847558013 -2.57920259052
absolute error = 1.905e-14
relative error = 7.251e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.72381115982 -1.42211368003
y1[1] (closed_form) = 3.72381115982 -1.42211368003
absolute error = 1.703e-14
relative error = 4.272e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.171
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.171
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16396.8MB, alloc=44.3MB, time=213.76
x[1] = 0.5049 1.802
h = 0.0001 0.004
y2[1] (numeric) = -0.50599606249 -2.58050278477
y2[1] (closed_form) = -0.50599606249 -2.58050278477
absolute error = 1.901e-14
relative error = 7.229e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.72488709138 -1.42619745435
y1[1] (closed_form) = 3.72488709138 -1.42619745435
absolute error = 1.703e-14
relative error = 4.270e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.189
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.189
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.505 1.806
h = 0.003 0.006
y2[1] (numeric) = -0.511986431038 -2.59127977001
y2[1] (closed_form) = -0.511986431038 -2.59127977001
absolute error = 2.001e-14
relative error = 7.576e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.7350797442 -1.4324919994
y1[1] (closed_form) = 3.7350797442 -1.4324919994
absolute error = 1.703e-14
relative error = 4.257e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.263
Order of pole (three term test) = 38.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.263
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16444.6MB, alloc=44.3MB, time=214.38
x[1] = 0.508 1.812
h = 0.0001 0.005
y2[1] (numeric) = -0.528853825573 -2.60340049252
y2[1] (closed_form) = -0.528853825573 -2.60340049252
absolute error = 2.001e-14
relative error = 7.533e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.74610255054 -1.44940646943
y1[1] (closed_form) = 3.74610255054 -1.44940646943
absolute error = 1.811e-14
relative error = 4.509e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.375
Order of pole (three term test) = 38.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.375
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16492.4MB, alloc=44.3MB, time=215.00
x[1] = 0.5081 1.817
h = 0.0001 0.003
y2[1] (numeric) = -0.536395906541 -2.61701788508
y2[1] (closed_form) = -0.536395906541 -2.61701788508
absolute error = 2.001e-14
relative error = 7.490e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.7590003078 -1.45733059711
y1[1] (closed_form) = 3.7590003078 -1.45733059711
absolute error = 1.712e-14
relative error = 4.246e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.469
Order of pole (three term test) = 38.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.469
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5082 1.82
h = 0.001 0.001
y2[1] (numeric) = -0.541051497352 -2.62516046725
y2[1] (closed_form) = -0.541051497352 -2.62516046725
absolute error = 2.101e-14
relative error = 7.837e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.76670969743 -1.46220887309
y1[1] (closed_form) = 3.76670969743 -1.46220887309
absolute error = 1.712e-14
relative error = 4.236e-13 %
Correct digits = 14
memory used=16540.3MB, alloc=44.3MB, time=215.63
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.526
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.526
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5092 1.821
h = 0.001 0.003
y2[1] (numeric) = -0.545283041517 -2.62646342561
y2[1] (closed_form) = -0.545283041517 -2.62646342561
absolute error = 2.105e-14
relative error = 7.846e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.7677923428 -1.46637785212
y1[1] (closed_form) = 3.7677923428 -1.46637785212
absolute error = 1.712e-14
relative error = 4.234e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.545
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.545
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16588.1MB, alloc=44.3MB, time=216.25
x[1] = 0.5102 1.824
h = 0.0001 0.004
y2[1] (numeric) = -0.552464044344 -2.63330629674
y2[1] (closed_form) = -0.552464044344 -2.63330629674
absolute error = 2.101e-14
relative error = 7.807e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.77413312325 -1.47365434959
y1[1] (closed_form) = 3.77413312325 -1.47365434959
absolute error = 1.712e-14
relative error = 4.225e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.602
Order of pole (three term test) = 38.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.602
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16636.0MB, alloc=44.3MB, time=216.87
x[1] = 0.5103 1.828
h = 0.003 0.006
y2[1] (numeric) = -0.558649558255 -2.64427592448
y2[1] (closed_form) = -0.558649558255 -2.64427592448
absolute error = 2.101e-14
relative error = 7.772e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.78453271859 -1.48014044657
y1[1] (closed_form) = 3.78453271859 -1.48014044657
absolute error = 1.712e-14
relative error = 4.212e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.679
Order of pole (three term test) = 38.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.679
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5133 1.834
h = 0.0001 0.005
y2[1] (numeric) = -0.575952789159 -2.65655029309
y2[1] (closed_form) = -0.575952789159 -2.65655029309
absolute error = 2.001e-14
relative error = 7.361e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.79573332059 -1.49749542029
y1[1] (closed_form) = 3.79573332059 -1.49749542029
absolute error = 1.811e-14
relative error = 4.438e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.796
Order of pole (three term test) = 38.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.796
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16683.8MB, alloc=44.3MB, time=217.49
x[1] = 0.5134 1.839
h = 0.0001 0.003
y2[1] (numeric) = -0.583740894099 -2.67041167214
y2[1] (closed_form) = -0.583740894099 -2.67041167214
absolute error = 2.102e-14
relative error = 7.690e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.80889271409 -1.5056609845
y1[1] (closed_form) = 3.80889271409 -1.5056609845
absolute error = 1.726e-14
relative error = 4.215e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.895
Order of pole (three term test) = 38.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.895
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16731.6MB, alloc=44.3MB, time=218.12
x[1] = 0.5135 1.842
h = 0.001 0.001
y2[1] (numeric) = -0.588546694386 -2.67869932449
y2[1] (closed_form) = -0.588546694386 -2.67869932449
absolute error = 2.101e-14
relative error = 7.661e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.81675776056 -1.51068686727
y1[1] (closed_form) = 3.81675776056 -1.51068686727
absolute error = 1.726e-14
relative error = 4.205e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.954
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.954
Order of pole (three term test) = 28.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16779.6MB, alloc=44.3MB, time=218.74
x[1] = 0.5145 1.843
h = 0.001 0.003
y2[1] (numeric) = -0.592876818148 -2.68000380539
y2[1] (closed_form) = -0.592876818148 -2.68000380539
absolute error = 2.103e-14
relative error = 7.661e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.81784640109 -1.51495693041
y1[1] (closed_form) = 3.81784640109 -1.51495693041
absolute error = 1.726e-14
relative error = 4.203e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.974
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.974
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5155 1.846
h = 0.0001 0.004
y2[1] (numeric) = -0.600253963627 -2.68694833093
y2[1] (closed_form) = -0.600253963627 -2.68694833093
absolute error = 2.103e-14
relative error = 7.640e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.82430026333 -1.52243009444
y1[1] (closed_form) = 3.82430026333 -1.52243009444
absolute error = 1.712e-14
relative error = 4.159e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.03
Order of pole (three term test) = 38.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.03
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16827.3MB, alloc=44.3MB, time=219.36
x[1] = 0.5156 1.85
h = 0.003 0.006
y2[1] (numeric) = -0.606640001328 -2.69811415991
y2[1] (closed_form) = -0.606640001328 -2.69811415991
absolute error = 2.204e-14
relative error = 7.971e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.83491002992 -1.52911312588
y1[1] (closed_form) = 3.83491002992 -1.52911312588
absolute error = 1.726e-14
relative error = 4.181e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.11
Order of pole (three term test) = 38.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.11
Order of pole (three term test) = 28.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16875.3MB, alloc=44.3MB, time=219.98
x[1] = 0.5186 1.856
h = 0.0001 0.005
y2[1] (numeric) = -0.624389820139 -2.71054373536
y2[1] (closed_form) = -0.624389820139 -2.71054373536
absolute error = 2.101e-14
relative error = 7.554e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.84628948669 -1.54691912799
y1[1] (closed_form) = 3.84628948669 -1.54691912799
absolute error = 1.712e-14
relative error = 4.129e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.24
Order of pole (three term test) = 38.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.24
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16923.1MB, alloc=44.3MB, time=220.61
x[1] = 0.5187 1.861
h = 0.0001 0.003
y2[1] (numeric) = -0.632430732545 -2.72465360429
y2[1] (closed_form) = -0.632430732545 -2.72465360429
absolute error = 2.104e-14
relative error = 7.522e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.85971461176 -1.5553329206
y1[1] (closed_form) = 3.85971461176 -1.5553329206
absolute error = 1.726e-14
relative error = 4.148e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.34
Order of pole (three term test) = 38.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.34
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5188 1.864
h = 0.001 0.001
y2[1] (numeric) = -0.637390866209 -2.73308898455
y2[1] (closed_form) = -0.637390866209 -2.73308898455
absolute error = 2.201e-14
relative error = 7.844e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.86773772881 -1.56051053584
y1[1] (closed_form) = 3.86773772881 -1.56051053584
absolute error = 1.726e-14
relative error = 4.139e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.4
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.4
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16970.8MB, alloc=44.3MB, time=221.23
x[1] = 0.5198 1.865
h = 0.001 0.003
y2[1] (numeric) = -0.641821847998 -2.73439457288
y2[1] (closed_form) = -0.641821847998 -2.73439457288
absolute error = 2.102e-14
relative error = 7.482e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.86883186496 -1.5648838838
y1[1] (closed_form) = 3.86883186496 -1.5648838838
absolute error = 1.726e-14
relative error = 4.136e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.42
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.42
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17018.7MB, alloc=44.3MB, time=221.85
x[1] = 0.5208 1.868
h = 0.0001 0.004
y2[1] (numeric) = -0.649400119124 -2.74144219853
y2[1] (closed_form) = -0.649400119124 -2.74144219853
absolute error = 2.105e-14
relative error = 7.470e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.87540000859 -1.57255862673
y1[1] (closed_form) = 3.87540000859 -1.57255862673
absolute error = 1.726e-14
relative error = 4.128e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.49
Order of pole (three term test) = 38.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.49
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17066.8MB, alloc=44.3MB, time=222.48
x[1] = 0.5209 1.872
h = 0.003 0.006
y2[1] (numeric) = -0.655992196226 -2.75280783015
y2[1] (closed_form) = -0.655992196226 -2.75280783015
absolute error = 2.105e-14
relative error = 7.437e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.88622322507 -1.57944411397
y1[1] (closed_form) = 3.88622322507 -1.57944411397
absolute error = 1.726e-14
relative error = 4.115e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.57
Order of pole (three term test) = 38.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.57
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5239 1.878
h = 0.0001 0.005
y2[1] (numeric) = -0.674199594287 -2.7653941398
y2[1] (closed_form) = -0.674199594287 -2.7653941398
absolute error = 2.103e-14
relative error = 7.390e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.89778257209 -1.59771191652
y1[1] (closed_form) = 3.89778257209 -1.59771191652
absolute error = 1.712e-14
relative error = 4.063e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.7
Order of pole (three term test) = 38.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.7
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17114.4MB, alloc=44.3MB, time=223.10
x[1] = 0.524 1.883
h = 0.0001 0.003
y2[1] (numeric) = -0.682500270865 -2.77975705634
y2[1] (closed_form) = -0.682500270865 -2.77975705634
absolute error = 2.104e-14
relative error = 7.351e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.91147758729 -1.60638090454
y1[1] (closed_form) = 3.91147758729 -1.60638090454
absolute error = 1.712e-14
relative error = 4.048e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 39.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.8
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17162.3MB, alloc=44.3MB, time=223.72
x[1] = 0.5241 1.886
h = 0.001 0.001
y2[1] (numeric) = -0.687618966624 -2.78834285361
y2[1] (closed_form) = -0.687618966624 -2.78834285361
absolute error = 2.102e-14
relative error = 7.319e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.91966122533 -1.61171448399
y1[1] (closed_form) = 3.91966122533 -1.61171448399
absolute error = 1.712e-14
relative error = 4.039e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.87
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.87
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17210.3MB, alloc=44.3MB, time=224.35
x[1] = 0.5251 1.887
h = 0.001 0.003
y2[1] (numeric) = -0.692153131112 -2.78964911122
y2[1] (closed_form) = -0.692153131112 -2.78964911122
absolute error = 2.103e-14
relative error = 7.316e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 3.92076033601 -1.61619336584
y1[1] (closed_form) = 3.92076033601 -1.61619336584
absolute error = 1.712e-14
relative error = 4.036e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.89
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.89
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5261 1.89
h = 0.0001 0.004
y2[1] (numeric) = -0.699937626624 -2.79680128276
y2[1] (closed_form) = -0.699937626624 -2.79680128276
absolute error = 2.201e-14
relative error = 7.636e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.9274439657 -1.62407471858
y1[1] (closed_form) = 3.9274439657 -1.62407471858
absolute error = 1.712e-14
relative error = 4.028e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.96
Order of pole (three term test) = 39.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.96
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17258.1MB, alloc=44.3MB, time=224.97
x[1] = 0.5262 1.894
h = 0.003 0.006
y2[1] (numeric) = -0.70674139927 -2.8083703615
y2[1] (closed_form) = -0.70674139927 -2.8083703615
absolute error = 2.103e-14
relative error = 7.263e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.9384839608 -1.63116832502
y1[1] (closed_form) = 3.9384839608 -1.63116832502
absolute error = 1.712e-14
relative error = 4.015e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.04
Order of pole (three term test) = 39.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.04
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17305.9MB, alloc=44.3MB, time=225.60
x[1] = 0.5292 1.9
h = 0.0001 0.005
y2[1] (numeric) = -0.725417613101 -2.82111489744
y2[1] (closed_form) = -0.725417613101 -2.82111489744
absolute error = 2.203e-14
relative error = 7.562e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.95022420787 -1.64990895256
y1[1] (closed_form) = 3.95022420787 -1.64990895256
absolute error = 1.712e-14
relative error = 3.998e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.18
Order of pole (three term test) = 39.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.18
Order of pole (three term test) = 28.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17353.7MB, alloc=44.3MB, time=226.22
x[1] = 0.5293 1.905
h = 0.0001 0.003
y2[1] (numeric) = -0.733985188005 -2.8357354741
y2[1] (closed_form) = -0.733985188005 -2.8357354741
absolute error = 2.103e-14
relative error = 7.181e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 3.96419333531 -1.65884028232
y1[1] (closed_form) = 3.96419333531 -1.65884028232
absolute error = 1.811e-14
relative error = 4.214e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.29
Order of pole (three term test) = 39.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.29
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5294 1.908
h = 0.001 0.001
y2[1] (numeric) = -0.73926678195 -2.84447440907
y2[1] (closed_form) = -0.73926678195 -2.84447440907
absolute error = 2.205e-14
relative error = 7.503e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 3.97253998156 -1.66433416623
y1[1] (closed_form) = 3.97253998156 -1.66433416623
absolute error = 1.811e-14
relative error = 4.205e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.36
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.36
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17401.6MB, alloc=44.3MB, time=226.84
x[1] = 0.5304 1.909
h = 0.0001 0.004
y2[1] (numeric) = -0.743906501008 -2.84578087407
y2[1] (closed_form) = -0.743906501008 -2.84578087407
absolute error = 2.205e-14
relative error = 7.497e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 3.97364352332 -1.66892088033
y1[1] (closed_form) = 3.97364352332 -1.66892088033
absolute error = 1.712e-14
relative error = 3.972e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.38
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.38
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17449.5MB, alloc=44.3MB, time=227.47
x[1] = 0.5305 1.913
h = 0.003 0.006
y2[1] (numeric) = -0.750894649895 -2.85753064089
y2[1] (closed_form) = -0.750894649895 -2.85753064089
absolute error = 2.207e-14
relative error = 7.471e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 3.98487539181 -1.67619563777
y1[1] (closed_form) = 3.98487539181 -1.67619563777
absolute error = 1.712e-14
relative error = 3.960e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.47
Order of pole (three term test) = 39.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.47
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5335 1.919
h = 0.0001 0.005
y2[1] (numeric) = -0.769981685553 -2.87041831057
y2[1] (closed_form) = -0.769981685553 -2.87041831057
absolute error = 2.302e-14
relative error = 7.746e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 3.99677795485 -1.6953501114
y1[1] (closed_form) = 3.99677795485 -1.6953501114
absolute error = 1.811e-14
relative error = 4.172e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.61
Order of pole (three term test) = 39.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.61
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17497.2MB, alloc=44.3MB, time=228.08
x[1] = 0.5336 1.924
h = 0.0001 0.003
y2[1] (numeric) = -0.778781704111 -2.88526770653
y2[1] (closed_form) = -0.778781704111 -2.88526770653
absolute error = 2.203e-14
relative error = 7.371e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.01098970289 -1.70450978391
y1[1] (closed_form) = 4.01098970289 -1.70450978391
absolute error = 1.811e-14
relative error = 4.156e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.73
Order of pole (three term test) = 39.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.73
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17545.0MB, alloc=44.3MB, time=228.70
x[1] = 0.5337 1.927
h = 0.001 0.001
y2[1] (numeric) = -0.784205202643 -2.89414267305
y2[1] (closed_form) = -0.784205202643 -2.89414267305
absolute error = 2.203e-14
relative error = 7.348e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.01948066303 -1.71014323015
y1[1] (closed_form) = 4.01948066303 -1.71014323015
absolute error = 1.811e-14
relative error = 4.146e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.8
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.8
Order of pole (three term test) = 28.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17592.9MB, alloc=44.3MB, time=229.34
x[1] = 0.5347 1.928
h = 0.001 0.003
y2[1] (numeric) = -0.788937721115 -2.8954502247
y2[1] (closed_form) = -0.788937721115 -2.8954502247
absolute error = 2.207e-14
relative error = 7.355e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.0205888888 -1.71482459787
y1[1] (closed_form) = 4.0205888888 -1.71482459787
absolute error = 1.811e-14
relative error = 4.143e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.82
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.82
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5357 1.931
h = 0.0001 0.004
y2[1] (numeric) = -0.797118644147 -2.90280338338
y2[1] (closed_form) = -0.797118644147 -2.90280338338
absolute error = 2.207e-14
relative error = 7.333e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.02749324057 -1.72310280025
y1[1] (closed_form) = 4.02749324057 -1.72310280025
absolute error = 1.811e-14
relative error = 4.134e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.89
Order of pole (three term test) = 39.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.89
Order of pole (three term test) = 28.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17640.6MB, alloc=44.3MB, time=229.96
x[1] = 0.5358 1.935
h = 0.003 0.006
y2[1] (numeric) = -0.804329354546 -2.91476356601
y2[1] (closed_form) = -0.804329354546 -2.91476356601
absolute error = 2.303e-14
relative error = 7.615e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.0389482873 -1.73059656385
y1[1] (closed_form) = 4.0389482873 -1.73059656385
absolute error = 1.811e-14
relative error = 4.122e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.99
Order of pole (three term test) = 39.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.99
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17688.5MB, alloc=44.3MB, time=230.58
x[1] = 0.5388 1.941
h = 0.0001 0.005
y2[1] (numeric) = -0.823906769178 -2.9278122789
y2[1] (closed_form) = -0.823906769178 -2.9278122789
absolute error = 2.305e-14
relative error = 7.578e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.0510336924 -1.75024505552
y1[1] (closed_form) = 4.0510336924 -1.75024505552
absolute error = 1.910e-14
relative error = 4.329e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.13
Order of pole (three term test) = 39.71 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.13
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17736.5MB, alloc=44.3MB, time=231.20
x[1] = 0.5389 1.946
h = 0.0001 0.003
y2[1] (numeric) = -0.832987391733 -2.94292815528
y2[1] (closed_form) = -0.832987391733 -2.94292815528
absolute error = 2.304e-14
relative error = 7.532e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.06552766938 -1.75968080709
y1[1] (closed_form) = 4.06552766938 -1.75968080709
absolute error = 1.825e-14
relative error = 4.119e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.26
Order of pole (three term test) = 39.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.26
Order of pole (three term test) = 28.8 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.539 1.949
h = 0.001 0.001
y2[1] (numeric) = -0.838582118356 -2.95196146174
y2[1] (closed_form) = -0.838582118356 -2.95196146174
absolute error = 2.304e-14
relative error = 7.507e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.07418641914 -1.76548290105
y1[1] (closed_form) = 4.07418641914 -1.76548290105
absolute error = 1.825e-14
relative error = 4.110e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.33
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.33
Order of pole (three term test) = 28.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17784.3MB, alloc=44.3MB, time=231.83
x[1] = 0.54 1.95
h = 0.001 0.003
y2[1] (numeric) = -0.843424740074 -2.95326832507
y2[1] (closed_form) = -0.843424740074 -2.95326832507
absolute error = 2.308e-14
relative error = 7.514e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.0752980314 -1.77027651919
y1[1] (closed_form) = 4.0752980314 -1.77027651919
absolute error = 1.811e-14
relative error = 4.076e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.35
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.35
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17832.2MB, alloc=44.3MB, time=232.45
x[1] = 0.541 1.953
h = 0.0001 0.004
y2[1] (numeric) = -0.851827119818 -2.96073022699
y2[1] (closed_form) = -0.851827119818 -2.96073022699
absolute error = 2.402e-14
relative error = 7.797e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.08232140286 -1.77877638708
y1[1] (closed_form) = 4.08232140286 -1.77877638708
absolute error = 1.811e-14
relative error = 4.067e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.43
Order of pole (three term test) = 39.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.43
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17880.1MB, alloc=44.3MB, time=233.08
x[1] = 0.5411 1.957
h = 0.003 0.006
y2[1] (numeric) = -0.859266468583 -2.97290459669
y2[1] (closed_form) = -0.859266468583 -2.97290459669
absolute error = 2.406e-14
relative error = 7.775e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.09400310278 -1.78649524493
y1[1] (closed_form) = 4.09400310278 -1.78649524493
absolute error = 1.903e-14
relative error = 4.259e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.53
Order of pole (three term test) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.53
Order of pole (three term test) = 28.82 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5441 1.963
h = 0.0001 0.005
y2[1] (numeric) = -0.879346231169 -2.98611573619
y2[1] (closed_form) = -0.879346231169 -2.98611573619
absolute error = 2.405e-14
relative error = 7.725e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.10627227759 -1.80664953138
y1[1] (closed_form) = 4.10627227759 -1.80664953138
absolute error = 1.910e-14
relative error = 4.259e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.68
Order of pole (three term test) = 39.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.68
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17927.8MB, alloc=44.3MB, time=233.70
x[1] = 0.5442 1.968
h = 0.0001 0.003
y2[1] (numeric) = -0.888715123074 -3.00150286692
y2[1] (closed_form) = -0.888715123074 -3.00150286692
absolute error = 2.506e-14
relative error = 8.005e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.12105289106 -1.81636904422
y1[1] (closed_form) = 4.12105289106 -1.81636904422
absolute error = 1.903e-14
relative error = 4.225e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.81
Order of pole (three term test) = 40.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.81
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17975.7MB, alloc=44.3MB, time=234.32
x[1] = 0.5443 1.971
h = 0.001 0.001
y2[1] (numeric) = -0.894485735279 -3.01069732701
y2[1] (closed_form) = -0.894485735279 -3.01069732701
absolute error = 2.506e-14
relative error = 7.978e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.12988202499 -1.8223444506
y1[1] (closed_form) = 4.12988202499 -1.8223444506
absolute error = 1.910e-14
relative error = 4.232e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.88
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.88
Order of pole (three term test) = 28.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18023.7MB, alloc=44.3MB, time=234.94
x[1] = 0.5453 1.972
h = 0.001 0.003
y2[1] (numeric) = -0.899440972887 -3.01200296845
y2[1] (closed_form) = -0.899440972887 -3.01200296845
absolute error = 2.409e-14
relative error = 7.664e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.1309964126 -1.82725276392
y1[1] (closed_form) = 4.1309964126 -1.82725276392
absolute error = 1.903e-14
relative error = 4.212e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.91
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.91
Order of pole (three term test) = 28.9 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5463 1.975
h = 0.0001 0.004
y2[1] (numeric) = -0.908070380428 -3.01957505609
y2[1] (closed_form) = -0.908070380428 -3.01957505609
absolute error = 2.507e-14
relative error = 7.951e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.13814002356 -1.83597981057
y1[1] (closed_form) = 4.13814002356 -1.83597981057
absolute error = 1.910e-14
relative error = 4.220e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.99
Order of pole (three term test) = 40.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.99
Order of pole (three term test) = 28.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18071.3MB, alloc=44.3MB, time=235.56
x[1] = 0.5464 1.979
h = 0.003 0.006
y2[1] (numeric) = -0.915744598606 -3.03196742845
y2[1] (closed_form) = -0.915744598606 -3.03196742845
absolute error = 2.503e-14
relative error = 7.904e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.15005190244 -1.84393000626
y1[1] (closed_form) = 4.15005190244 -1.84393000626
absolute error = 2.010e-14
relative error = 4.426e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.09
Order of pole (three term test) = 40.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.09
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18119.3MB, alloc=44.3MB, time=236.19
x[1] = 0.5494 1.985
h = 0.0001 0.005
y2[1] (numeric) = -0.93633894504 -3.04534233485
y2[1] (closed_form) = -0.93633894504 -3.04534233485
absolute error = 2.503e-14
relative error = 7.856e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.16250574041 -1.86460213767
y1[1] (closed_form) = 4.16250574041 -1.86460213767
absolute error = 2.010e-14
relative error = 4.407e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.25
Order of pole (three term test) = 40.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.25
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18167.1MB, alloc=44.3MB, time=236.81
x[1] = 0.5495 1.99
h = 0.0001 0.003
y2[1] (numeric) = -0.946003966337 -3.06100555027
y2[1] (closed_form) = -0.946003966337 -3.06100555027
absolute error = 2.503e-14
relative error = 7.814e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.17757746242 -1.87461329023
y1[1] (closed_form) = 4.17757746242 -1.87461329023
absolute error = 2.002e-14
relative error = 4.373e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.38
Order of pole (three term test) = 40.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.38
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5496 1.993
h = 0.001 0.001
y2[1] (numeric) = -0.951955239389 -3.07036401017
y2[1] (closed_form) = -0.951955239389 -3.07036401017
absolute error = 2.507e-14
relative error = 7.800e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.18657961237 -1.88076679246
y1[1] (closed_form) = 4.18657961237 -1.88076679246
absolute error = 2.002e-14
relative error = 4.363e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.46
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.46
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18214.9MB, alloc=44.3MB, time=237.43
x[1] = 0.5506 1.994
h = 0.001 0.003
y2[1] (numeric) = -0.957025656593 -3.07166786934
y2[1] (closed_form) = -0.957025656593 -3.07166786934
absolute error = 2.506e-14
relative error = 7.791e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.1876961387 -1.88579229866
y1[1] (closed_form) = 4.1876961387 -1.88579229866
absolute error = 1.9e-14
relative error = 4.137e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.49
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.49
Order of pole (three term test) = 29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18262.7MB, alloc=44.3MB, time=238.06
x[1] = 0.5516 1.997
h = 0.0001 0.004
y2[1] (numeric) = -0.965887792219 -3.07935158244
y2[1] (closed_form) = -0.965887792219 -3.07935158244
absolute error = 2.408e-14
relative error = 7.460e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.19496121079 -1.89475216896
y1[1] (closed_form) = 4.19496121079 -1.89475216896
absolute error = 1.9e-14
relative error = 4.128e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.57
Order of pole (three term test) = 40.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.57
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5517 2.001
h = 0.003 0.006
y2[1] (numeric) = -0.973803268782 -3.09196581766
y2[1] (closed_form) = -0.973803268782 -3.09196581766
absolute error = 2.408e-14
relative error = 7.429e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.2071068454 -1.90294010523
y1[1] (closed_form) = 4.2071068454 -1.90294010523
absolute error = 2.0e-14
relative error = 4.331e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.68
Order of pole (three term test) = 40.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.68
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18310.6MB, alloc=44.3MB, time=238.68
x[1] = 0.5547 2.007
h = 0.0001 0.005
y2[1] (numeric) = -0.99492470776 -3.10550578593
y2[1] (closed_form) = -0.99492470776 -3.10550578593
absolute error = 2.406e-14
relative error = 7.378e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.21974620341 -1.92414241094
y1[1] (closed_form) = 4.21974620341 -1.92414241094
absolute error = 2.002e-14
relative error = 4.318e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.84
Order of pole (three term test) = 40.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.84
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18358.2MB, alloc=44.3MB, time=239.30
x[1] = 0.5548 2.012
h = 0.0001 0.003
y2[1] (numeric) = -1.00489391789 -3.12144997321
y2[1] (closed_form) = -1.00489391789 -3.12144997321
absolute error = 2.408e-14
relative error = 7.344e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.23511357073 -1.93445328254
y1[1] (closed_form) = 4.23511357073 -1.93445328254
absolute error = 2.002e-14
relative error = 4.301e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.98
Order of pole (three term test) = 40.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.98
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18406.3MB, alloc=44.3MB, time=239.92
x[1] = 0.5549 2.015
h = 0.001 0.001
y2[1] (numeric) = -1.01103074767 -3.13097531169
y2[1] (closed_form) = -1.01103074767 -3.13097531169
absolute error = 2.408e-14
relative error = 7.320e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.24429140587 -1.94078978559
y1[1] (closed_form) = 4.24429140587 -1.94078978559
absolute error = 2.102e-14
relative error = 4.505e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.07
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.07
Order of pole (three term test) = 29.11 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5559 2.016
h = 0.0001 0.004
y2[1] (numeric) = -1.01621896027 -3.13227680055
y2[1] (closed_form) = -1.01621896027 -3.13227680055
absolute error = 2.408e-14
relative error = 7.313e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.24540940793 -1.94593503632
y1[1] (closed_form) = 4.24540940793 -1.94593503632
absolute error = 2.102e-14
relative error = 4.502e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.1
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.1
Order of pole (three term test) = 29.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18454.0MB, alloc=44.3MB, time=240.54
x[1] = 0.556 2.02
h = 0.003 0.006
y2[1] (numeric) = -1.02434463728 -3.14508811377
y2[1] (closed_form) = -1.02434463728 -3.14508811377
absolute error = 2.402e-14
relative error = 7.262e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.25776209368 -1.95433001975
y1[1] (closed_form) = 4.25776209368 -1.95433001975
absolute error = 2.102e-14
relative error = 4.488e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.21
Order of pole (three term test) = 40.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.21
Order of pole (three term test) = 29.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18501.9MB, alloc=44.3MB, time=241.17
x[1] = 0.559 2.026
h = 0.0001 0.005
y2[1] (numeric) = -1.04592802297 -3.1587776491
y2[1] (closed_form) = -1.04592802297 -3.1587776491
absolute error = 2.402e-14
relative error = 7.219e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.27056831816 -1.97599654921
y1[1] (closed_form) = 4.27056831816 -1.97599654921
absolute error = 2.102e-14
relative error = 4.468e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.38
Order of pole (three term test) = 40.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.38
Order of pole (three term test) = 29.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18549.8MB, alloc=44.3MB, time=241.80
x[1] = 0.5591 2.031
h = 0.0001 0.003
y2[1] (numeric) = -1.05616225107 -3.17497140266
y2[1] (closed_form) = -1.05616225107 -3.17497140266
absolute error = 2.502e-14
relative error = 7.478e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.28619755461 -1.98656843903
y1[1] (closed_form) = 4.28619755461 -1.98656843903
absolute error = 2.102e-14
relative error = 4.450e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.53
Order of pole (three term test) = 40.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.53
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5592 2.034
h = 0.001 0.001
y2[1] (numeric) = -1.06246078148 -3.18464500699
y2[1] (closed_form) = -1.06246078148 -3.18464500699
absolute error = 2.502e-14
relative error = 7.453e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.2955310414 -1.99306434906
y1[1] (closed_form) = 4.2955310414 -1.99306434906
absolute error = 2.202e-14
relative error = 4.651e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.61
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.61
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18597.6MB, alloc=44.3MB, time=242.42
x[1] = 0.5602 2.035
h = 0.001 0.003
y2[1] (numeric) = -1.06775256195 -3.18594540945
y2[1] (closed_form) = -1.06775256195 -3.18594540945
absolute error = 2.402e-14
relative error = 7.149e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.29665123082 -1.99831475075
y1[1] (closed_form) = 4.29665123082 -1.99831475075
absolute error = 2.202e-14
relative error = 4.648e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.64
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.64
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18645.4MB, alloc=44.3MB, time=243.04
x[1] = 0.5612 2.038
h = 0.0001 0.004
y2[1] (numeric) = -1.07706200658 -3.19384359015
y2[1] (closed_form) = -1.07706200658 -3.19384359015
absolute error = 2.408e-14
relative error = 7.145e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.30414850674 -2.00772185709
y1[1] (closed_form) = 4.30414850674 -2.00772185709
absolute error = 2.2e-14
relative error = 4.632e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.73
Order of pole (three term test) = 41.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.73
Order of pole (three term test) = 29.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18693.3MB, alloc=44.3MB, time=243.66
x[1] = 0.5613 2.042
h = 0.003 0.006
y2[1] (numeric) = -1.08544121655 -3.20688414955
y2[1] (closed_form) = -1.08544121655 -3.20688414955
absolute error = 2.508e-14
relative error = 7.408e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.31674182085 -2.01636688756
y1[1] (closed_form) = 4.31674182085 -2.01636688756
absolute error = 2.2e-14
relative error = 4.618e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.85
Order of pole (three term test) = 41.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.85
Order of pole (three term test) = 29.3 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5643 2.048
h = 0.0001 0.005
y2[1] (numeric) = -1.10757570324 -3.2207411846
y2[1] (closed_form) = -1.10757570324 -3.2207411846
absolute error = 2.408e-14
relative error = 7.071e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.3297352089 -2.03858728735
y1[1] (closed_form) = 4.3297352089 -2.03858728735
absolute error = 2.202e-14
relative error = 4.602e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.03
Order of pole (three term test) = 41.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.03
Order of pole (three term test) = 29.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18741.0MB, alloc=44.3MB, time=244.28
x[1] = 0.5644 2.053
h = 0.0001 0.003
y2[1] (numeric) = -1.11812960437 -3.2372252581
y2[1] (closed_form) = -1.11812960437 -3.2372252581
absolute error = 2.408e-14
relative error = 7.032e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.34566880747 -2.04947442494
y1[1] (closed_form) = 4.34566880747 -2.04947442494
absolute error = 2.302e-14
relative error = 4.791e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.18
Order of pole (three term test) = 41.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.18
Order of pole (three term test) = 29.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18788.8MB, alloc=44.3MB, time=244.91
x[1] = 0.5645 2.056
h = 0.001 0.001
y2[1] (numeric) = -1.12462309739 -3.24707124707
y2[1] (closed_form) = -1.12462309739 -3.24707124707
absolute error = 2.508e-14
relative error = 7.298e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.3551831078 -2.05616276333
y1[1] (closed_form) = 4.3551831078 -2.05616276333
absolute error = 2.302e-14
relative error = 4.780e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.27
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.27
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18836.8MB, alloc=44.3MB, time=245.53
x[1] = 0.5655 2.057
h = 0.001 0.003
y2[1] (numeric) = -1.13003769077 -3.24836814098
y2[1] (closed_form) = -1.13003769077 -3.24836814098
absolute error = 2.408e-14
relative error = 7.002e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.35630349799 -2.06153781323
y1[1] (closed_form) = 4.35630349799 -2.06153781323
absolute error = 2.402e-14
relative error = 4.984e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.3
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.3
Order of pole (three term test) = 29.44 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5665 2.06
h = 0.0001 0.004
y2[1] (numeric) = -1.13959689371 -3.25638211815
y2[1] (closed_form) = -1.13959689371 -3.25638211815
absolute error = 2.408e-14
relative error = 6.981e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.36392580584 -2.07119462999
y1[1] (closed_form) = 4.36392580584 -2.07119462999
absolute error = 2.302e-14
relative error = 4.766e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.39
Order of pole (three term test) = 41.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.39
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18884.5MB, alloc=44.3MB, time=246.15
x[1] = 0.5666 2.064
h = 0.003 0.006
y2[1] (numeric) = -1.1482364982 -3.26965591504
y2[1] (closed_form) = -1.1482364982 -3.26965591504
absolute error = 2.408e-14
relative error = 6.950e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.37676347372 -2.08009658595
y1[1] (closed_form) = 4.37676347372 -2.08009658595
absolute error = 2.402e-14
relative error = 4.957e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.52
Order of pole (three term test) = 41.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.52
Order of pole (three term test) = 29.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18932.4MB, alloc=44.3MB, time=246.78
x[1] = 0.5696 2.07
h = 0.0001 0.005
y2[1] (numeric) = -1.17093540923 -3.2836816054
y2[1] (closed_form) = -1.17093540923 -3.2836816054
absolute error = 2.408e-14
relative error = 6.908e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.38994476712 -2.10288401714
y1[1] (closed_form) = 4.38994476712 -2.10288401714
absolute error = 2.408e-14
relative error = 4.948e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.7
Order of pole (three term test) = 41.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.7
Order of pole (three term test) = 29.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18980.2MB, alloc=44.3MB, time=247.40
x[1] = 0.5697 2.075
h = 0.0001 0.003
y2[1] (numeric) = -1.18181763952 -3.30046105296
y2[1] (closed_form) = -1.18181763952 -3.30046105296
absolute error = 2.508e-14
relative error = 7.154e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.40618745323 -2.1140950822
y1[1] (closed_form) = 4.40618745323 -2.1140950822
absolute error = 2.408e-14
relative error = 4.928e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.86
Order of pole (three term test) = 41.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.86
Order of pole (three term test) = 29.61 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5698 2.078
h = 0.001 0.001
y2[1] (numeric) = -1.18851135195 -3.31048240117
y2[1] (closed_form) = -1.18851135195 -3.31048240117
absolute error = 2.502e-14
relative error = 7.113e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.41588534504 -2.12098111721
y1[1] (closed_form) = 4.41588534504 -2.12098111721
absolute error = 2.408e-14
relative error = 4.916e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.96
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.96
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19028.1MB, alloc=44.3MB, time=248.02
x[1] = 0.5708 2.079
h = 0.001 0.003
y2[1] (numeric) = -1.19405152932 -3.31177511504
y2[1] (closed_form) = -1.19405152932 -3.31177511504
absolute error = 2.402e-14
relative error = 6.823e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.41700519327 -2.12648352722
y1[1] (closed_form) = 4.41700519327 -2.12648352722
absolute error = 2.408e-14
relative error = 4.913e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.99
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.99
Order of pole (three term test) = 29.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19075.9MB, alloc=44.3MB, time=248.64
x[1] = 0.5718 2.082
h = 0.0001 0.004
y2[1] (numeric) = -1.20386671783 -3.31990631307
y2[1] (closed_form) = -1.20386671783 -3.31990631307
absolute error = 2.408e-14
relative error = 6.820e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.42475375608 -2.13639623483
y1[1] (closed_form) = 4.42475375608 -2.13639623483
absolute error = 2.518e-14
relative error = 5.125e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.08
Order of pole (three term test) = 41.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.08
Order of pole (three term test) = 29.69 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5719 2.086
h = 0.003 0.006
y2[1] (numeric) = -1.21277375154 -3.33341738436
y2[1] (closed_form) = -1.21277375154 -3.33341738436
absolute error = 2.408e-14
relative error = 6.789e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.43783955463 -2.14556216886
y1[1] (closed_form) = 4.43783955463 -2.14556216886
absolute error = 2.518e-14
relative error = 5.108e-13 %
Correct digits = 14
memory used=19124.0MB, alloc=44.3MB, time=249.27
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.21
Order of pole (three term test) = 41.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.21
Order of pole (three term test) = 29.71 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5749 2.092
h = 0.0001 0.005
y2[1] (numeric) = -1.23605070687 -3.34761283087
y2[1] (closed_form) = -1.23605070687 -3.34761283087
absolute error = 2.402e-14
relative error = 6.731e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.45120944861 -2.16893009487
y1[1] (closed_form) = 4.45120944861 -2.16893009487
absolute error = 2.617e-14
relative error = 5.286e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.41
Order of pole (three term test) = 41.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.41
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19171.6MB, alloc=44.3MB, time=249.89
x[1] = 0.575 2.097
h = 0.0001 0.003
y2[1] (numeric) = -1.24727014106 -3.36469276468
y2[1] (closed_form) = -1.24727014106 -3.36469276468
absolute error = 2.309e-14
relative error = 6.434e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.46776601303 -2.18047398685
y1[1] (closed_form) = 4.46776601303 -2.18047398685
absolute error = 2.518e-14
relative error = 5.065e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.57
Order of pole (three term test) = 42.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.57
Order of pole (three term test) = 29.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19219.5MB, alloc=44.3MB, time=250.51
x[1] = 0.5751 2.1
h = 0.001 0.001
y2[1] (numeric) = -1.25416946186 -3.37489248002
y2[1] (closed_form) = -1.25416946186 -3.37489248002
absolute error = 2.309e-14
relative error = 6.412e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.47765031187 -2.18756311972
y1[1] (closed_form) = 4.47765031187 -2.18756311972
absolute error = 2.631e-14
relative error = 5.279e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.67
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.67
Order of pole (three term test) = 29.86 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5761 2.101
h = 0.001 0.003
y2[1] (numeric) = -1.25983805061 -3.37618031115
y2[1] (closed_form) = -1.25983805061 -3.37618031115
absolute error = 2.309e-14
relative error = 6.407e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.47876884545 -2.19319565968
y1[1] (closed_form) = 4.47876884545 -2.19319565968
absolute error = 2.631e-14
relative error = 5.275e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.71
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.71
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19267.3MB, alloc=44.3MB, time=251.13
x[1] = 0.5771 2.104
h = 0.0001 0.004
y2[1] (numeric) = -1.269915596 -3.38443014816
y2[1] (closed_form) = -1.269915596 -3.38443014816
absolute error = 2.319e-14
relative error = 6.417e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.48664488415 -2.20337058466
y1[1] (closed_form) = 4.48664488415 -2.20337058466
absolute error = 2.631e-14
relative error = 5.263e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.81
Order of pole (three term test) = 42.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.81
Order of pole (three term test) = 29.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19315.1MB, alloc=44.3MB, time=251.75
x[1] = 0.5772 2.108
h = 0.003 0.006
y2[1] (numeric) = -1.27909727085 -3.39818257659
y2[1] (closed_form) = -1.27909727085 -3.39818257659
absolute error = 2.319e-14
relative error = 6.388e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.49998264181 -2.21280772757
y1[1] (closed_form) = 4.49998264181 -2.21280772757
absolute error = 2.648e-14
relative error = 5.280e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.94
Order of pole (three term test) = 42.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.94
Order of pole (three term test) = 29.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19363.1MB, alloc=44.3MB, time=252.38
x[1] = 0.5802 2.114
h = 0.0001 0.005
y2[1] (numeric) = -1.30296619363 -3.41254882267
y2[1] (closed_form) = -1.30296619363 -3.41254882267
absolute error = 2.319e-14
relative error = 6.350e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.51354178219 -2.23676992047
y1[1] (closed_form) = 4.51354178219 -2.23676992047
absolute error = 2.648e-14
relative error = 5.256e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.15
Order of pole (three term test) = 42.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.15
Order of pole (three term test) = 30.09 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5803 2.119
h = 0.0001 0.003
y2[1] (numeric) = -1.31453193025 -3.4299344133
y2[1] (closed_form) = -1.31453193025 -3.4299344133
absolute error = 2.319e-14
relative error = 6.315e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.53041708123 -2.24865576378
y1[1] (closed_form) = 4.53041708123 -2.24865576378
absolute error = 2.648e-14
relative error = 5.235e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.32
Order of pole (three term test) = 42.49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.32
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19410.8MB, alloc=44.3MB, time=253.00
x[1] = 0.5804 2.122
h = 0.001 0.001
y2[1] (numeric) = -1.32164238373 -3.440315537
y2[1] (closed_form) = -1.32164238373 -3.440315537
absolute error = 2.408e-14
relative error = 6.535e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.54049064025 -2.25595353178
y1[1] (closed_form) = 4.54049064025 -2.25595353178
absolute error = 2.746e-14
relative error = 5.416e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.42
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.42
Order of pole (three term test) = 30.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19458.8MB, alloc=44.3MB, time=253.62
x[1] = 0.5814 2.123
h = 0.0001 0.004
y2[1] (numeric) = -1.32744226864 -3.44159775053
y2[1] (closed_form) = -1.32744226864 -3.44159775053
absolute error = 2.309e-14
relative error = 6.259e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.54160705553 -2.26171903056
y1[1] (closed_form) = 4.54160705553 -2.26171903056
absolute error = 2.648e-14
relative error = 5.218e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.46
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.46
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19506.8MB, alloc=44.3MB, time=254.25
x[1] = 0.5815 2.127
h = 0.003 0.006
y2[1] (numeric) = -1.33686331695 -3.45556462738
y2[1] (closed_form) = -1.33686331695 -3.45556462738
absolute error = 2.408e-14
relative error = 6.500e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.55516814758 -2.27139248606
y1[1] (closed_form) = 4.55516814758 -2.27139248606
absolute error = 2.746e-14
relative error = 5.395e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.6
Order of pole (three term test) = 42.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.6
Order of pole (three term test) = 30.2 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5845 2.133
h = 0.0001 0.005
y2[1] (numeric) = -1.36125112078 -3.47008596468
y2[1] (closed_form) = -1.36125112078 -3.47008596468
absolute error = 2.408e-14
relative error = 6.461e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.56889797026 -2.29587520898
y1[1] (closed_form) = 4.56889797026 -2.29587520898
absolute error = 2.746e-14
relative error = 5.370e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.81
Order of pole (three term test) = 42.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.81
Order of pole (three term test) = 30.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19554.4MB, alloc=44.3MB, time=254.87
x[1] = 0.5846 2.138
h = 0.0001 0.003
y2[1] (numeric) = -1.3731186778 -3.48774311659
y2[1] (closed_form) = -1.3731186778 -3.48774311659
absolute error = 2.408e-14
relative error = 6.425e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.58605578976 -2.30805899813
y1[1] (closed_form) = 4.58605578976 -2.30805899813
absolute error = 2.746e-14
relative error = 5.348e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.99
Order of pole (three term test) = 42.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.99
Order of pole (three term test) = 30.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19602.3MB, alloc=44.3MB, time=255.49
x[1] = 0.5847 2.141
h = 0.001 0.001
y2[1] (numeric) = -1.38041318584 -3.49828545858
y2[1] (closed_form) = -1.38041318584 -3.49828545858
absolute error = 2.419e-14
relative error = 6.431e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.59629714873 -2.31553859124
y1[1] (closed_form) = 4.59629714873 -2.31553859124
absolute error = 2.746e-14
relative error = 5.335e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.1
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.1
Order of pole (three term test) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19650.3MB, alloc=44.3MB, time=256.12
x[1] = 0.5857 2.142
h = 0.001 0.003
y2[1] (numeric) = -1.38632852029 -3.49956383476
y2[1] (closed_form) = -1.38632852029 -3.49956383476
absolute error = 2.419e-14
relative error = 6.426e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.5974127035 -2.32142088655
y1[1] (closed_form) = 4.5974127035 -2.32142088655
absolute error = 2.729e-14
relative error = 5.300e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.13
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.13
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5867 2.145
h = 0.0001 0.004
y2[1] (numeric) = -1.39691026223 -3.50804149198
y2[1] (closed_form) = -1.39691026223 -3.50804149198
absolute error = 2.518e-14
relative error = 6.668e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.60553249203 -2.33209953621
y1[1] (closed_form) = 4.60553249203 -2.33209953621
absolute error = 2.746e-14
relative error = 5.319e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.24
Order of pole (three term test) = 42.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.24
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19697.9MB, alloc=44.3MB, time=256.74
x[1] = 0.5868 2.149
h = 0.003 0.006
y2[1] (numeric) = -1.40661980788 -3.52225753658
y2[1] (closed_form) = -1.40661980788 -3.52225753658
absolute error = 2.518e-14
relative error = 6.639e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.61935289583 -2.34205809711
y1[1] (closed_form) = 4.61935289583 -2.34205809711
absolute error = 2.746e-14
relative error = 5.302e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.39
Order of pole (three term test) = 43.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.39
Order of pole (three term test) = 30.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19745.7MB, alloc=44.3MB, time=257.36
x[1] = 0.5898 2.155
h = 0.0001 0.005
y2[1] (numeric) = -1.43162630562 -3.53695162734
y2[1] (closed_form) = -1.43162630562 -3.53695162734
absolute error = 2.518e-14
relative error = 6.599e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.63327319814 -2.36716155095
y1[1] (closed_form) = 4.63327319814 -2.36716155095
absolute error = 2.746e-14
relative error = 5.278e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.61
Order of pole (three term test) = 43.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.61
Order of pole (three term test) = 30.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19793.6MB, alloc=44.3MB, time=257.98
x[1] = 0.5899 2.16
h = 0.0001 0.003
y2[1] (numeric) = -1.44385764621 -3.55492432831
y2[1] (closed_form) = -1.44385764621 -3.55492432831
absolute error = 2.518e-14
relative error = 6.562e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.65075907846 -2.37970482705
y1[1] (closed_form) = 4.65075907846 -2.37970482705
absolute error = 2.844e-14
relative error = 5.444e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.8
Order of pole (three term test) = 43.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.8
Order of pole (three term test) = 30.72 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.59 2.163
h = 0.001 0.001
y2[1] (numeric) = -1.45137390054 -3.5656538966
y2[1] (closed_form) = -1.45137390054 -3.5656538966
absolute error = 2.508e-14
relative error = 6.515e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.66119517679 -2.38740369699
y1[1] (closed_form) = 4.66119517679 -2.38740369699
absolute error = 2.844e-14
relative error = 5.431e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.91
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.91
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19841.4MB, alloc=44.3MB, time=258.61
x[1] = 0.591 2.164
h = 0.001 0.003
y2[1] (numeric) = -1.45742606549 -3.56692523469
y2[1] (closed_form) = -1.45742606549 -3.56692523469
absolute error = 2.508e-14
relative error = 6.509e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.66230706737 -2.39342438636
y1[1] (closed_form) = 4.66230706737 -2.39342438636
absolute error = 2.844e-14
relative error = 5.427e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.95
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.95
Order of pole (three term test) = 30.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19889.4MB, alloc=44.3MB, time=259.23
x[1] = 0.592 2.167
h = 0.0001 0.004
y2[1] (numeric) = -1.46828919926 -3.57552562754
y2[1] (closed_form) = -1.46828919926 -3.57552562754
absolute error = 2.508e-14
relative error = 6.489e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.67055788601 -2.40438417325
y1[1] (closed_form) = 4.67055788601 -2.40438417325
absolute error = 2.828e-14
relative error = 5.384e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.06
Order of pole (three term test) = 43.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.06
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19937.3MB, alloc=44.3MB, time=259.86
x[1] = 0.5921 2.171
h = 0.003 0.006
y2[1] (numeric) = -1.47829498449 -3.58999505687
y2[1] (closed_form) = -1.47829498449 -3.58999505687
absolute error = 2.508e-14
relative error = 6.460e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.68464158009 -2.41463560306
y1[1] (closed_form) = 4.68464158009 -2.41463560306
absolute error = 2.844e-14
relative error = 5.397e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.22
Order of pole (three term test) = 43.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.22
Order of pole (three term test) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5951 2.177
h = 0.0001 0.005
y2[1] (numeric) = -1.5039350041 -3.60486276852
y2[1] (closed_form) = -1.5039350041 -3.60486276852
absolute error = 2.508e-14
relative error = 6.421e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.69875285405 -2.44037447951
y1[1] (closed_form) = 4.69875285405 -2.44037447951
absolute error = 2.844e-14
relative error = 5.372e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.45
Order of pole (three term test) = 43.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.45
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19985.0MB, alloc=44.3MB, time=260.48
x[1] = 0.5952 2.182
h = 0.0001 0.003
y2[1] (numeric) = -1.51653989636 -3.62315636013
y2[1] (closed_form) = -1.51653989636 -3.62315636013
absolute error = 2.518e-14
relative error = 6.411e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.7165718421 -2.45328703935
y1[1] (closed_form) = 4.7165718421 -2.45328703935
absolute error = 2.844e-14
relative error = 5.350e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.65
Order of pole (three term test) = 43.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.65
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20032.9MB, alloc=44.3MB, time=261.10
x[1] = 0.5953 2.185
h = 0.001 0.001
y2[1] (numeric) = -1.52428382614 -3.63407629366
y2[1] (closed_form) = -1.52428382614 -3.63407629366
absolute error = 2.617e-14
relative error = 6.641e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.72720564232 -2.46121113009
y1[1] (closed_form) = 4.72720564232 -2.46121113009
absolute error = 2.844e-14
relative error = 5.337e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.76
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.76
Order of pole (three term test) = 31.14 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5963 2.186
h = 0.001 0.003
y2[1] (numeric) = -1.53047587741 -3.63533976182
y2[1] (closed_form) = -1.53047587741 -3.63533976182
absolute error = 2.518e-14
relative error = 6.384e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.72831297152 -2.46737321779
y1[1] (closed_form) = 4.72831297152 -2.46737321779
absolute error = 2.844e-14
relative error = 5.333e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.8
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.8
Order of pole (three term test) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20080.8MB, alloc=44.3MB, time=261.72
x[1] = 0.5973 2.189
h = 0.0001 0.004
y2[1] (numeric) = -1.54162736153 -3.64406427794
y2[1] (closed_form) = -1.54162736153 -3.64406427794
absolute error = 2.518e-14
relative error = 6.364e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.736696026 -2.47862106298
y1[1] (closed_form) = 4.736696026 -2.47862106298
absolute error = 2.844e-14
relative error = 5.320e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.92
Order of pole (three term test) = 43.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.92
Order of pole (three term test) = 31.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20128.6MB, alloc=44.3MB, time=262.34
x[1] = 0.5974 2.193
h = 0.003 0.006
y2[1] (numeric) = -1.55193732273 -3.65879135542
y2[1] (closed_form) = -1.55193732273 -3.65879135542
absolute error = 2.617e-14
relative error = 6.585e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.75104704061 -2.48917332011
y1[1] (closed_form) = 4.75104704061 -2.48917332011
absolute error = 2.844e-14
relative error = 5.303e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.08
Order of pole (three term test) = 44.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.08
Order of pole (three term test) = 31.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20176.5MB, alloc=44.3MB, time=262.97
x[1] = 0.6004 2.199
h = 0.0001 0.005
y2[1] (numeric) = -1.57822602149 -3.67383348676
y2[1] (closed_form) = -1.57822602149 -3.67383348676
absolute error = 2.617e-14
relative error = 6.546e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.76534971711 -2.51556264512
y1[1] (closed_form) = 4.76534971711 -2.51556264512
absolute error = 2.844e-14
relative error = 5.278e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.32
Order of pole (three term test) = 44.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.32
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6005 2.204
h = 0.0001 0.003
y2[1] (numeric) = -1.59121447866 -3.69245336982
y2[1] (closed_form) = -1.59121447866 -3.69245336982
absolute error = 2.617e-14
relative error = 6.509e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.78350692552 -2.52885453152
y1[1] (closed_form) = 4.78350692552 -2.52885453152
absolute error = 2.927e-14
relative error = 5.410e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.53
Order of pole (three term test) = 44.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.53
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20224.2MB, alloc=44.3MB, time=263.59
x[1] = 0.6006 2.207
h = 0.001 0.001
y2[1] (numeric) = -1.59919216125 -3.7035668412
y2[1] (closed_form) = -1.59919216125 -3.7035668412
absolute error = 2.617e-14
relative error = 6.488e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.7943414278 -2.53700993584
y1[1] (closed_form) = 4.7943414278 -2.53700993584
absolute error = 2.927e-14
relative error = 5.397e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.65
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.65
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20272.2MB, alloc=44.3MB, time=264.21
x[1] = 0.6016 2.208
h = 0.001 0.003
y2[1] (numeric) = -1.6055272166 -3.70482157139
y2[1] (closed_form) = -1.6055272166 -3.70482157139
absolute error = 2.617e-14
relative error = 6.482e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.79544326336 -2.54331648955
y1[1] (closed_form) = 4.79544326336 -2.54331648955
absolute error = 2.915e-14
relative error = 5.371e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.69
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.69
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20320.2MB, alloc=44.3MB, time=264.84
x[1] = 0.6026 2.211
h = 0.0001 0.004
y2[1] (numeric) = -1.61697417 -3.71367158775
y2[1] (closed_form) = -1.61697417 -3.71367158775
absolute error = 2.617e-14
relative error = 6.462e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.8039597525 -2.55485947626
y1[1] (closed_form) = 4.8039597525 -2.55485947626
absolute error = 2.915e-14
relative error = 5.358e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.82
Order of pole (three term test) = 44.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.82
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6027 2.215
h = 0.003 0.006
y2[1] (numeric) = -1.62759644233 -3.72866062332
y2[1] (closed_form) = -1.62759644233 -3.72866062332
absolute error = 2.617e-14
relative error = 6.433e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.81858216963 -2.56572071865
y1[1] (closed_form) = 4.81858216963 -2.56572071865
absolute error = 2.927e-14
relative error = 5.363e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.99
Order of pole (three term test) = 44.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.99
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20368.0MB, alloc=44.3MB, time=265.46
x[1] = 0.6057 2.221
h = 0.0001 0.005
y2[1] (numeric) = -1.65454931394 -3.74387790143
y2[1] (closed_form) = -1.65454931394 -3.74387790143
absolute error = 2.532e-14
relative error = 6.185e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.83307661513 -2.59277585934
y1[1] (closed_form) = 4.83307661513 -2.59277585934
absolute error = 2.915e-14
relative error = 5.316e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.24
Order of pole (three term test) = 44.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.24
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20415.7MB, alloc=44.3MB, time=266.08
x[1] = 0.6058 2.226
h = 0.0001 0.003
y2[1] (numeric) = -1.66793160025 -3.76282953601
y2[1] (closed_form) = -1.66793160025 -3.76282953601
absolute error = 2.631e-14
relative error = 6.391e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.85157722229 -2.60645736697
y1[1] (closed_form) = 4.85157722229 -2.60645736697
absolute error = 2.915e-14
relative error = 5.294e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.45
Order of pole (three term test) = 44.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.45
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20463.7MB, alloc=44.3MB, time=266.71
x[1] = 0.6059 2.229
h = 0.001 0.001
y2[1] (numeric) = -1.67614926471 -3.77413975159
y2[1] (closed_form) = -1.67614926471 -3.77413975159
absolute error = 2.532e-14
relative error = 6.131e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.86261546433 -2.61485032989
y1[1] (closed_form) = 4.86261546433 -2.61485032989
absolute error = 2.915e-14
relative error = 5.281e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.58
Order of pole (three term test) = 44.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.58
Order of pole (three term test) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6069 2.23
h = 0.0001 0.004
y2[1] (numeric) = -1.68263050506 -3.77538483842
y2[1] (closed_form) = -1.68263050506 -3.77538483842
absolute error = 2.631e-14
relative error = 6.364e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.86371083781 -2.62130448189
y1[1] (closed_form) = 4.86371083781 -2.62130448189
absolute error = 2.915e-14
relative error = 5.277e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.62
Order of pole (three term test) = 44.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.62
Order of pole (three term test) = 32.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20511.3MB, alloc=44.3MB, time=267.34
x[1] = 0.607 2.234
h = 0.003 0.006
y2[1] (numeric) = -1.69352508289 -3.79060670154
y2[1] (closed_form) = -1.69352508289 -3.79060670154
absolute error = 2.617e-14
relative error = 6.304e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.87857399405 -2.63243507682
y1[1] (closed_form) = 4.87857399405 -2.63243507682
absolute error = 2.915e-14
relative error = 5.259e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.8
Order of pole (three term test) = 45.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.8
Order of pole (three term test) = 32.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20559.2MB, alloc=44.3MB, time=267.96
x[1] = 0.61 2.24
h = 0.0001 0.005
y2[1] (numeric) = -1.72106022476 -3.80598343431
y2[1] (closed_form) = -1.72106022476 -3.80598343431
absolute error = 2.631e-14
relative error = 6.298e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.89324193641 -2.66007361175
y1[1] (closed_form) = 4.89324193641 -2.66007361175
absolute error = 2.915e-14
relative error = 5.235e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.06
Order of pole (three term test) = 45.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.06
Order of pole (three term test) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20607.1MB, alloc=44.3MB, time=268.58
x[1] = 0.6101 2.245
h = 0.0001 0.003
y2[1] (numeric) = -1.73478587995 -3.82522990964
y2[1] (closed_form) = -1.73478587995 -3.82522990964
absolute error = 2.617e-14
relative error = 6.231e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.91204713947 -2.67409475692
y1[1] (closed_form) = 4.91204713947 -2.67409475692
absolute error = 3.015e-14
relative error = 5.391e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.28
Order of pole (three term test) = 45.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.28
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6102 2.248
h = 0.001 0.001
y2[1] (numeric) = -1.74321282313 -3.83671503191
y2[1] (closed_form) = -1.74321282313 -3.83671503191
absolute error = 2.617e-14
relative error = 6.211e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.92326614897 -2.68269484522
y1[1] (closed_form) = 4.92326614897 -2.68269484522
absolute error = 2.907e-14
relative error = 5.185e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.42
Order of pole (three term test) = 45.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.42
Order of pole (three term test) = 32.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20654.8MB, alloc=44.3MB, time=269.20
x[1] = 0.6112 2.249
h = 0.001 0.003
y2[1] (numeric) = -1.74982262126 -3.8379528578
y2[1] (closed_form) = -1.74982262126 -3.8379528578
absolute error = 2.617e-14
relative error = 6.205e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.92435696629 -2.6892786967
y1[1] (closed_form) = 4.92435696629 -2.6892786967
absolute error = 2.907e-14
relative error = 5.181e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.46
Order of pole (three term test) = 45.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.46
Order of pole (three term test) = 32.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20702.6MB, alloc=44.3MB, time=269.83
x[1] = 0.6122 2.252
h = 0.0001 0.004
y2[1] (numeric) = -1.76183735255 -3.84704375246
y2[1] (closed_form) = -1.76183735255 -3.84704375246
absolute error = 2.617e-14
relative error = 6.185e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 4.93312863143 -2.70138867251
y1[1] (closed_form) = 4.93312863143 -2.70138867251
absolute error = 3.007e-14
relative error = 5.346e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.6
Order of pole (three term test) = 45.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.6
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20750.7MB, alloc=44.3MB, time=270.45
x[1] = 0.6123 2.256
h = 0.003 0.006
y2[1] (numeric) = -1.77305987175 -3.86253582025
y2[1] (closed_form) = -1.77305987175 -3.86253582025
absolute error = 2.617e-14
relative error = 6.158e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 4.9482710263 -2.71284392966
y1[1] (closed_form) = 4.9482710263 -2.71284392966
absolute error = 3.007e-14
relative error = 5.328e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.78
Order of pole (three term test) = 45.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.78
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6153 2.262
h = 0.0001 0.005
y2[1] (numeric) = -1.80128893047 -3.87808904471
y2[1] (closed_form) = -1.80128893047 -3.87808904471
absolute error = 2.617e-14
relative error = 6.121e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 4.96313142925 -2.74117780503
y1[1] (closed_form) = 4.96313142925 -2.74117780503
absolute error = 3.007e-14
relative error = 5.303e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.05
Order of pole (three term test) = 45.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.05
Order of pole (three term test) = 32.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20798.3MB, alloc=44.3MB, time=271.07
x[1] = 0.6154 2.267
h = 0.0001 0.003
y2[1] (numeric) = -1.81542813586 -3.89767771929
y2[1] (closed_form) = -1.81542813586 -3.89767771929
absolute error = 2.729e-14
relative error = 6.348e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 4.98228997162 -2.75560835439
y1[1] (closed_form) = 4.98228997162 -2.75560835439
absolute error = 3.007e-14
relative error = 5.281e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.28
Order of pole (three term test) = 45.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.28
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20846.3MB, alloc=44.3MB, time=271.70
x[1] = 0.6155 2.27
h = 0.001 0.001
y2[1] (numeric) = -1.82410702873 -3.90936572043
y2[1] (closed_form) = -1.82410702873 -3.90936572043
absolute error = 2.717e-14
relative error = 6.297e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 4.9937185519 -2.76445800211
y1[1] (closed_form) = 4.9937185519 -2.76445800211
absolute error = 3.007e-14
relative error = 5.268e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.42
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.42
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6165 2.271
h = 0.001 0.003
y2[1] (numeric) = -1.83086911506 -3.91059215462
y2[1] (closed_form) = -1.83086911506 -3.91059215462
absolute error = 2.729e-14
relative error = 6.321e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 4.99480104389 -2.77119546894
y1[1] (closed_form) = 4.99480104389 -2.77119546894
absolute error = 3.007e-14
relative error = 5.264e-13 %
Correct digits = 14
memory used=20894.3MB, alloc=44.3MB, time=272.32
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.47
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.47
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6175 2.274
h = 0.0001 0.004
y2[1] (numeric) = -1.84320058341 -3.91981251202
y2[1] (closed_form) = -1.84320058341 -3.91981251202
absolute error = 2.717e-14
relative error = 6.272e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.00370961631 -2.78362176308
y1[1] (closed_form) = 5.00370961631 -2.78362176308
absolute error = 3.007e-14
relative error = 5.251e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.61
Order of pole (three term test) = 46.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.61
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20942.0MB, alloc=44.3MB, time=272.94
x[1] = 0.6176 2.278
h = 0.003 0.006
y2[1] (numeric) = -1.85475977361 -3.93557923036
y2[1] (closed_form) = -1.85475977361 -3.93557923036
absolute error = 2.631e-14
relative error = 6.046e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.01913548201 -2.79541043664
y1[1] (closed_form) = 5.01913548201 -2.79541043664
absolute error = 3.007e-14
relative error = 5.233e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.8
Order of pole (three term test) = 46.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.8
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20990.0MB, alloc=44.3MB, time=273.56
x[1] = 0.6206 2.284
h = 0.0001 0.005
y2[1] (numeric) = -1.88369924671 -3.95130945406
y2[1] (closed_form) = -1.88369924671 -3.95130945406
absolute error = 2.631e-14
relative error = 6.010e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.0341885128 -2.82445603622
y1[1] (closed_form) = 5.0341885128 -2.82445603622
absolute error = 3.102e-14
relative error = 5.373e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.09
Order of pole (three term test) = 46.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.09
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6207 2.289
h = 0.0001 0.003
y2[1] (numeric) = -1.89826301712 -3.9712459613
y2[1] (closed_form) = -1.89826301712 -3.9712459613
absolute error = 2.631e-14
relative error = 5.976e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.05370576382 -2.83930703709
y1[1] (closed_form) = 5.05370576382 -2.83930703709
absolute error = 3.007e-14
relative error = 5.187e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.33
Order of pole (three term test) = 46.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.33
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21037.7MB, alloc=44.3MB, time=274.18
x[1] = 0.6208 2.292
h = 0.001 0.001
y2[1] (numeric) = -1.90720054244 -3.98314014607
y2[1] (closed_form) = -1.90720054244 -3.98314014607
absolute error = 2.631e-14
relative error = 5.957e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.06534706154 -2.84841294434
y1[1] (closed_form) = 5.06534706154 -2.84841294434
absolute error = 3.106e-14
relative error = 5.346e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.48
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.48
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21085.7MB, alloc=44.3MB, time=274.80
x[1] = 0.6218 2.293
h = 0.001 0.003
y2[1] (numeric) = -1.914118286 -3.98435417068
y2[1] (closed_form) = -1.914118286 -3.98435417068
absolute error = 2.631e-14
relative error = 5.951e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.06642015043 -2.85530735073
y1[1] (closed_form) = 5.06642015043 -2.85530735073
absolute error = 3.106e-14
relative error = 5.342e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.53
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.53
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21133.5MB, alloc=44.3MB, time=275.43
x[1] = 0.6228 2.296
h = 0.0001 0.004
y2[1] (numeric) = -1.92677426394 -3.99370531867
y2[1] (closed_form) = -1.92677426394 -3.99370531867
absolute error = 2.631e-14
relative error = 5.932e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.07546679373 -2.86805770628
y1[1] (closed_form) = 5.07546679373 -2.86805770628
absolute error = 3.102e-14
relative error = 5.320e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.67
Order of pole (three term test) = 46.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.67
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6229 2.3
h = 0.003 0.006
y2[1] (numeric) = -1.93867907232 -4.00975118017
y2[1] (closed_form) = -1.93867907232 -4.00975118017
absolute error = 2.631e-14
relative error = 5.906e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.09118041393 -2.88018876856
y1[1] (closed_form) = 5.09118041393 -2.88018876856
absolute error = 3.007e-14
relative error = 5.140e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.87
Order of pole (three term test) = 46.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.87
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21181.3MB, alloc=44.3MB, time=276.05
x[1] = 0.6259 2.306
h = 0.0001 0.005
y2[1] (numeric) = -1.96834582255 -4.02565882568
y2[1] (closed_form) = -1.96834582255 -4.02565882568
absolute error = 2.729e-14
relative error = 6.091e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.10642616163 -2.90996284553
y1[1] (closed_form) = 5.10642616163 -2.90996284553
absolute error = 3.002e-14
relative error = 5.107e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.17
Order of pole (three term test) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.17
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21229.1MB, alloc=44.3MB, time=276.67
x[1] = 0.626 2.311
h = 0.0001 0.003
y2[1] (numeric) = -1.98334544747 -4.04594885855
y2[1] (closed_form) = -1.98334544747 -4.04594885855
absolute error = 2.729e-14
relative error = 6.058e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.12630755614 -2.9252456206
y1[1] (closed_form) = 5.12630755614 -2.9252456206
absolute error = 3.102e-14
relative error = 5.255e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.43
Order of pole (three term test) = 47.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.43
Order of pole (three term test) = 34.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21277.0MB, alloc=44.3MB, time=277.30
x[1] = 0.6261 2.314
h = 0.001 0.001
y2[1] (numeric) = -1.992548454 -4.0580525654
y2[1] (closed_form) = -1.992548454 -4.0580525654
absolute error = 2.717e-14
relative error = 6.009e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.13816475517 -2.93461465391
y1[1] (closed_form) = 5.13816475517 -2.93461465391
absolute error = 3.102e-14
relative error = 5.242e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.58
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.58
Order of pole (three term test) = 34.49 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6271 2.315
h = 0.001 0.003
y2[1] (numeric) = -1.99962529186 -4.05925312059
y2[1] (closed_form) = -1.99962529186 -4.05925312059
absolute error = 2.729e-14
relative error = 6.032e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.13922732232 -2.94166939345
y1[1] (closed_form) = 5.13922732232 -2.94166939345
absolute error = 3.102e-14
relative error = 5.238e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.63
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.63
Order of pole (three term test) = 34.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21324.7MB, alloc=44.3MB, time=277.92
x[1] = 0.6281 2.318
h = 0.0001 0.004
y2[1] (numeric) = -2.01261373041 -4.06873637096
y2[1] (closed_form) = -2.01261373041 -4.06873637096
absolute error = 2.828e-14
relative error = 6.231e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.14841318746 -2.95475173342
y1[1] (closed_form) = 5.14841318746 -2.95475173342
absolute error = 3.102e-14
relative error = 5.225e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.78
Order of pole (three term test) = 47.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.78
Order of pole (three term test) = 34.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21372.6MB, alloc=44.3MB, time=278.54
x[1] = 0.6282 2.322
h = 0.003 0.006
y2[1] (numeric) = -2.02487332681 -4.08506591489
y2[1] (closed_form) = -2.02487332681 -4.08506591489
absolute error = 2.844e-14
relative error = 6.238e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.16441889718 -2.96723437995
y1[1] (closed_form) = 5.16441889718 -2.96723437995
absolute error = 3.102e-14
relative error = 5.207e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.99
Order of pole (three term test) = 47.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.99
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21420.5MB, alloc=44.3MB, time=279.16
x[1] = 0.6312 2.328
h = 0.0001 0.005
y2[1] (numeric) = -2.05528458987 -4.10115131606
y2[1] (closed_form) = -2.05528458987 -4.10115131606
absolute error = 2.828e-14
relative error = 6.166e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.17985736882 -2.99775406456
y1[1] (closed_form) = 5.17985736882 -2.99775406456
absolute error = 3.102e-14
relative error = 5.183e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.31
Order of pole (three term test) = 47.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.31
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6313 2.333
h = 0.0001 0.003
y2[1] (numeric) = -2.07073163997 -4.12180062707
y2[1] (closed_form) = -2.07073163997 -4.12180062707
absolute error = 2.943e-14
relative error = 6.380e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.20010840701 -3.01348021829
y1[1] (closed_form) = 5.20010840701 -3.01348021829
absolute error = 3.202e-14
relative error = 5.327e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.57
Order of pole (three term test) = 47.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.57
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21468.2MB, alloc=44.3MB, time=279.78
x[1] = 0.6314 2.336
h = 0.001 0.001
y2[1] (numeric) = -2.08020714636 -4.13411722804
y2[1] (closed_form) = -2.08020714636 -4.13411722804
absolute error = 2.943e-14
relative error = 6.359e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.21218472829 -3.02311941454
y1[1] (closed_form) = 5.21218472829 -3.02311941454
absolute error = 3.106e-14
relative error = 5.156e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.73
Order of pole (three term test) = 47.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.73
Order of pole (three term test) = 35.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21516.2MB, alloc=44.3MB, time=280.41
x[1] = 0.6324 2.337
h = 0.0001 0.004
y2[1] (numeric) = -2.08744658502 -4.13530321073
y2[1] (closed_form) = -2.08744658502 -4.13530321073
absolute error = 2.943e-14
relative error = 6.353e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.21323561284 -3.03033795145
y1[1] (closed_form) = 5.21323561284 -3.03033795145
absolute error = 3.206e-14
relative error = 5.317e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.78
Order of pole (three term test) = 47.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.78
Order of pole (three term test) = 35.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21564.2MB, alloc=44.3MB, time=281.03
x[1] = 0.6325 2.341
h = 0.003 0.006
y2[1] (numeric) = -2.10001563431 -4.15188498863
y2[1] (closed_form) = -2.10001563431 -4.15188498863
absolute error = 2.943e-14
relative error = 6.325e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.22950059531 -3.04312721717
y1[1] (closed_form) = 5.22950059531 -3.04312721717
absolute error = 3.202e-14
relative error = 5.291e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27
Order of pole (three term test) = 48.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6355 2.347
h = 0.0001 0.005
y2[1] (numeric) = -2.13107972055 -4.1681327478
y2[1] (closed_form) = -2.13107972055 -4.1681327478
absolute error = 3.041e-14
relative error = 6.497e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.24511406388 -3.07430041286
y1[1] (closed_form) = 5.24511406388 -3.07430041286
absolute error = 3.302e-14
relative error = 5.430e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.32
Order of pole (three term test) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.32
Order of pole (three term test) = 35.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21611.9MB, alloc=44.3MB, time=281.65
x[1] = 0.6356 2.352
h = 0.0001 0.003
y2[1] (numeric) = -2.1469170103 -4.18910148795
y2[1] (closed_form) = -2.1469170103 -4.18910148795
absolute error = 3.059e-14
relative error = 6.499e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.26569320812 -3.09041323113
y1[1] (closed_form) = 5.26569320812 -3.09041323113
absolute error = 3.302e-14
relative error = 5.407e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.6
Order of pole (three term test) = 48.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.6
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21659.7MB, alloc=44.3MB, time=282.28
x[1] = 0.6357 2.355
h = 0.001 0.001
y2[1] (numeric) = -2.15663023723 -4.20160742994
y2[1] (closed_form) = -2.15663023723 -4.20160742994
absolute error = 2.961e-14
relative error = 6.271e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.27796408543 -3.10028807943
y1[1] (closed_form) = 5.27796408543 -3.10028807943
absolute error = 3.302e-14
relative error = 5.394e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.76
Order of pole (three term test) = 48.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.76
Order of pole (three term test) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21707.6MB, alloc=44.3MB, time=282.90
x[1] = 0.6367 2.356
h = 0.001 0.003
y2[1] (numeric) = -2.16401269139 -4.20278194686
y2[1] (closed_form) = -2.16401269139 -4.20278194686
absolute error = 2.961e-14
relative error = 6.265e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.27900595988 -3.10765059541
y1[1] (closed_form) = 5.27900595988 -3.10765059541
absolute error = 3.401e-14
relative error = 5.553e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.82
Order of pole (three term test) = 48.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.82
Order of pole (three term test) = 36.06 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6377 2.359
h = 0.0001 0.004
y2[1] (numeric) = -2.17763994142 -4.21251863259
y2[1] (closed_form) = -2.17763994142 -4.21251863259
absolute error = 2.961e-14
relative error = 6.245e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.28845808499 -3.12137071078
y1[1] (closed_form) = 5.28845808499 -3.12137071078
absolute error = 3.401e-14
relative error = 5.539e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.99
Order of pole (three term test) = 48.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.99
Order of pole (three term test) = 36.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21755.3MB, alloc=44.3MB, time=283.52
x[1] = 0.6378 2.363
h = 0.003 0.006
y2[1] (numeric) = -2.19058139701 -4.2293927791
y2[1] (closed_form) = -2.19058139701 -4.2293927791
absolute error = 2.961e-14
relative error = 6.218e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.30502347555 -3.13452923039
y1[1] (closed_form) = 5.30502347555 -3.13452923039
absolute error = 3.401e-14
relative error = 5.520e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.21
Order of pole (three term test) = 48.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.21
Order of pole (three term test) = 36.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21803.2MB, alloc=44.3MB, time=284.14
x[1] = 0.6408 2.369
h = 0.0001 0.005
y2[1] (numeric) = -2.22242308632 -4.24581888182
y2[1] (closed_form) = -2.22242308632 -4.24581888182
absolute error = 2.983e-14
relative error = 6.225e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.3208296641 -3.16648094202
y1[1] (closed_form) = 5.3208296641 -3.16648094202
absolute error = 3.4e-14
relative error = 5.491e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.55
Order of pole (three term test) = 49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.55
Order of pole (three term test) = 36.63 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6409 2.374
h = 0.0001 0.003
y2[1] (numeric) = -2.23873003246 -4.2671579084
y2[1] (closed_form) = -2.23873003246 -4.2671579084
absolute error = 3.059e-14
relative error = 6.349e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.34178900616 -3.18305943739
y1[1] (closed_form) = 5.34178900616 -3.18305943739
absolute error = 3.401e-14
relative error = 5.470e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.84
Order of pole (three term test) = 49.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.84
Order of pole (three term test) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21851.0MB, alloc=44.3MB, time=284.76
x[1] = 0.641 2.377
h = 0.001 0.001
y2[1] (numeric) = -2.24872924415 -4.27988319678
y2[1] (closed_form) = -2.24872924415 -4.27988319678
absolute error = 3.059e-14
relative error = 6.328e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.354285186 -3.19321797012
y1[1] (closed_form) = 5.354285186 -3.19321797012
absolute error = 3.401e-14
relative error = 5.456e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.01
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.01
Order of pole (three term test) = 36.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21898.9MB, alloc=44.3MB, time=285.39
x[1] = 0.642 2.378
h = 0.001 0.003
y2[1] (numeric) = -2.25628102758 -4.28104101275
y2[1] (closed_form) = -2.25628102758 -4.28104101275
absolute error = 3.081e-14
relative error = 6.366e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.35531314422 -3.20075093719
y1[1] (closed_form) = 5.35531314422 -3.20075093719
absolute error = 3.401e-14
relative error = 5.452e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.07
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.07
Order of pole (three term test) = 36.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21946.8MB, alloc=44.3MB, time=286.01
x[1] = 0.643 2.381
h = 0.0001 0.004
y2[1] (numeric) = -2.27026449028 -4.29091355576
y2[1] (closed_form) = -2.27026449028 -4.29091355576
absolute error = 3.178e-14
relative error = 6.547e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.36490780396 -3.21482671857
y1[1] (closed_form) = 5.36490780396 -3.21482671857
absolute error = 3.501e-14
relative error = 5.598e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.25
Order of pole (three term test) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.25
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6431 2.385
h = 0.003 0.006
y2[1] (numeric) = -2.28358818782 -4.30808474599
y2[1] (closed_form) = -2.28358818782 -4.30808474599
absolute error = 3.081e-14
relative error = 6.318e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.38177808635 -3.22836435468
y1[1] (closed_form) = 5.38177808635 -3.22836435468
absolute error = 3.501e-14
relative error = 5.579e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.48
Order of pole (three term test) = 49.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.48
Order of pole (three term test) = 37.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21994.5MB, alloc=44.3MB, time=286.63
x[1] = 0.6461 2.391
h = 0.0001 0.005
y2[1] (numeric) = -2.3162258284 -4.32468925527
y2[1] (closed_form) = -2.3162258284 -4.32468925527
absolute error = 3.178e-14
relative error = 6.478e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.39777674958 -3.26111283605
y1[1] (closed_form) = 5.39777674958 -3.26111283605
absolute error = 3.501e-14
relative error = 5.552e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.84
Order of pole (three term test) = 49.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.84
Order of pole (three term test) = 37.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22042.4MB, alloc=44.3MB, time=287.26
x[1] = 0.6462 2.396
h = 0.0001 0.003
y2[1] (numeric) = -2.33301484229 -4.34640449415
y2[1] (closed_form) = -2.33301484229 -4.34640449415
absolute error = 3.178e-14
relative error = 6.442e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.41912197889 -3.27816945511
y1[1] (closed_form) = 5.41912197889 -3.27816945511
absolute error = 3.501e-14
relative error = 5.528e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.14
Order of pole (three term test) = 50.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.14
Order of pole (three term test) = 37.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22090.4MB, alloc=44.3MB, time=287.88
x[1] = 0.6463 2.399
h = 0.001 0.001
y2[1] (numeric) = -2.34330756538 -4.35935259868
y2[1] (closed_form) = -2.34330756538 -4.35935259868
absolute error = 3.178e-14
relative error = 6.421e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.43184678939 -3.28861921811
y1[1] (closed_form) = 5.43184678939 -3.28861921811
absolute error = 3.501e-14
relative error = 5.514e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.32
Order of pole (three term test) = 50.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.32
Order of pole (three term test) = 37.87 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6473 2.4
h = 0.001 0.003
y2[1] (numeric) = -2.35103239112 -4.36049248037
y2[1] (closed_form) = -2.35103239112 -4.36049248037
absolute error = 3.081e-14
relative error = 6.218e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.43285954324 -3.29632631046
y1[1] (closed_form) = 5.43285954324 -3.29632631046
absolute error = 3.401e-14
relative error = 5.353e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.38
Order of pole (three term test) = 50.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.38
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22138.1MB, alloc=44.3MB, time=288.50
x[1] = 0.6483 2.403
h = 0.0001 0.004
y2[1] (numeric) = -2.36538074432 -4.37050212057
y2[1] (closed_form) = -2.36538074432 -4.37050212057
absolute error = 3.081e-14
relative error = 6.199e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.4425978293 -3.31076641297
y1[1] (closed_form) = 5.4425978293 -3.31076641297
absolute error = 3.501e-14
relative error = 5.496e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.56
Order of pole (three term test) = 50.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.56
Order of pole (three term test) = 38.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22185.9MB, alloc=44.3MB, time=289.13
x[1] = 0.6484 2.407
h = 0.003 0.006
y2[1] (numeric) = -2.37909676302 -4.38797507595
y2[1] (closed_form) = -2.37909676302 -4.38797507595
absolute error = 3.178e-14
relative error = 6.367e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.45977753786 -3.32469327214
y1[1] (closed_form) = 5.45977753786 -3.32469327214
absolute error = 3.5e-14
relative error = 5.475e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.81
Order of pole (three term test) = 50.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.81
Order of pole (three term test) = 38.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22233.8MB, alloc=44.3MB, time=289.76
x[1] = 0.6514 2.413
h = 0.0001 0.005
y2[1] (numeric) = -2.41254910758 -4.40475795047
y2[1] (closed_form) = -2.41254910758 -4.40475795047
absolute error = 3.178e-14
relative error = 6.328e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.47596833239 -3.3582571852
y1[1] (closed_form) = 5.47596833239 -3.3582571852
absolute error = 3.5e-14
relative error = 5.449e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.18
Order of pole (three term test) = 50.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.18
Order of pole (three term test) = 38.62 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6515 2.418
h = 0.0001 0.003
y2[1] (numeric) = -2.42983290809 -4.42685538664
y2[1] (closed_form) = -2.42983290809 -4.42685538664
absolute error = 3.178e-14
relative error = 6.293e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.49770520283 -3.37580468256
y1[1] (closed_form) = 5.49770520283 -3.37580468256
absolute error = 3.501e-14
relative error = 5.427e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.49
Order of pole (three term test) = 50.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.49
Order of pole (three term test) = 38.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22281.5MB, alloc=44.3MB, time=290.38
x[1] = 0.6516 2.421
h = 0.001 0.001
y2[1] (numeric) = -2.44042685499 -4.44002981021
y2[1] (closed_form) = -2.44042685499 -4.44002981021
absolute error = 3.178e-14
relative error = 6.273e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.51066200847 -3.38655340776
y1[1] (closed_form) = 5.51066200847 -3.38655340776
absolute error = 3.501e-14
relative error = 5.413e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.68
Order of pole (three term test) = 51.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.68
Order of pole (three term test) = 38.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22329.3MB, alloc=44.3MB, time=291.01
x[1] = 0.6526 2.422
h = 0.001 0.003
y2[1] (numeric) = -2.44832851081 -4.44115047575
y2[1] (closed_form) = -2.44832851081 -4.44115047575
absolute error = 3.178e-14
relative error = 6.267e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.51165822224 -3.39443837542
y1[1] (closed_form) = 5.51165822224 -3.39443837542
absolute error = 3.501e-14
relative error = 5.409e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.75
Order of pole (three term test) = 51.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.75
Order of pole (three term test) = 39.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22377.3MB, alloc=44.3MB, time=291.64
x[1] = 0.6536 2.425
h = 0.0001 0.004
y2[1] (numeric) = -2.46305063068 -4.45129843048
y2[1] (closed_form) = -2.46305063068 -4.45129843048
absolute error = 3.202e-14
relative error = 6.293e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.52154120685 -3.40925165377
y1[1] (closed_form) = 5.52154120685 -3.40925165377
absolute error = 3.501e-14
relative error = 5.396e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.94
Order of pole (three term test) = 51.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.94
Order of pole (three term test) = 39.18 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6537 2.429
h = 0.003 0.006
y2[1] (numeric) = -2.47716929898 -4.46907791851
y2[1] (closed_form) = -2.47716929898 -4.46907791851
absolute error = 3.276e-14
relative error = 6.411e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.53903492619 -3.42357809219
y1[1] (closed_form) = 5.53903492619 -3.42357809219
absolute error = 3.501e-14
relative error = 5.377e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.19
Order of pole (three term test) = 51.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.19
Order of pole (three term test) = 39.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22425.1MB, alloc=44.3MB, time=292.25
x[1] = 0.6567 2.435
h = 0.0001 0.005
y2[1] (numeric) = -2.51145551328 -4.48603900829
y2[1] (closed_form) = -2.51145551328 -4.48603900829
absolute error = 3.298e-14
relative error = 6.416e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.55541740609 -3.45797651547
y1[1] (closed_form) = 5.55541740609 -3.45797651547
absolute error = 3.501e-14
relative error = 5.351e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.58
Order of pole (three term test) = 51.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.58
Order of pole (three term test) = 39.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22472.9MB, alloc=44.3MB, time=292.88
x[1] = 0.6568 2.44
h = 0.0001 0.003
y2[1] (numeric) = -2.529247134 -4.50852468558
y2[1] (closed_form) = -2.529247134 -4.50852468558
absolute error = 3.298e-14
relative error = 6.381e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.5775517356 -3.47602796084
y1[1] (closed_form) = 5.5775517356 -3.47602796084
absolute error = 3.501e-14
relative error = 5.328e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.91
Order of pole (three term test) = 51.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.91
Order of pole (three term test) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22521.0MB, alloc=44.3MB, time=293.50
x[1] = 0.6569 2.443
h = 0.001 0.001
y2[1] (numeric) = -2.54015020724 -4.52192896401
y2[1] (closed_form) = -2.54015020724 -4.52192896401
absolute error = 3.298e-14
relative error = 6.360e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.59074393688 -3.48708357059
y1[1] (closed_form) = 5.59074393688 -3.48708357059
absolute error = 3.601e-14
relative error = 5.466e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.11
Order of pole (three term test) = 51.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.11
Order of pole (three term test) = 40.06 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6579 2.444
h = 0.0001 0.004
y2[1] (numeric) = -2.54823255705 -4.52302908153
y2[1] (closed_form) = -2.54823255705 -4.52302908153
absolute error = 3.396e-14
relative error = 6.541e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.59172222586 -3.49515024083
y1[1] (closed_form) = 5.59172222586 -3.49515024083
absolute error = 3.601e-14
relative error = 5.461e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.17
Order of pole (three term test) = 51.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.17
Order of pole (three term test) = 40.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22568.8MB, alloc=44.3MB, time=294.12
x[1] = 0.658 2.448
h = 0.003 0.006
y2[1] (numeric) = -2.56270254849 -4.54108124387
y2[1] (closed_form) = -2.56270254849 -4.54108124387
absolute error = 3.396e-14
relative error = 6.512e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.60949487706 -3.50982529582
y1[1] (closed_form) = 5.60949487706 -3.50982529582
absolute error = 3.6e-14
relative error = 5.440e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.44
Order of pole (three term test) = 52.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.44
Order of pole (three term test) = 40.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22616.7MB, alloc=44.3MB, time=294.75
x[1] = 0.661 2.454
h = 0.0001 0.005
y2[1] (numeric) = -2.59772008088 -4.55820578055
y2[1] (closed_form) = -2.59772008088 -4.55820578055
absolute error = 3.493e-14
relative error = 6.658e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.62605217232 -3.54495536553
y1[1] (closed_form) = 5.62605217232 -3.54495536553
absolute error = 3.6e-14
relative error = 5.414e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.84
Order of pole (three term test) = 52.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.84
Order of pole (three term test) = 40.74 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6611 2.459
h = 0.0001 0.003
y2[1] (numeric) = -2.61595477519 -4.58103679374
y2[1] (closed_form) = -2.61595477519 -4.58103679374
absolute error = 3.396e-14
relative error = 6.437e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.64853954973 -3.56344647442
y1[1] (closed_form) = 5.64853954973 -3.56344647442
absolute error = 3.6e-14
relative error = 5.390e-13 %
Correct digits = 14
memory used=22664.5MB, alloc=44.3MB, time=295.37
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.18
Order of pole (three term test) = 52.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.18
Order of pole (three term test) = 40.96 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6612 2.462
h = 0.001 0.001
y2[1] (numeric) = -2.62712761469 -4.59464559397
y2[1] (closed_form) = -2.62712761469 -4.59464559397
absolute error = 3.396e-14
relative error = 6.416e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.66194090971 -3.57476987297
y1[1] (closed_form) = 5.66194090971 -3.57476987297
absolute error = 3.6e-14
relative error = 5.376e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.39
Order of pole (three term test) = 52.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.39
Order of pole (three term test) = 41.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22712.5MB, alloc=44.3MB, time=295.99
x[1] = 0.6622 2.463
h = 0.001 0.003
y2[1] (numeric) = -2.63536892048 -4.59572913514
y2[1] (closed_form) = -2.63536892048 -4.59572913514
absolute error = 3.396e-14
relative error = 6.410e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.66290485018 -3.58299630844
y1[1] (closed_form) = 5.66290485018 -3.58299630844
absolute error = 3.6e-14
relative error = 5.372e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.46
Order of pole (three term test) = 52.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.46
Order of pole (three term test) = 41.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22760.4MB, alloc=44.3MB, time=296.62
x[1] = 0.6632 2.466
h = 0.0001 0.004
y2[1] (numeric) = -2.65080917389 -4.60614232864
y2[1] (closed_form) = -2.65080917389 -4.60614232864
absolute error = 3.396e-14
relative error = 6.389e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.67306456932 -3.59852649588
y1[1] (closed_form) = 5.67306456932 -3.59852649588
absolute error = 3.6e-14
relative error = 5.359e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.67
Order of pole (three term test) = 52.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.67
Order of pole (three term test) = 41.38 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6633 2.47
h = 0.003 0.006
y2[1] (numeric) = -2.6657016591 -4.62451014697
y2[1] (closed_form) = -2.6657016591 -4.62451014697
absolute error = 3.396e-14
relative error = 6.361e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.69116002563 -3.61362102885
y1[1] (closed_form) = 5.69116002563 -3.61362102885
absolute error = 3.6e-14
relative error = 5.340e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.94
Order of pole (three term test) = 53.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.94
Order of pole (three term test) = 41.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22808.3MB, alloc=44.3MB, time=297.24
x[1] = 0.6663 2.476
h = 0.0001 0.005
y2[1] (numeric) = -2.70158985853 -4.64181255524
y2[1] (closed_form) = -2.70158985853 -4.64181255524
absolute error = 3.396e-14
relative error = 6.322e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.70790812678 -3.64962225621
y1[1] (closed_form) = 5.70790812678 -3.64962225621
absolute error = 3.6e-14
relative error = 5.314e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.37
Order of pole (three term test) = 53.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.37
Order of pole (three term test) = 42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22856.1MB, alloc=44.3MB, time=297.86
x[1] = 0.6664 2.481
h = 0.0001 0.003
y2[1] (numeric) = -2.72035741483 -4.66504337581
y2[1] (closed_form) = -2.72035741483 -4.66504337581
absolute error = 3.517e-14
relative error = 6.513e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.73080412314 -3.66864242567
y1[1] (closed_form) = 5.73080412314 -3.66864242567
absolute error = 3.601e-14
relative error = 5.293e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.72
Order of pole (three term test) = 53.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.72
Order of pole (three term test) = 42.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22904.1MB, alloc=44.3MB, time=298.49
x[1] = 0.6665 2.484
h = 0.001 0.001
y2[1] (numeric) = -2.73185456364 -4.67888879678
y2[1] (closed_form) = -2.73185456364 -4.67888879678
absolute error = 3.517e-14
relative error = 6.491e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.74444740117 -3.68028793084
y1[1] (closed_form) = 5.74444740117 -3.68028793084
absolute error = 3.6e-14
relative error = 5.277e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.94
Order of pole (three term test) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.94
Order of pole (three term test) = 42.39 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6675 2.485
h = 0.001 0.003
y2[1] (numeric) = -2.74028397821 -4.67994922159
y2[1] (closed_form) = -2.74028397821 -4.67994922159
absolute error = 3.396e-14
relative error = 6.261e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.74539075231 -3.68870341896
y1[1] (closed_form) = 5.74539075231 -3.68870341896
absolute error = 3.6e-14
relative error = 5.273e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.01
Order of pole (three term test) = 53.85 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.01
Order of pole (three term test) = 42.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22951.8MB, alloc=44.3MB, time=299.11
x[1] = 0.6685 2.488
h = 0.0001 0.004
y2[1] (numeric) = -2.75612451186 -4.69050418762
y2[1] (closed_form) = -2.75612451186 -4.69050418762
absolute error = 3.421e-14
relative error = 6.287e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.75569822927 -3.70463324263
y1[1] (closed_form) = 5.75569822927 -3.70463324263
absolute error = 3.7e-14
relative error = 5.406e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.22
Order of pole (three term test) = 53.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.22
Order of pole (three term test) = 42.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22999.7MB, alloc=44.3MB, time=299.73
x[1] = 0.6686 2.492
h = 0.003 0.006
y2[1] (numeric) = -2.77145056436 -4.70919256305
y2[1] (closed_form) = -2.77145056436 -4.70919256305
absolute error = 3.396e-14
relative error = 6.214e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.7741212205 -3.7201583557
y1[1] (closed_form) = 5.7741212205 -3.7201583557
absolute error = 3.701e-14
relative error = 5.389e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.52
Order of pole (three term test) = 54.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.52
Order of pole (three term test) = 42.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23047.6MB, alloc=44.3MB, time=300.36
x[1] = 0.6716 2.498
h = 0.0001 0.005
y2[1] (numeric) = -2.80822982829 -4.7266723617
y2[1] (closed_form) = -2.80822982829 -4.7266723617
absolute error = 3.493e-14
relative error = 6.353e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.79105936726 -3.75705106045
y1[1] (closed_form) = 5.79105936726 -3.75705106045
absolute error = 3.7e-14
relative error = 5.360e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.96
Order of pole (three term test) = 54.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.96
Order of pole (three term test) = 43.36 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6717 2.503
h = 0.0001 0.003
y2[1] (numeric) = -2.82754422098 -4.7503092042
y2[1] (closed_form) = -2.82754422098 -4.7503092042
absolute error = 3.517e-14
relative error = 6.362e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.81436998555 -3.77661430197
y1[1] (closed_form) = 5.81436998555 -3.77661430197
absolute error = 3.7e-14
relative error = 5.337e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.33
Order of pole (three term test) = 54.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.33
Order of pole (three term test) = 43.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23095.3MB, alloc=44.3MB, time=300.98
x[1] = 0.6718 2.506
h = 0.001 0.001
y2[1] (numeric) = -2.8393741499 -4.76439487701
y2[1] (closed_form) = -2.8393741499 -4.76439487701
absolute error = 3.517e-14
relative error = 6.341e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.82825868595 -3.78859040506
y1[1] (closed_form) = 5.82825868595 -3.78859040506
absolute error = 3.701e-14
relative error = 5.325e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.55
Order of pole (three term test) = 54.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.55
Order of pole (three term test) = 43.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23143.1MB, alloc=44.3MB, time=301.60
x[1] = 0.6728 2.507
h = 0.001 0.003
y2[1] (numeric) = -2.84799576374 -4.76543070305
y2[1] (closed_form) = -2.84799576374 -4.76543070305
absolute error = 3.493e-14
relative error = 6.292e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.82917991522 -3.79719900265
y1[1] (closed_form) = 5.82917991522 -3.79719900265
absolute error = 3.7e-14
relative error = 5.318e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.63
Order of pole (three term test) = 54.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.63
Order of pole (three term test) = 43.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23191.1MB, alloc=44.3MB, time=302.23
x[1] = 0.6738 2.51
h = 0.0001 0.004
y2[1] (numeric) = -2.86424626128 -4.77612855955
y2[1] (closed_form) = -2.86424626128 -4.77612855955
absolute error = 3.493e-14
relative error = 6.272e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.8396361343 -3.8135381292
y1[1] (closed_form) = 5.8396361343 -3.8135381292
absolute error = 3.8e-14
relative error = 5.448e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.85
Order of pole (three term test) = 55.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.85
Order of pole (three term test) = 44.09 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6739 2.514
h = 0.003 0.006
y2[1] (numeric) = -2.88001722702 -4.79514243824
y2[1] (closed_form) = -2.88001722702 -4.79514243824
absolute error = 3.396e-14
relative error = 6.071e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.85839143919 -3.8295051972
y1[1] (closed_form) = 5.85839143919 -3.8295051972
absolute error = 3.8e-14
relative error = 5.429e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.16
Order of pole (three term test) = 55.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.16
Order of pole (three term test) = 44.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23238.7MB, alloc=44.3MB, time=302.85
x[1] = 0.6769 2.52
h = 0.0001 0.005
y2[1] (numeric) = -2.91770840057 -4.81279901914
y2[1] (closed_form) = -2.91770840057 -4.81279901914
absolute error = 3.396e-14
relative error = 6.033e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.87551875 -3.86731014983
y1[1] (closed_form) = 5.87551875 -3.86731014983
absolute error = 3.8e-14
relative error = 5.402e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.62
Order of pole (three term test) = 55.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.62
Order of pole (three term test) = 44.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23286.6MB, alloc=44.3MB, time=303.48
x[1] = 0.677 2.525
h = 0.0001 0.003
y2[1] (numeric) = -2.93758394804 -4.83684815568
y2[1] (closed_form) = -2.93758394804 -4.83684815568
absolute error = 3.421e-14
relative error = 6.044e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.89925005558 -3.88743081918
y1[1] (closed_form) = 5.89925005558 -3.88743081918
absolute error = 3.9e-14
relative error = 5.520e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.01
Order of pole (three term test) = 55.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.01
Order of pole (three term test) = 45.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23334.6MB, alloc=44.3MB, time=304.10
x[1] = 0.6771 2.528
h = 0.001 0.001
y2[1] (numeric) = -2.94975533565 -4.85117774336
y2[1] (closed_form) = -2.94975533565 -4.85117774336
absolute error = 3.517e-14
relative error = 6.195e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.91338771749 -3.89974621946
y1[1] (closed_form) = 5.91338771749 -3.89974621946
absolute error = 3.9e-14
relative error = 5.506e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.24
Order of pole (three term test) = 56.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.24
Order of pole (three term test) = 45.25 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6781 2.529
h = 0.001 0.003
y2[1] (numeric) = -2.95857332111 -4.85218743216
y2[1] (closed_form) = -2.95857332111 -4.85218743216
absolute error = 3.517e-14
relative error = 6.189e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 5.91428523721 -3.90855206623
y1[1] (closed_form) = 5.91428523721 -3.90855206623
absolute error = 3.8e-14
relative error = 5.360e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.32
Order of pole (three term test) = 56.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.32
Order of pole (three term test) = 45.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23382.5MB, alloc=44.3MB, time=304.72
x[1] = 0.6791 2.532
h = 0.0001 0.004
y2[1] (numeric) = -2.97524368644 -4.86302926663
y2[1] (closed_form) = -2.97524368644 -4.86302926663
absolute error = 3.517e-14
relative error = 6.169e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 5.92489115507 -3.92531038362
y1[1] (closed_form) = 5.92489115507 -3.92531038362
absolute error = 3.801e-14
relative error = 5.349e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.56
Order of pole (three term test) = 56.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.56
Order of pole (three term test) = 45.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23430.4MB, alloc=44.3MB, time=305.35
x[1] = 0.6792 2.536
h = 0.003 0.006
y2[1] (numeric) = -2.99147119016 -4.88237363938
y2[1] (closed_form) = -2.99147119016 -4.88237363938
absolute error = 3.517e-14
relative error = 6.142e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 5.94398360079 -3.94173106036
y1[1] (closed_form) = 5.94398360079 -3.94173106036
absolute error = 3.801e-14
relative error = 5.330e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.87
Order of pole (three term test) = 56.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.87
Order of pole (three term test) = 45.82 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6822 2.542
h = 0.0001 0.005
y2[1] (numeric) = -3.03009557541 -4.9002062623
y2[1] (closed_form) = -3.03009557541 -4.9002062623
absolute error = 3.544e-14
relative error = 6.151e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 5.9612990676 -3.9804694914
y1[1] (closed_form) = 5.9612990676 -3.9804694914
absolute error = 3.801e-14
relative error = 5.303e-13 %
Correct digits = 14
memory used=23478.2MB, alloc=44.3MB, time=305.97
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.36
Order of pole (three term test) = 56.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.36
Order of pole (three term test) = 46.34 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6823 2.547
h = 0.0001 0.003
y2[1] (numeric) = -3.05054694806 -4.9246740221
y2[1] (closed_form) = -3.05054694806 -4.9246740221
absolute error = 3.544e-14
relative error = 6.118e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 5.9854571876 -4.00116229662
y1[1] (closed_form) = 5.9854571876 -4.00116229662
absolute error = 3.801e-14
relative error = 5.280e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.76
Order of pole (three term test) = 57.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.76
Order of pole (three term test) = 46.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23525.9MB, alloc=44.3MB, time=306.59
x[1] = 0.6824 2.55
h = 0.001 0.001
y2[1] (numeric) = -3.06306868549 -4.93925121926
y2[1] (closed_form) = -3.06306868549 -4.93925121926
absolute error = 3.544e-14
relative error = 6.098e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 5.99984738453 -4.01382590613
y1[1] (closed_form) = 5.99984738453 -4.01382590613
absolute error = 3.801e-14
relative error = 5.266e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.01
Order of pole (three term test) = 57.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.01
Order of pole (three term test) = 46.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23573.9MB, alloc=44.3MB, time=307.21
x[1] = 0.6834 2.551
h = 0.0001 0.004
y2[1] (numeric) = -3.07208729836 -4.94023317466
y2[1] (closed_form) = -3.07208729836 -4.94023317466
absolute error = 3.544e-14
relative error = 6.092e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.00071955024 -4.02283322617
y1[1] (closed_form) = 6.00071955024 -4.02283322617
absolute error = 3.801e-14
relative error = 5.262e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.09
Order of pole (three term test) = 57.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.09
Order of pole (three term test) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6835 2.555
h = 0.003 0.006
y2[1] (numeric) = -3.08871328253 -4.95987168794
y2[1] (closed_form) = -3.08871328253 -4.95987168794
absolute error = 3.544e-14
relative error = 6.065e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.02011169522 -4.03964980887
y1[1] (closed_form) = 6.02011169522 -4.03964980887
absolute error = 3.801e-14
relative error = 5.243e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.42
Order of pole (three term test) = 57.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.42
Order of pole (three term test) = 47.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23621.7MB, alloc=44.3MB, time=307.83
x[1] = 0.6865 2.561
h = 0.0001 0.005
y2[1] (numeric) = -3.12815627694 -4.97786661488
y2[1] (closed_form) = -3.12815627694 -4.97786661488
absolute error = 3.640e-14
relative error = 6.191e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.03759968511 -4.07920688354
y1[1] (closed_form) = 6.03759968511 -4.07920688354
absolute error = 3.805e-14
relative error = 5.222e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.92
Order of pole (three term test) = 57.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.92
Order of pole (three term test) = 47.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23669.5MB, alloc=44.3MB, time=308.45
x[1] = 0.6866 2.566
h = 0.0001 0.003
y2[1] (numeric) = -3.14911023287 -5.00270692683
y2[1] (closed_form) = -3.14911023287 -5.00270692683
absolute error = 3.669e-14
relative error = 6.206e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.0621372063 -4.10039903231
y1[1] (closed_form) = 6.0621372063 -4.10039903231
absolute error = 3.805e-14
relative error = 5.199e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.34
Order of pole (three term test) = 58.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.34
Order of pole (three term test) = 48.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23717.5MB, alloc=44.3MB, time=309.08
x[1] = 0.6867 2.569
h = 0.001 0.001
y2[1] (numeric) = -3.16193781543 -5.01750456186
y2[1] (closed_form) = -3.16193781543 -5.01750456186
absolute error = 3.669e-14
relative error = 6.186e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.07675196084 -4.11336660451
y1[1] (closed_form) = 6.07675196083 -4.11336660451
absolute error = 3.805e-14
relative error = 5.186e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.6
Order of pole (three term test) = 58.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.6
Order of pole (three term test) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6877 2.57
h = 0.001 0.003
y2[1] (numeric) = -3.17113295182 -5.01846378221
y2[1] (closed_form) = -3.17113295182 -5.01846378221
absolute error = 3.669e-14
relative error = 6.180e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.07760341115 -4.12255112393
y1[1] (closed_form) = 6.07760341115 -4.12255112393
absolute error = 3.805e-14
relative error = 5.182e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.68
Order of pole (three term test) = 58.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.68
Order of pole (three term test) = 48.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23765.3MB, alloc=44.3MB, time=309.70
x[1] = 0.6887 2.573
h = 0.0001 0.004
y2[1] (numeric) = -3.18860998293 -5.02958159913
y2[1] (closed_form) = -3.18860998293 -5.02958159913
absolute error = 3.669e-14
relative error = 6.161e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.08849560928 -4.14011474387
y1[1] (closed_form) = 6.08849560928 -4.14011474387
absolute error = 3.805e-14
relative error = 5.168e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.94
Order of pole (three term test) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.94
Order of pole (three term test) = 48.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23813.1MB, alloc=44.3MB, time=310.32
x[1] = 0.6888 2.577
h = 0.003 0.006
y2[1] (numeric) = -3.20571483943 -5.04956015707
y2[1] (closed_form) = -3.20571483943 -5.04956015707
absolute error = 3.669e-14
relative error = 6.134e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.1082341514 -4.15740732624
y1[1] (closed_form) = 6.1082341514 -4.15740732624
absolute error = 3.812e-14
relative error = 5.159e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.28
Order of pole (three term test) = 58.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 43.28
Order of pole (three term test) = 48.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23861.1MB, alloc=44.3MB, time=310.95
x[1] = 0.6918 2.583
h = 0.0001 0.005
y2[1] (numeric) = -3.24613194566 -5.06772964592
y2[1] (closed_form) = -3.24613194566 -5.06772964592
absolute error = 3.764e-14
relative error = 6.255e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.12590833246 -4.19793865708
y1[1] (closed_form) = 6.12590833246 -4.19793865708
absolute error = 3.912e-14
relative error = 5.267e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.8
Order of pole (three term test) = 59.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 43.8
Order of pole (three term test) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6919 2.588
h = 0.0001 0.003
y2[1] (numeric) = -3.26768991294 -5.09300069347
y2[1] (closed_form) = -3.26768991294 -5.09300069347
absolute error = 3.764e-14
relative error = 6.221e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.15088441702 -4.21973120078
y1[1] (closed_form) = 6.15088441702 -4.21973120078
absolute error = 3.912e-14
relative error = 5.244e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.24
Order of pole (three term test) = 59.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.24
Order of pole (three term test) = 49.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23908.9MB, alloc=44.3MB, time=311.57
x[1] = 0.692 2.591
h = 0.001 0.001
y2[1] (numeric) = -3.28088492741 -5.10805300755
y2[1] (closed_form) = -3.28088492741 -5.10805300755
absolute error = 3.764e-14
relative error = 6.201e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.16575855835 -4.23306410499
y1[1] (closed_form) = 6.16575855835 -4.23306410499
absolute error = 4.011e-14
relative error = 5.363e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.51
Order of pole (three term test) = 59.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.51
Order of pole (three term test) = 50 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23956.9MB, alloc=44.3MB, time=312.19
x[1] = 0.693 2.592
h = 0.001 0.003
y2[1] (numeric) = -3.29028885844 -5.10898141798
y2[1] (closed_form) = -3.29028885844 -5.10898141798
absolute error = 3.860e-14
relative error = 6.352e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.16658149024 -4.24245820896
y1[1] (closed_form) = 6.16658149024 -4.24245820896
absolute error = 4.011e-14
relative error = 5.359e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.6
Order of pole (three term test) = 59.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.6
Order of pole (three term test) = 50.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24004.8MB, alloc=44.3MB, time=312.82
x[1] = 0.694 2.595
h = 0.0001 0.004
y2[1] (numeric) = -3.30821533779 -5.12024626641
y2[1] (closed_form) = -3.30821533779 -5.12024626641
absolute error = 3.764e-14
relative error = 6.175e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.17762608131 -4.26047056157
y1[1] (closed_form) = 6.17762608131 -4.26047056157
absolute error = 3.920e-14
relative error = 5.224e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.87
Order of pole (three term test) = 59.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.87
Order of pole (three term test) = 50.39 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6941 2.599
h = 0.003 0.006
y2[1] (numeric) = -3.32581152448 -5.14056998853
y2[1] (closed_form) = -3.32581152448 -5.14056998853
absolute error = 3.764e-14
relative error = 6.148e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.19771598689 -4.27825163107
y1[1] (closed_form) = 6.19771598689 -4.27825163107
absolute error = 3.912e-14
relative error = 5.194e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.23
Order of pole (three term test) = 60.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 45.23
Order of pole (three term test) = 50.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24052.6MB, alloc=44.3MB, time=313.44
x[1] = 0.6971 2.605
h = 0.0001 0.005
y2[1] (numeric) = -3.36722540705 -5.15891289718
y2[1] (closed_form) = -3.36722540705 -5.15891289718
absolute error = 3.764e-14
relative error = 6.110e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.21557496455 -4.31977981918
y1[1] (closed_form) = 6.21557496455 -4.31977981918
absolute error = 3.920e-14
relative error = 5.179e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.77
Order of pole (three term test) = 60.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 45.77
Order of pole (three term test) = 51.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24100.4MB, alloc=44.3MB, time=314.06
x[1] = 0.6972 2.61
h = 0.0001 0.003
y2[1] (numeric) = -3.38940310811 -5.18462117427
y2[1] (closed_form) = -3.38940310811 -5.18462117427
absolute error = 3.764e-14
relative error = 6.077e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.24099591723 -4.34218851839
y1[1] (closed_form) = 6.24099591723 -4.34218851839
absolute error = 3.920e-14
relative error = 5.157e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.23
Order of pole (three term test) = 61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.23
Order of pole (three term test) = 51.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24148.4MB, alloc=44.3MB, time=314.69
x[1] = 0.6973 2.613
h = 0.001 0.001
y2[1] (numeric) = -3.40297508086 -5.19993195279
y2[1] (closed_form) = -3.40297508086 -5.19993195279
absolute error = 3.764e-14
relative error = 6.057e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.25613311736 -4.3558963023
y1[1] (closed_form) = 6.25613311736 -4.3558963023
absolute error = 3.920e-14
relative error = 5.143e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.51
Order of pole (three term test) = 61.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.51
Order of pole (three term test) = 51.86 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6983 2.614
h = 0.001 0.003
y2[1] (numeric) = -3.41259231051 -5.20082778343
y2[1] (closed_form) = -3.41259231051 -5.20082778343
absolute error = 3.764e-14
relative error = 6.051e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.25692571513 -4.36550446573
y1[1] (closed_form) = 6.25692571513 -4.36550446573
absolute error = 4.020e-14
relative error = 5.269e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.61
Order of pole (three term test) = 61.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.61
Order of pole (three term test) = 51.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24196.2MB, alloc=44.3MB, time=315.31
x[1] = 0.6993 2.617
h = 0.0001 0.004
y2[1] (numeric) = -3.43097903838 -5.21224061848
y2[1] (closed_form) = -3.43097903838 -5.21224061848
absolute error = 3.764e-14
relative error = 6.032e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.26812353383 -4.38397633904
y1[1] (closed_form) = 6.26812353383 -4.38397633904
absolute error = 4.020e-14
relative error = 5.255e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.89
Order of pole (three term test) = 61.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.89
Order of pole (three term test) = 52.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24244.0MB, alloc=44.3MB, time=315.93
x[1] = 0.6994 2.621
h = 0.003 0.006
y2[1] (numeric) = -3.4490793176 -5.23291466709
y2[1] (closed_form) = -3.4490793176 -5.23291466709
absolute error = 3.860e-14
relative error = 6.159e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.28856981546 -4.4022586878
y1[1] (closed_form) = 6.28856981546 -4.4022586878
absolute error = 4.020e-14
relative error = 5.237e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.26
Order of pole (three term test) = 61.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 47.26
Order of pole (three term test) = 52.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24291.8MB, alloc=44.3MB, time=316.55
x[1] = 0.7024 2.627
h = 0.0001 0.005
y2[1] (numeric) = -3.49151313593 -5.25142970004
y2[1] (closed_form) = -3.49151313593 -5.25142970004
absolute error = 3.736e-14
relative error = 5.925e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.30661204693 -4.44480683185
y1[1] (closed_form) = 6.30661204693 -4.44480683185
absolute error = 4.020e-14
relative error = 5.210e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.83
Order of pole (three term test) = 62.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 47.83
Order of pole (three term test) = 53.2 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7025 2.632
h = 0.0001 0.003
y2[1] (numeric) = -3.51432667772 -5.27758175544
y2[1] (closed_form) = -3.51432667772 -5.27758175544
absolute error = 3.833e-14
relative error = 6.045e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.33248423162 -4.46784783182
y1[1] (closed_form) = 6.33248423162 -4.46784783182
absolute error = 4.020e-14
relative error = 5.187e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 48.31
Order of pole (three term test) = 62.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 48.31
Order of pole (three term test) = 53.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24339.5MB, alloc=44.3MB, time=317.17
x[1] = 0.7026 2.635
h = 0.001 0.001
y2[1] (numeric) = -3.52828536726 -5.29315481371
y2[1] (closed_form) = -3.52828536726 -5.29315481371
absolute error = 3.833e-14
relative error = 6.025e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.34788819504 -4.48194027538
y1[1] (closed_form) = 6.34788819504 -4.48194027538
absolute error = 4.020e-14
relative error = 5.173e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 48.61
Order of pole (three term test) = 62.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 48.61
Order of pole (three term test) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24387.5MB, alloc=44.3MB, time=317.80
x[1] = 0.7036 2.636
h = 0.001 0.003
y2[1] (numeric) = -3.53812048918 -5.29401623007
y2[1] (closed_form) = -3.53812048918 -5.29401623007
absolute error = 3.956e-14
relative error = 6.213e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.34864857927 -4.49176706371
y1[1] (closed_form) = 6.34864857927 -4.49176706371
absolute error = 4.020e-14
relative error = 5.169e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 48.7
Order of pole (three term test) = 62.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 48.7
Order of pole (three term test) = 53.97 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7046 2.639
h = 0.0001 0.004
y2[1] (numeric) = -3.55697851016 -5.30557796701
y2[1] (closed_form) = -3.55697851016 -5.30557796701
absolute error = 3.956e-14
relative error = 6.193e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.36000042297 -4.510709491
y1[1] (closed_form) = 6.36000042297 -4.510709491
absolute error = 4.020e-14
relative error = 5.156e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49
Order of pole (three term test) = 63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49
Order of pole (three term test) = 54.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24435.3MB, alloc=44.3MB, time=318.42
x[1] = 0.7047 2.643
h = 0.003 0.006
y2[1] (numeric) = -3.5755959558 -5.32660754657
y2[1] (closed_form) = -3.5755959558 -5.32660754657
absolute error = 3.956e-14
relative error = 6.166e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.3808081388 -4.52950622277
y1[1] (closed_form) = 6.3808081388 -4.52950622277
absolute error = 4.011e-14
relative error = 5.126e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.39
Order of pole (three term test) = 63.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49.39
Order of pole (three term test) = 54.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24483.2MB, alloc=44.3MB, time=319.04
x[1] = 0.7077 2.649
h = 0.0001 0.005
y2[1] (numeric) = -3.61907337448 -5.34529324893
y2[1] (closed_form) = -3.61907337448 -5.34529324893
absolute error = 3.985e-14
relative error = 6.173e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.39903192696 -4.57309792921
y1[1] (closed_form) = 6.39903192696 -4.57309792921
absolute error = 4.111e-14
relative error = 5.227e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.99
Order of pole (three term test) = 63.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49.99
Order of pole (three term test) = 55.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24531.0MB, alloc=44.3MB, time=319.67
x[1] = 0.7078 2.654
h = 0.0001 0.003
y2[1] (numeric) = -3.64253925732 -5.37189568543
y2[1] (closed_form) = -3.64253925732 -5.37189568543
absolute error = 3.985e-14
relative error = 6.140e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.42536176581 -4.5967877687
y1[1] (closed_form) = 6.42536176581 -4.5967877687
absolute error = 4.111e-14
relative error = 5.204e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.49
Order of pole (three term test) = 64.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.49
Order of pole (three term test) = 55.66 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7079 2.657
h = 0.001 0.001
y2[1] (numeric) = -3.65689465966 -5.38773486814
y2[1] (closed_form) = -3.65689465966 -5.38773486814
absolute error = 3.985e-14
relative error = 6.120e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.44103622892 -4.61127488947
y1[1] (closed_form) = 6.44103622892 -4.61127488947
absolute error = 4.119e-14
relative error = 5.200e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.79
Order of pole (three term test) = 64.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.79
Order of pole (three term test) = 55.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24578.7MB, alloc=44.3MB, time=320.30
x[1] = 0.7089 2.658
h = 0.0001 0.004
y2[1] (numeric) = -3.66695235879 -5.38855996923
y2[1] (closed_form) = -3.66695235879 -5.38855996923
absolute error = 3.985e-14
relative error = 6.114e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.44176245451 -4.62132496028
y1[1] (closed_form) = 6.44176245451 -4.62132496028
absolute error = 4.119e-14
relative error = 5.196e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.89
Order of pole (three term test) = 64.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.89
Order of pole (three term test) = 56.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24626.7MB, alloc=44.3MB, time=320.92
x[1] = 0.709 2.662
h = 0.003 0.006
y2[1] (numeric) = -3.6860213562 -5.40990615561
y2[1] (closed_form) = -3.6860213562 -5.40990615561
absolute error = 4.080e-14
relative error = 6.233e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.4628917112 -4.64057080396
y1[1] (closed_form) = 6.4628917112 -4.64057080396
absolute error = 4.119e-14
relative error = 5.178e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.3
Order of pole (three term test) = 64.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 51.3
Order of pole (three term test) = 56.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24674.5MB, alloc=44.3MB, time=321.54
x[1] = 0.712 2.668
h = 0.0001 0.005
y2[1] (numeric) = -3.73041440826 -5.42875029776
y2[1] (closed_form) = -3.73041440826 -5.42875029776
absolute error = 4.080e-14
relative error = 6.195e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.48128311905 -4.68507794062
y1[1] (closed_form) = 6.48128311905 -4.68507794062
absolute error = 4.130e-14
relative error = 5.165e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.92
Order of pole (three term test) = 65.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 51.92
Order of pole (three term test) = 57.08 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7121 2.673
h = 0.0001 0.003
y2[1] (numeric) = -3.75444985165 -5.45575378092
y2[1] (closed_form) = -3.75444985165 -5.45575378092
absolute error = 4.052e-14
relative error = 6.119e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.50802008238 -4.70933427373
y1[1] (closed_form) = 6.50802008238 -4.70933427373
absolute error = 4.130e-14
relative error = 5.142e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.44
Order of pole (three term test) = 65.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.44
Order of pole (three term test) = 57.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24722.2MB, alloc=44.3MB, time=322.16
x[1] = 0.7122 2.676
h = 0.001 0.001
y2[1] (numeric) = -3.76915168808 -5.47183002762
y2[1] (closed_form) = -3.76915168808 -5.47183002762
absolute error = 3.956e-14
relative error = 5.954e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.52393526683 -4.72416604332
y1[1] (closed_form) = 6.52393526683 -4.72416604332
absolute error = 4.130e-14
relative error = 5.128e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.76
Order of pole (three term test) = 65.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.76
Order of pole (three term test) = 57.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24770.1MB, alloc=44.3MB, time=322.79
x[1] = 0.7132 2.677
h = 0.001 0.003
y2[1] (numeric) = -3.77940526148 -5.47262502427
y2[1] (closed_form) = -3.77940526148 -5.47262502427
absolute error = 4.052e-14
relative error = 6.093e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.52463321759 -4.73441254921
y1[1] (closed_form) = 6.52463321759 -4.73441254921
absolute error = 4.130e-14
relative error = 5.124e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.86
Order of pole (three term test) = 65.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.86
Order of pole (three term test) = 57.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24818.0MB, alloc=44.3MB, time=323.41
x[1] = 0.7142 2.68
h = 0.0001 0.004
y2[1] (numeric) = -3.79916870601 -5.48447205971
y2[1] (closed_form) = -3.79916870601 -5.48447205971
absolute error = 4.052e-14
relative error = 6.074e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.53627957839 -4.75425893965
y1[1] (closed_form) = 6.53627957839 -4.75425893965
absolute error = 4.230e-14
relative error = 5.233e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 53.18
Order of pole (three term test) = 66.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 53.18
Order of pole (three term test) = 58.26 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7143 2.684
h = 0.003 0.006
y2[1] (numeric) = -3.81877998797 -5.50618373601
y2[1] (closed_form) = -3.81877998797 -5.50618373601
absolute error = 3.985e-14
relative error = 5.947e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.55777996522 -4.77404434203
y1[1] (closed_form) = 6.55777996522 -4.77404434203
absolute error = 4.130e-14
relative error = 5.092e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 53.61
Order of pole (three term test) = 66.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 53.61
Order of pole (three term test) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24865.7MB, alloc=44.3MB, time=324.03
x[1] = 0.7173 2.69
h = 0.0001 0.005
y2[1] (numeric) = -3.86426207717 -5.5251956914
y2[1] (closed_form) = -3.86426207717 -5.5251956914
absolute error = 4.080e-14
relative error = 6.052e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.57634963541 -4.81964037906
y1[1] (closed_form) = 6.57634963541 -4.81964037906
absolute error = 4.130e-14
relative error = 5.066e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.26
Order of pole (three term test) = 66.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 54.26
Order of pole (three term test) = 59.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24913.5MB, alloc=44.3MB, time=324.66
x[1] = 0.7174 2.695
h = 0.0001 0.003
y2[1] (numeric) = -3.88898156298 -5.55266219087
y2[1] (closed_form) = -3.88898156298 -5.55266219087
absolute error = 4.080e-14
relative error = 6.019e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.60355656335 -4.84457732686
y1[1] (closed_form) = 6.60355656335 -4.84457732686
absolute error = 4.119e-14
relative error = 5.030e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.8
Order of pole (three term test) = 67.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 54.8
Order of pole (three term test) = 59.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24961.4MB, alloc=44.3MB, time=325.28
x[1] = 0.7175 2.698
h = 0.001 0.001
y2[1] (numeric) = -3.90409931665 -5.56901191832
y2[1] (closed_form) = -3.90409931665 -5.56901191832
absolute error = 4.080e-14
relative error = 6.000e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.6197494091 -4.85982301965
y1[1] (closed_form) = 6.6197494091 -4.85982301965
absolute error = 4.130e-14
relative error = 5.030e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 55.13
Order of pole (three term test) = 67.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 55.13
Order of pole (three term test) = 60.09 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7185 2.699
h = 0.001 0.003
y2[1] (numeric) = -3.91458445834 -5.56976693711
y2[1] (closed_form) = -3.91458445834 -5.56976693711
absolute error = 4.052e-14
relative error = 5.952e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.62040945839 -4.87030175086
y1[1] (closed_form) = 6.62040945839 -4.87030175086
absolute error = 4.130e-14
relative error = 5.025e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 55.24
Order of pole (three term test) = 67.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 55.24
Order of pole (three term test) = 60.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25009.3MB, alloc=44.3MB, time=325.90
x[1] = 0.7195 2.702
h = 0.0001 0.004
y2[1] (numeric) = -3.93485217969 -5.5817653948
y2[1] (closed_form) = -3.93485217969 -5.5817653948
absolute error = 4.052e-14
relative error = 5.934e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.63221204088 -4.89065165251
y1[1] (closed_form) = 6.63221204088 -4.89065165251
absolute error = 4.130e-14
relative error = 5.012e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 55.57
Order of pole (three term test) = 67.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 55.57
Order of pole (three term test) = 60.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25057.2MB, alloc=44.3MB, time=326.53
x[1] = 0.7196 2.706
h = 0.003 0.006
y2[1] (numeric) = -3.95501975098 -5.60384788617
y2[1] (closed_form) = -3.95501975098 -5.60384788617
absolute error = 4.052e-14
relative error = 5.908e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.65408874605 -4.91099064848
y1[1] (closed_form) = 6.65408874605 -4.91099064848
absolute error = 4.144e-14
relative error = 5.010e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.02
Order of pole (three term test) = 68.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 56.02
Order of pole (three term test) = 60.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25105.0MB, alloc=44.3MB, time=327.16
x[1] = 0.7226 2.712
h = 0.0001 0.005
y2[1] (numeric) = -4.00161604755 -5.62302571555
y2[1] (closed_form) = -4.00161604755 -5.62302571555
absolute error = 4.052e-14
relative error = 5.871e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.67283451111 -4.95770070494
y1[1] (closed_form) = 6.67283451111 -4.95770070494
absolute error = 4.243e-14
relative error = 5.104e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.7
Order of pole (three term test) = 68.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 56.7
Order of pole (three term test) = 61.72 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7227 2.717
h = 0.0001 0.003
y2[1] (numeric) = -4.02703725163 -5.65096198892
y2[1] (closed_form) = -4.02703725163 -5.65096198892
absolute error = 3.956e-14
relative error = 5.701e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.70051799219 -4.98333598188
y1[1] (closed_form) = 6.70051799219 -4.98333598188
absolute error = 4.243e-14
relative error = 5.081e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.27
Order of pole (three term test) = 69.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.27
Order of pole (three term test) = 62.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25152.6MB, alloc=44.3MB, time=327.78
x[1] = 0.7228 2.72
h = 0.001 0.001
y2[1] (numeric) = -4.04258162813 -5.6675891256
y2[1] (closed_form) = -4.04258162813 -5.6675891256
absolute error = 3.956e-14
relative error = 5.683e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.71699232636 -4.99900632519
y1[1] (closed_form) = 6.71699232636 -4.99900632519
absolute error = 4.243e-14
relative error = 5.067e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.61
Order of pole (three term test) = 69.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.61
Order of pole (three term test) = 62.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25200.6MB, alloc=44.3MB, time=328.40
x[1] = 0.7238 2.721
h = 0.001 0.003
y2[1] (numeric) = -4.05330329461 -5.66830206545
y2[1] (closed_form) = -4.05330329461 -5.66830206545
absolute error = 3.956e-14
relative error = 5.677e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.71761233128 -5.00972221315
y1[1] (closed_form) = 6.71761233128 -5.00972221315
absolute error = 4.243e-14
relative error = 5.063e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.73
Order of pole (three term test) = 69.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.73
Order of pole (three term test) = 62.67 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7248 2.724
h = 0.0001 0.004
y2[1] (numeric) = -4.07408733153 -5.68045268896
y2[1] (closed_form) = -4.07408733153 -5.68045268896
absolute error = 3.985e-14
relative error = 5.701e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.72957177056 -5.03058765657
y1[1] (closed_form) = 6.72957177056 -5.03058765657
absolute error = 4.230e-14
relative error = 5.034e-13 %
Correct digits = 14
memory used=25248.5MB, alloc=44.3MB, time=329.03
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 58.07
Order of pole (three term test) = 69.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 58.07
Order of pole (three term test) = 63.03 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7249 2.728
h = 0.003 0.006
y2[1] (numeric) = -4.09482553705 -5.70291135989
y2[1] (closed_form) = -4.09482553705 -5.70291135989
absolute error = 3.956e-14
relative error = 5.635e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.75183002475 -5.05149462117
y1[1] (closed_form) = 6.75183002475 -5.05149462117
absolute error = 4.243e-14
relative error = 5.031e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 58.54
Order of pole (three term test) = 70.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 58.54
Order of pole (three term test) = 63.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25296.3MB, alloc=44.3MB, time=329.65
x[1] = 0.7279 2.734
h = 0.0001 0.005
y2[1] (numeric) = -4.14256175792 -5.72225293979
y2[1] (closed_form) = -4.14256175792 -5.72225293979
absolute error = 4.052e-14
relative error = 5.736e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.77074953768 -5.09934436508
y1[1] (closed_form) = 6.77074953768 -5.09934436508
absolute error = 4.342e-14
relative error = 5.122e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 59.25
Order of pole (three term test) = 70.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 59.25
Order of pole (three term test) = 64.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25344.1MB, alloc=44.3MB, time=330.27
x[1] = 0.728 2.739
h = 0.0001 0.003
y2[1] (numeric) = -4.1687027856 -5.75066579516
y2[1] (closed_form) = -4.1687027856 -5.75066579516
absolute error = 4.052e-14
relative error = 5.705e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.79891621483 -5.12569611516
y1[1] (closed_form) = 6.79891621483 -5.12569611516
absolute error = 4.243e-14
relative error = 4.983e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 59.84
Order of pole (three term test) = 71.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 59.84
Order of pole (three term test) = 64.74 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7281 2.742
h = 0.001 0.001
y2[1] (numeric) = -4.1846847497 -5.76757429654
y2[1] (closed_form) = -4.1846847497 -5.76757429654
absolute error = 4.052e-14
relative error = 5.687e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.81567589384 -5.14180209556
y1[1] (closed_form) = 6.81567589384 -5.14180209556
absolute error = 4.243e-14
relative error = 4.969e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 60.2
Order of pole (three term test) = 71.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 60.2
Order of pole (three term test) = 65.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25391.9MB, alloc=44.3MB, time=330.89
x[1] = 0.7291 2.743
h = 0.001 0.003
y2[1] (numeric) = -4.19564799549 -5.768242982
y2[1] (closed_form) = -4.19564799549 -5.768242982
absolute error = 4.052e-14
relative error = 5.681e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 6.81625363793 -5.15276017047
y1[1] (closed_form) = 6.81625363793 -5.15276017047
absolute error = 4.342e-14
relative error = 5.081e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 60.32
Order of pole (three term test) = 71.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 60.32
Order of pole (three term test) = 65.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25439.8MB, alloc=44.3MB, time=331.52
x[1] = 0.7301 2.746
h = 0.0001 0.004
y2[1] (numeric) = -4.21696065765 -5.78054646388
y2[1] (closed_form) = -4.21696065765 -5.78054646388
absolute error = 4.052e-14
relative error = 5.663e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.8283705204 -5.17415345786
y1[1] (closed_form) = 6.8283705204 -5.17415345786
absolute error = 4.342e-14
relative error = 5.068e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 60.69
Order of pole (three term test) = 71.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 60.69
Order of pole (three term test) = 65.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25487.8MB, alloc=44.3MB, time=332.14
x[1] = 0.7302 2.75
h = 0.003 0.006
y2[1] (numeric) = -4.23828419016 -5.80338671727
y2[1] (closed_form) = -4.23828419016 -5.80338671727
absolute error = 4.148e-14
relative error = 5.773e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.85101559577 -5.19564311407
y1[1] (closed_form) = 6.85101559577 -5.19564311407
absolute error = 4.342e-14
relative error = 5.049e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.17
Order of pole (three term test) = 72.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 61.17
Order of pole (three term test) = 66.03 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7332 2.756
h = 0.0001 0.005
y2[1] (numeric) = -4.28718661017 -5.82288973302
y2[1] (closed_form) = -4.28718661017 -5.82288973302
absolute error = 4.148e-14
relative error = 5.737e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.87010632302 -5.24465877359
y1[1] (closed_form) = 6.87010632302 -5.24465877359
absolute error = 4.357e-14
relative error = 5.041e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.91
Order of pole (three term test) = 72.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 61.91
Order of pole (three term test) = 66.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25535.4MB, alloc=44.3MB, time=332.76
x[1] = 0.7333 2.761
h = 0.0001 0.003
y2[1] (numeric) = -4.31406600613 -5.8517860279
y2[1] (closed_form) = -4.31406600613 -5.8517860279
absolute error = 4.148e-14
relative error = 5.706e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.89876289237 -5.27174558012
y1[1] (closed_form) = 6.89876289237 -5.27174558012
absolute error = 4.455e-14
relative error = 5.131e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.53
Order of pole (three term test) = 73.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 62.53
Order of pole (three term test) = 67.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25583.2MB, alloc=44.3MB, time=333.38
x[1] = 0.7334 2.764
h = 0.001 0.001
y2[1] (numeric) = -4.33049678774 -5.86897987568
y2[1] (closed_form) = -4.33049678774 -5.86897987568
absolute error = 4.176e-14
relative error = 5.726e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 6.91581180114 -5.28829844935
y1[1] (closed_form) = 6.91581180114 -5.28829844935
absolute error = 4.455e-14
relative error = 5.118e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.91
Order of pole (three term test) = 73.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 62.91
Order of pole (three term test) = 67.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25631.1MB, alloc=44.3MB, time=334.03
x[1] = 0.7344 2.765
h = 0.0001 0.004
y2[1] (numeric) = -4.34170676718 -5.8696020548
y2[1] (closed_form) = -4.34170676718 -5.8696020548
absolute error = 4.176e-14
relative error = 5.720e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 6.91634499219 -5.299503842
y1[1] (closed_form) = 6.91634499219 -5.299503842
absolute error = 4.455e-14
relative error = 5.113e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.04
Order of pole (three term test) = 73.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 63.04
Order of pole (three term test) = 67.92 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7345 2.769
h = 0.003 0.006
y2[1] (numeric) = -4.36354153305 -5.89278233398
y2[1] (closed_form) = -4.36354153305 -5.89278233398
absolute error = 4.272e-14
relative error = 5.826e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 6.93933446939 -5.32150242698
y1[1] (closed_form) = 6.93933446939 -5.32150242698
absolute error = 4.455e-14
relative error = 5.095e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.54
Order of pole (three term test) = 74.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 63.54
Order of pole (three term test) = 68.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25678.8MB, alloc=44.3MB, time=334.66
x[1] = 0.7375 2.775
h = 0.0001 0.005
y2[1] (numeric) = -4.41346737115 -5.91243663179
y2[1] (closed_form) = -4.41346737115 -5.91243663179
absolute error = 4.272e-14
relative error = 5.790e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 6.95858471973 -5.3715411118
y1[1] (closed_form) = 6.95858471973 -5.3715411118
absolute error = 4.455e-14
relative error = 5.068e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.31
Order of pole (three term test) = 74.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 64.31
Order of pole (three term test) = 69.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25726.7MB, alloc=44.3MB, time=335.28
x[1] = 0.7376 2.78
h = 0.0001 0.003
y2[1] (numeric) = -4.44099165205 -5.94176368786
y2[1] (closed_form) = -4.44099165205 -5.94176368786
absolute error = 4.368e-14
relative error = 5.888e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 6.98767743931 -5.39926990921
y1[1] (closed_form) = 6.98767743931 -5.39926990921
absolute error = 4.571e-14
relative error = 5.176e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 64.96
Order of pole (three term test) = 75.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 64.96
Order of pole (three term test) = 69.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25774.6MB, alloc=44.3MB, time=335.90
x[1] = 0.7377 2.783
h = 0.001 0.001
y2[1] (numeric) = -4.45781449624 -5.95921189356
y2[1] (closed_form) = -4.45781449624 -5.95921189356
absolute error = 4.368e-14
relative error = 5.869e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 7.00498395025 -5.41621315365
y1[1] (closed_form) = 7.00498395025 -5.41621315365
absolute error = 4.571e-14
relative error = 5.162e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.35
Order of pole (three term test) = 75.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 65.35
Order of pole (three term test) = 70.15 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7387 2.784
h = 0.001 0.003
y2[1] (numeric) = -4.46924165275 -5.95979520273
y2[1] (closed_form) = -4.46924165275 -5.95979520273
absolute error = 4.438e-14
relative error = 5.958e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 7.00547992763 -5.42763618519
y1[1] (closed_form) = 7.00547992763 -5.42763618519
absolute error = 4.554e-14
relative error = 5.139e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.48
Order of pole (three term test) = 75.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 65.48
Order of pole (three term test) = 70.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25822.4MB, alloc=44.3MB, time=336.53
x[1] = 0.7397 2.787
h = 0.0001 0.004
y2[1] (numeric) = -4.49156983992 -5.97239143227
y2[1] (closed_form) = -4.49156983992 -5.97239143227
absolute error = 4.438e-14
relative error = 5.939e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 7.01789780476 -5.4500434746
y1[1] (closed_form) = 7.01789780476 -5.4500434746
absolute error = 4.669e-14
relative error = 5.255e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.87
Order of pole (three term test) = 76.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 65.87
Order of pole (three term test) = 70.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25870.3MB, alloc=44.3MB, time=337.15
x[1] = 0.7398 2.791
h = 0.003 0.006
y2[1] (numeric) = -4.51401816056 -5.99596363155
y2[1] (closed_form) = -4.51401816056 -5.99596363155
absolute error = 4.464e-14
relative error = 5.948e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 7.04128420583 -5.47265303667
y1[1] (closed_form) = 7.04128420583 -5.47265303667
absolute error = 4.669e-14
relative error = 5.236e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 66.4
Order of pole (three term test) = 76.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 66.4
Order of pole (three term test) = 71.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25918.2MB, alloc=44.3MB, time=337.78
x[1] = 0.7428 2.797
h = 0.0001 0.005
y2[1] (numeric) = -4.56516064664 -6.01577485375
y2[1] (closed_form) = -4.56516064664 -6.01577485375
absolute error = 4.464e-14
relative error = 5.912e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 7.06070076316 -5.52390800724
y1[1] (closed_form) = 7.06070076316 -5.52390800724
absolute error = 4.669e-14
relative error = 5.208e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.2
Order of pole (three term test) = 77.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 67.2
Order of pole (three term test) = 72.11 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7429 2.802
h = 0.0001 0.003
y2[1] (numeric) = -4.593458924 -6.04559847064
y2[1] (closed_form) = -4.593458924 -6.04559847064
absolute error = 4.438e-14
relative error = 5.846e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 7.09029620623 -5.55240756302
y1[1] (closed_form) = 7.09029620623 -5.55240756302
absolute error = 4.669e-14
relative error = 5.185e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.88
Order of pole (three term test) = 77.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 67.88
Order of pole (three term test) = 72.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25965.9MB, alloc=44.3MB, time=338.40
x[1] = 0.743 2.805
h = 0.001 0.001
y2[1] (numeric) = -4.61075216025 -6.06333964027
y2[1] (closed_form) = -4.61075216025 -6.06333964027
absolute error = 4.438e-14
relative error = 5.827e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 7.10789939053 -5.56981931263
y1[1] (closed_form) = 7.10789939053 -5.56981931263
absolute error = 4.768e-14
relative error = 5.280e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 68.29
Order of pole (three term test) = 78.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 68.29
Order of pole (three term test) = 73.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26013.8MB, alloc=44.3MB, time=339.02
x[1] = 0.744 2.806
h = 0.001 0.003
y2[1] (numeric) = -4.62243594247 -6.0638721057
y2[1] (closed_form) = -4.62243594247 -6.0638721057
absolute error = 4.438e-14
relative error = 5.821e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 7.1083464043 -5.58149951248
y1[1] (closed_form) = 7.1083464043 -5.58149951248
absolute error = 4.768e-14
relative error = 5.275e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 68.42
Order of pole (three term test) = 78.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 68.42
Order of pole (three term test) = 73.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26061.7MB, alloc=44.3MB, time=339.65
x[1] = 0.745 2.809
h = 0.0001 0.004
y2[1] (numeric) = -4.64532951202 -6.0766230277
y2[1] (closed_form) = -4.64532951202 -6.0766230277
absolute error = 4.438e-14
relative error = 5.803e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 7.12092326737 -5.60447138662
y1[1] (closed_form) = 7.12092326737 -5.60447138662
absolute error = 4.687e-14
relative error = 5.172e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 68.84
Order of pole (three term test) = 78.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 68.84
Order of pole (three term test) = 73.71 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7451 2.813
h = 0.003 0.006
y2[1] (numeric) = -4.66840711958 -6.10059265885
y2[1] (closed_form) = -4.66840711958 -6.10059265885
absolute error = 4.438e-14
relative error = 5.778e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 7.14471198176 -5.62770768812
y1[1] (closed_form) = 7.14471198176 -5.62770768812
absolute error = 4.785e-14
relative error = 5.262e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 69.39
Order of pole (three term test) = 78.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 69.39
Order of pole (three term test) = 74.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26109.4MB, alloc=44.3MB, time=340.27
x[1] = 0.7481 2.819
h = 0.0001 0.005
y2[1] (numeric) = -4.72079419099 -6.12055791047
y2[1] (closed_form) = -4.72079419099 -6.12055791047
absolute error = 4.438e-14
relative error = 5.742e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 7.16429174495 -5.68020684104
y1[1] (closed_form) = 7.16429174495 -5.68020684104
absolute error = 4.785e-14
relative error = 5.234e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.23
Order of pole (three term test) = 79.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 70.23
Order of pole (three term test) = 75.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26157.3MB, alloc=44.3MB, time=340.89
x[1] = 0.7482 2.824
h = 0.0001 0.003
y2[1] (numeric) = -4.74988632203 -6.1508850858
y2[1] (closed_form) = -4.74988632203 -6.1508850858
absolute error = 4.535e-14
relative error = 5.836e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 7.19439675816 -5.70949705097
y1[1] (closed_form) = 7.19439675816 -5.70949705097
absolute error = 4.785e-14
relative error = 5.210e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.93
Order of pole (three term test) = 80.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 70.93
Order of pole (three term test) = 75.79 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7483 2.827
h = 0.001 0.001
y2[1] (numeric) = -4.76766197228 -6.16892327487
y2[1] (closed_form) = -4.76766197228 -6.16892327487
absolute error = 4.535e-14
relative error = 5.817e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 7.21230058077 -5.72738934953
y1[1] (closed_form) = 7.21230058077 -5.72738934953
absolute error = 4.884e-14
relative error = 5.303e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 71.36
Order of pole (three term test) = 80.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 71.36
Order of pole (three term test) = 76.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26205.0MB, alloc=44.3MB, time=341.51
x[1] = 0.7493 2.828
h = 0.001 0.003
y2[1] (numeric) = -4.7796078313 -6.16940241445
y2[1] (closed_form) = -4.7796078313 -6.16940241445
absolute error = 4.561e-14
relative error = 5.844e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 7.2126961107 -5.73933214721
y1[1] (closed_form) = 7.2126961107 -5.73933214721
absolute error = 4.785e-14
relative error = 5.192e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 71.5
Order of pole (three term test) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 71.5
Order of pole (three term test) = 76.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26252.9MB, alloc=44.3MB, time=342.14
x[1] = 0.7503 2.831
h = 0.0001 0.004
y2[1] (numeric) = -4.80308019466 -6.18230850318
y2[1] (closed_form) = -4.80308019466 -6.18230850318
absolute error = 4.657e-14
relative error = 5.949e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 7.22543233635 -5.76288201264
y1[1] (closed_form) = 7.22543233635 -5.76288201264
absolute error = 4.903e-14
relative error = 5.305e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 71.93
Order of pole (three term test) = 80.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 71.93
Order of pole (three term test) = 76.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26300.9MB, alloc=44.3MB, time=342.76
x[1] = 0.7504 2.835
h = 0.003 0.006
y2[1] (numeric) = -4.8268032009 -6.20668111238
y2[1] (closed_form) = -4.8268032009 -6.20668111238
absolute error = 4.561e-14
relative error = 5.800e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 7.24962879076 -5.78676119548
y1[1] (closed_form) = 7.24962879076 -5.78676119548
absolute error = 4.805e-14
relative error = 5.180e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 72.51
Order of pole (three term test) = 81.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 72.51
Order of pole (three term test) = 77.36 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7534 2.841
h = 0.0001 0.005
y2[1] (numeric) = -4.88046339835 -6.22679727845
y2[1] (closed_form) = -4.88046339835 -6.22679727845
absolute error = 4.561e-14
relative error = 5.765e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 7.26936844293 -5.84053303266
y1[1] (closed_form) = 7.26936844293 -5.84053303266
absolute error = 4.924e-14
relative error = 5.281e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 73.38
Order of pole (three term test) = 82.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 73.38
Order of pole (three term test) = 78.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26348.7MB, alloc=44.3MB, time=343.38
x[1] = 0.7535 2.846
h = 0.0001 0.003
y2[1] (numeric) = -4.91036971968 -6.25763505427
y2[1] (closed_form) = -4.91036971968 -6.25763505427
absolute error = 4.561e-14
relative error = 5.734e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 7.29998992085 -5.87063427183
y1[1] (closed_form) = 7.29998992085 -5.87063427183
absolute error = 4.903e-14
relative error = 5.234e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 74.12
Order of pole (three term test) = 82.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 74.12
Order of pole (three term test) = 79.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26396.7MB, alloc=44.3MB, time=344.00
x[1] = 0.7536 2.849
h = 0.001 0.001
y2[1] (numeric) = -4.92864009507 -6.2759743412
y2[1] (closed_form) = -4.92864009507 -6.2759743412
absolute error = 4.561e-14
relative error = 5.715e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 7.31819837173 -5.88901945234
y1[1] (closed_form) = 7.31819837173 -5.88901945234
absolute error = 5.022e-14
relative error = 5.346e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 74.57
Order of pole (three term test) = 83.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 74.57
Order of pole (three term test) = 79.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26444.7MB, alloc=44.3MB, time=344.63
x[1] = 0.7546 2.85
h = 0.001 0.003
y2[1] (numeric) = -4.94085358901 -6.27639758741
y2[1] (closed_form) = -4.94085358901 -6.27639758741
absolute error = 4.657e-14
relative error = 5.830e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 7.31853981289 -5.90123038509
y1[1] (closed_form) = 7.31853981289 -5.90123038509
absolute error = 5.022e-14
relative error = 5.342e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 74.72
Order of pole (three term test) = 83.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 74.72
Order of pole (three term test) = 79.62 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7556 2.853
h = 0.0001 0.004
y2[1] (numeric) = -4.9649184577 -6.28945925286
y2[1] (closed_form) = -4.9649184577 -6.28945925286
absolute error = 4.684e-14
relative error = 5.846e-13 %
Correct digits = 14
h = 0.0001 0.004
y1[1] (numeric) = 7.3314357156 -5.92537194904
y1[1] (closed_form) = 7.3314357156 -5.92537194904
absolute error = 4.903e-14
relative error = 5.201e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.17
Order of pole (three term test) = 83.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 75.17
Order of pole (three term test) = 80.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26492.4MB, alloc=44.3MB, time=345.25
x[1] = 0.7557 2.857
h = 0.003 0.006
y2[1] (numeric) = -4.9893033626 -6.31424041951
y2[1] (closed_form) = -4.9893033626 -6.31424041951
absolute error = 4.561e-14
relative error = 5.667e-13 %
Correct digits = 14
h = 0.003 0.006
y1[1] (numeric) = 7.3560453727 -5.94991054332
y1[1] (closed_form) = 7.3560453727 -5.94991054332
absolute error = 4.903e-14
relative error = 5.182e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.77
Order of pole (three term test) = 84.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 75.77
Order of pole (three term test) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26540.3MB, alloc=44.3MB, time=345.87
x[1] = 0.7587 2.863
h = 0.0001 0.005
y2[1] (numeric) = -5.04426584244 -6.33450415695
y2[1] (closed_form) = -5.04426584244 -6.33450415695
absolute error = 4.684e-14
relative error = 5.784e-13 %
Correct digits = 14
h = 0.0001 0.005
y1[1] (numeric) = 7.37594137307 -6.0049841842
y1[1] (closed_form) = 7.37594137307 -6.0049841842
absolute error = 5.001e-14
relative error = 5.258e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 76.69
Order of pole (three term test) = 84.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 76.69
Order of pole (three term test) = 81.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26588.2MB, alloc=44.3MB, time=346.50
x[1] = 0.7588 2.868
h = 0.0001 0.003
y2[1] (numeric) = -5.07500718095 -6.36585961822
y2[1] (closed_form) = -5.07500718095 -6.36585961822
absolute error = 4.684e-14
relative error = 5.753e-13 %
Correct digits = 14
h = 0.0001 0.003
y1[1] (numeric) = 7.40708625658 -6.03591731793
y1[1] (closed_form) = 7.40708625658 -6.03591731793
absolute error = 5.001e-14
relative error = 5.234e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 77.46
Order of pole (three term test) = 85.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 77.46
Order of pole (three term test) = 82.39 0
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7589 2.871
h = 0.001 0.001
y2[1] (numeric) = -5.09378488842 -6.38450410333
y2[1] (closed_form) = -5.09378488842 -6.38450410333
absolute error = 4.684e-14
relative error = 5.735e-13 %
Correct digits = 14
h = 0.001 0.001
y1[1] (numeric) = 7.42560334963 -6.05480800915
y1[1] (closed_form) = 7.42560334963 -6.05480800915
absolute error = 5.022e-14
relative error = 5.241e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 77.92
Order of pole (three term test) = 86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 77.92
Order of pole (three term test) = 82.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26635.9MB, alloc=44.3MB, time=347.12
x[1] = 0.7599 2.872
h = 0.001 0.003
y2[1] (numeric) = -5.1062716844 -6.38486880073
y2[1] (closed_form) = -5.1062716844 -6.38486880073
absolute error = 4.657e-14
relative error = 5.697e-13 %
Correct digits = 14
h = 0.001 0.003
y1[1] (numeric) = 7.42588800987 -6.06729272384
y1[1] (closed_form) = 7.42588800987 -6.06729272384
absolute error = 5.001e-14
relative error = 5.215e-13 %
Correct digits = 14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 78.08
Order of pole (three term test) = 86.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 78.08
Order of pole (three term test) = 83.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26684.5MB, alloc=44.3MB, time=347.76
Finished!
Maximum Time Reached before Solution Completed!
diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ;
diff ( y1 , x , 1 ) = y2 - 1.0 ;
Iterations = 754
Total Elapsed Time = 5 Minutes 47 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 5 Minutes 47 Seconds
> quit
memory used=26697.4MB, alloc=44.3MB, time=347.92