|\^/| Maple 2019 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> 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 6
# Begin Function number 7
> 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 0
> 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 1
> 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 2
> 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 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> 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 7
# Begin Function number 8
> 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 3
> 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 4
> 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 5
> 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 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> 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 8
# Begin Function number 9
> 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 9
# Begin Function number 10
> 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 6
> 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 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> 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 10
# Begin Function number 11
> 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 6
> 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 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> 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 11
# Begin Function number 12
> 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 12
# Begin Function number 13
> 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 13
# Begin Function number 14
> 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 14
# Begin Function number 15
> 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 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> 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 17
# Begin Function number 18
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> 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 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> 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 21
# Begin Function number 22
> 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 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> 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 22
# Begin Function number 23
> 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 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> 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 23
# Begin Function number 24
> 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 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> 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 24
# Begin Function number 25
> 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 12
> 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 12;
> 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 25
# Begin Function number 26
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 26
# Begin Function number 27
> 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 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> 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 27
# Begin Function number 28
> 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 28
# Begin Function number 29
> 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 12
> 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 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> 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 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> 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
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> 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 := 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> 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 32
# Begin Function number 33
> 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 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> 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 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> 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 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(2.0) - cos(c(x)));
> end;
exact_soln_y := proc(x) return c(2.0) - cos(c(x)) 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 := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) 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 (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_float(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 (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_float(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 (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_float(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
> ;
> 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 := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing 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 array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(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 array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(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 array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(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
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> 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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> 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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[1]) < min_size then
min_size := float_abs(array_y[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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> 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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> 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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := 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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> 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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> glob_good_digits := Digits;
> 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;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * c(100.0),20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> 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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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 reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := round(-log10(relerr))
else glob_good_digits := Digits
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;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*17*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*c(100.0), 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> 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 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_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;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> 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 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_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 6;
> fi;# end if 5;
> #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[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_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_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[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := 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[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_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_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[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> 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 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_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 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> 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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y_higher[1, last_no - 1],
array_y_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_y_higher[1, last_no - 1],
array_y_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[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_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_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_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_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[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_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_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_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_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;
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_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_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 reached_interval() then display_poles() end if
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_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_h,
> 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,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1);
> array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2);
> array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3);
> array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4);
> array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_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 sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_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_y_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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_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_y_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_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_h,
> 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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(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_y_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 <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) 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_y[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_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1_g[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_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_y_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_y_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_y_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 <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_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 <= 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 <=2) 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 <=2) 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 <=2) 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_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> 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_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_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_h := 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 := 1000;
> 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_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := 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 := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############R:\Temp/sin_backpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_start := c(-0.1);");
> omniout_str(ALWAYS,"x_end := c(-1.0);");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=12;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=2;");
> omniout_str(ALWAYS,"glob_max_iter:=1000000;");
> 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,"glob_h_reason:=1;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(2.0) - cos(c(x)));");
> omniout_str(ALWAYS,"");
> 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 := c(-0.1);
> x_end := c(-1.0);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=12;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=2;
> glob_max_iter:=1000000;
> 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_h_reason:=1;
> #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
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_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;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_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 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> 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_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_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 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> 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;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_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 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2020-05-26T00:32:59-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sin_back")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> 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 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> 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 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> 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 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 310 | ")
> ;
> logitem_str(html_log_file,"sin_back diffeq.mxt")
> ;
> logitem_str(html_log_file,"sin_back maple results")
> ;
> logitem_str(html_log_file,"False singularity in three term test")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
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;
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_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_h,
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_y_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_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ATS_MAX_TERMS := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_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 <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y[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_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1_g[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_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_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_y_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_y_higher_work2[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_y_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 <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 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 <= 2 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 <= 2 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_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
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_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_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_h := 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 := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 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 := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############R:Temp/sin_backpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_start := c(-0.1);");
omniout_str(ALWAYS, "x_end := c(-1.0);");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=12;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=2;");
omniout_str(ALWAYS, "glob_max_iter:=1000000;");
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, "glob_h_reason:=1;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(2.0) - cos(c(x)));");
omniout_str(ALWAYS, "");
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 := c(-0.1);
x_end := c(-1.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 12;
glob_max_minutes := 3.0;
glob_subiter_method := 2;
glob_max_iter := 1000000;
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_h_reason := 1;
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_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;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_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_y_higher[r_order, term_no] :=
array_y_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;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
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_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then
glob_next_display :=
glob_next_display + glob_display_interval
end if;
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_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_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 ( y , x , 1 ) = sin ( x ) ; ");
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, "2020-05-26T00:32:59-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sin_back");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
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
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
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, " 310 | ");
logitem_str(html_log_file, "sin_back diffeq.mxt");
logitem_str(html_log_file, "sin_back maple results");
logitem_str(html_log_file,
"False singularity in three term test");
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();
##############ECHO OF PROBLEM#################
##############R:Temp/sin_backpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-0.1);
x_end := c(-1.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=12;
glob_max_minutes:=(3.0);
glob_subiter_method:=2;
glob_max_iter:=1000000;
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_h_reason:=1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(2.0) - cos(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -0.101
y[1] (closed_form) = 1.005096165624023340621597000171
y[1] (numeric) = 1.005096165624023340621597000171
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 14
Correct digits = 32
h = -0.001
memory used=4.3MB, alloc=40.3MB, time=0.09
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1003
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.102
y[1] (closed_form) = 1.0051974914298239146653143235401
y[1] (numeric) = 1.0051974914298239146653143235401
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1013
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.103
y[1] (closed_form) = 1.0052998120380501586788328071734
y[1] (numeric) = 1.0052998120380501586788328071733
absolute error = 1e-31
relative error = 9.9472812789320449697981767287103e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1023
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.104
y[1] (closed_form) = 1.0054031273463814729626255055154
y[1] (numeric) = 1.0054031273463814729626255055153
absolute error = 1e-31
relative error = 9.9462590954869788504619490995116e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1033
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.105
y[1] (closed_form) = 1.0055074372515025577949868753959
y[1] (numeric) = 1.0055074372515025577949868753959
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1042
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.106
y[1] (closed_form) = 1.0056127416491035167473238881278
y[1] (numeric) = 1.0056127416491035167473238881277
absolute error = 1e-31
relative error = 9.9441858538914375101877095183376e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1052
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.107
y[1] (closed_form) = 1.0057190404338799609940437656082
y[1] (numeric) = 1.0057190404338799609940437656081
absolute error = 1e-31
relative error = 9.9431348099821924983009246296662e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1062
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.108
y[1] (closed_form) = 1.0058263334995331146169340305467
y[1] (numeric) = 1.0058263334995331146169340305466
absolute error = 1e-31
relative error = 9.9420741602652042805188552925067e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1072
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.109
y[1] (closed_form) = 1.0059346207387699209039295664461
y[1] (numeric) = 1.005934620738769920903929566446
absolute error = 1e-31
relative error = 9.9410039120195359477852278641993e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1081
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (closed_form) = 1.0060439020433031496421603885802
y[1] (numeric) = 1.0060439020433031496421603885801
absolute error = 1e-31
relative error = 9.9399240725874107832453568516521e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1091
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.111
y[1] (closed_form) = 1.006154177303851505405172832928
y[1] (numeric) = 1.006154177303851505405172832928
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1101
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.112
y[1] (closed_form) = 1.0062654464101397368342158758533
y[1] (numeric) = 1.0062654464101397368342158758533
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1111
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.113
y[1] (closed_form) = 1.0063777092508987469134833032516
y[1] (numeric) = 1.0063777092508987469134833032515
absolute error = 1e-31
relative error = 9.9366270815393355624247019446757e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.112
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.114
y[1] (closed_form) = 1.0064909657138657042392014539315
y[1] (numeric) = 1.0064909657138657042392014539314
absolute error = 1e-31
relative error = 9.9355089520424864469352688007190e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.113
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.115
y[1] (closed_form) = 1.0066052156857841552824512681535
y[1] (numeric) = 1.0066052156857841552824512681534
absolute error = 1e-31
relative error = 9.9343812690133527007168064857172e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.114
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.116
y[1] (closed_form) = 1.006720459052404137645612378511
y[1] (numeric) = 1.0067204590524041376456123785109
absolute error = 1e-31
relative error = 9.9332440401704967357293435859319e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.115
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.117
y[1] (closed_form) = 1.006836695698482294312315986721
y[1] (numeric) = 1.0068366956984822943123159867209
absolute error = 1e-31
relative error = 9.9320972732947580036462414903544e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1159
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.118
y[1] (closed_form) = 1.00695392550778198889079227638
y[1] (numeric) = 1.0069539255077819888907922763799
absolute error = 1e-31
relative error = 9.9309409762291229358218249095572e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1169
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.119
y[1] (closed_form) = 1.0070721483630734218504971183478
y[1] (numeric) = 1.0070721483630734218504971183478
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1179
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (closed_form) = 1.0071913641461337477519018321424
y[1] (numeric) = 1.0071913641461337477519018321423
absolute error = 1e-31
relative error = 9.9285998232100573272046486262470e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1189
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.121
y[1] (closed_form) = 1.0073115727377471934693287735644
y[1] (numeric) = 1.0073115727377471934693287735643
absolute error = 1e-31
relative error = 9.9274149832521505646917778195947e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1198
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.122
y[1] (closed_form) = 1.007432774017705177406714525728
y[1] (numeric) = 1.0074327740177051774067145257279
absolute error = 1e-31
relative error = 9.9262206450951282060438490869793e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1208
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.123
y[1] (closed_form) = 1.0075549678648064297061814777427
y[1] (numeric) = 1.0075549678648064297061814777425
absolute error = 2e-31
relative error = 1.9850033633781454311089551351548e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1218
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.124
y[1] (closed_form) = 1.007678154156857113449297582485
y[1] (numeric) = 1.0076781541568571134492975824848
absolute error = 2e-31
relative error = 1.9847607013704061758348239022002e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1227
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.125
y[1] (closed_form) = 1.0078023327706709468509030922118
y[1] (numeric) = 1.0078023327706709468509030922116
absolute error = 2e-31
relative error = 1.9845161446506665393994812214058e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1237
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.126
y[1] (closed_form) = 1.0079275035820693264453820781963
y[1] (numeric) = 1.0079275035820693264453820781961
absolute error = 2e-31
relative error = 1.9842696948859996284987992722659e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1247
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.127
y[1] (closed_form) = 1.0080536664658814512652555481279
y[1] (numeric) = 1.0080536664658814512652555481277
absolute error = 2e-31
relative error = 1.9840213537556652786093371430120e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1256
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.128
y[1] (closed_form) = 1.0081808212959444480119719826911
y[1] (numeric) = 1.0081808212959444480119719826909
absolute error = 2e-31
relative error = 1.9837711229510821551684250766351e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1266
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.129
y[1] (closed_form) = 1.0083089679451034972187701205446
y[1] (numeric) = 1.0083089679451034972187701205444
absolute error = 2e-31
relative error = 1.9835190041757996706911755916302e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1276
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (closed_form) = 1.0084381062852119604054878288482
y[1] (numeric) = 1.008438106285211960405487828848
absolute error = 2e-31
relative error = 1.9832649991454697186840859402028e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1285
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.131
y[1] (closed_form) = 1.0085682361871315082251899045384
y[1] (numeric) = 1.0085682361871315082251899045382
absolute error = 2e-31
relative error = 1.9830091095878182252197566580888e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1295
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.132
y[1] (closed_form) = 1.008699357520732249602486659737
y[1] (numeric) = 1.0086993575207322496024866597367
absolute error = 3e-31
relative error = 2.9741270058639247785631040277301e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1305
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.133
y[1] (closed_form) = 1.0088314701548928618634141529829
y[1] (numeric) = 1.0088314701548928618634141529827
absolute error = 2e-31
relative error = 1.9824916838616525210759431749345e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1314
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.134
y[1] (closed_form) = 1.0089645739575007218567459364203
y[1] (numeric) = 1.0089645739575007218567459364201
absolute error = 2e-31
relative error = 1.9822301512087017542205234809191e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1324
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.135
y[1] (closed_form) = 1.0090986687954520380666051976395
y[1] (numeric) = 1.0090986687954520380666051976393
absolute error = 2e-31
relative error = 1.9819667410594981743093477272186e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1334
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.136
y[1] (closed_form) = 1.009233754534651983716245183572
y[1] (numeric) = 1.0092337545346519837162451835718
absolute error = 2e-31
relative error = 1.9817014552017048231256826639682e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1343
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.137
y[1] (closed_form) = 1.0093698310400148308628648026684
y[1] (numeric) = 1.0093698310400148308628648026682
absolute error = 2e-31
relative error = 1.9814342954348843043658329987874e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1353
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.138
y[1] (closed_form) = 1.0095068981754640854833253105562
y[1] (numeric) = 1.0095068981754640854833253105559
absolute error = 3e-31
relative error = 2.9717478953557036251716773702130e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1363
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.139
y[1] (closed_form) = 1.0096449558039326235506329934705
y[1] (numeric) = 1.0096449558039326235506329934703
absolute error = 2e-31
relative error = 1.9808943614317316120670678512873e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1372
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (closed_form) = 1.0097840037873628281010517729886
y[1] (numeric) = 1.0097840037873628281010517729884
absolute error = 2e-31
relative error = 1.9806215908537542784061947291135e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1382
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.141
y[1] (closed_form) = 1.0099240419867067272917086649643
y[1] (numeric) = 1.0099240419867067272917086649641
absolute error = 2e-31
relative error = 1.9803469536833991839084739948141e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1391
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.142
y[1] (closed_form) = 1.0100650702619261334485540350706
y[1] (numeric) = 1.0100650702619261334485540350704
absolute error = 2e-31
relative error = 1.9800704517792777475313765866455e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1401
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.143
y[1] (closed_form) = 1.0102070884719927831045376030009
y[1] (numeric) = 1.0102070884719927831045376030007
absolute error = 2e-31
relative error = 1.9797920870117201383989867026587e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1411
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.144
y[1] (closed_form) = 1.0103500964748884780278601571639
y[1] (numeric) = 1.0103500964748884780278601571638
absolute error = 1e-31
relative error = 9.8975593063137226888868359982296e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.142
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.145
y[1] (closed_form) = 1.010494094127605227240159951634
y[1] (numeric) = 1.0104940941276052272401599516339
absolute error = 1e-31
relative error = 9.8961488821301311565046413159335e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.143
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.146
y[1] (closed_form) = 1.0106390812861453900244917671803
y[1] (numeric) = 1.0106390812861453900244917671802
absolute error = 1e-31
relative error = 9.8947291720343326619105078758322e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1439
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.147
y[1] (closed_form) = 1.0107850578055218199229556284092
y[1] (numeric) = 1.010785057805521819922955628409
absolute error = 2e-31
relative error = 1.9786600371221615377407914083725e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1449
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.148
y[1] (closed_form) = 1.0109320235397580097238311794022
y[1] (numeric) = 1.010932023539758009723831179402
absolute error = 2e-31
relative error = 1.9783723865003707159941987580660e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1458
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.149
y[1] (closed_form) = 1.0110799783418882374380727307282
y[1] (numeric) = 1.011079978341888237438072730728
absolute error = 2e-31
relative error = 1.9780828844814853302516946394199e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1468
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (closed_form) = 1.0112289220639577132650190013457
y[1] (numeric) = 1.0112289220639577132650190013455
absolute error = 2e-31
relative error = 1.9777915330169966956634539021488e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1478
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.151
y[1] (closed_form) = 1.0113788545570227275471705896988
y[1] (numeric) = 1.0113788545570227275471705896986
absolute error = 2e-31
relative error = 1.9774983340698642728755512072646e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1487
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.152
y[1] (closed_form) = 1.0115297756711507997138872192414
y[1] (numeric) = 1.0115297756711507997138872192412
absolute error = 2e-31
relative error = 1.9772032896144835983481660465194e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1497
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.153
y[1] (closed_form) = 1.0116816852554208282138558147042
y[1] (numeric) = 1.011681685255420828213855814704
absolute error = 2e-31
relative error = 1.9769064016366540524974437366093e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1506
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.154
y[1] (closed_form) = 1.0118345831579232414361794766499
y[1] (numeric) = 1.0118345831579232414361794766497
absolute error = 2e-31
relative error = 1.9766076721335464666254140645369e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1516
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.155
y[1] (closed_form) = 1.0119884692257601496199364332395
y[1] (numeric) = 1.0119884692257601496199364332394
absolute error = 1e-31
relative error = 9.8815355155683528480308928884575e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1525
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.156
y[1] (closed_form) = 1.0121433433050454977520570596639
y[1] (numeric) = 1.0121433433050454977520570596638
absolute error = 1e-31
relative error = 9.8800234829842113765017064262592e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1535
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.157
y[1] (closed_form) = 1.0122992052409052194533660673757
y[1] (numeric) = 1.0122992052409052194533660673755
absolute error = 2e-31
relative error = 1.9757004546141508116733756526007e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1544
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.158
y[1] (closed_form) = 1.0124560548774773918526359770927
y[1] (numeric) = 1.0124560548774773918526359770926
absolute error = 1e-31
relative error = 9.8769718960396284629864655838113e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1554
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.159
y[1] (closed_form) = 1.0126138920579123914484970015328
y[1] (numeric) = 1.0126138920579123914484970015327
absolute error = 1e-31
relative error = 9.8754323621585176665930241036470e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1563
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (closed_form) = 1.0127727166243730509590474759817
y[1] (numeric) = 1.0127727166243730509590474759815
absolute error = 2e-31
relative error = 1.9747767363501947105791487532903e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1573
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.161
y[1] (closed_form) = 1.0129325284180348171590079870976
y[1] (numeric) = 1.0129325284180348171590079870975
absolute error = 1e-31
relative error = 9.8723258651962493418994444351344e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1582
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.162
y[1] (closed_form) = 1.0130933272790859097042613628125
y[1] (numeric) = 1.0130933272790859097042613628124
absolute error = 1e-31
relative error = 9.8707589229291313519064056603120e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1592
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.163
y[1] (closed_form) = 1.0132551130467274809436196988004
y[1] (numeric) = 1.0132551130467274809436196988003
absolute error = 1e-31
relative error = 9.8691828654397699996862143573932e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1601
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.164
y[1] (closed_form) = 1.0134178855591737767176586097624
y[1] (numeric) = 1.0134178855591737767176586097623
absolute error = 1e-31
relative error = 9.8675977032735100438157921187662e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1611
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.165
y[1] (closed_form) = 1.0135816446536522981444579067051
y[1] (numeric) = 1.0135816446536522981444579067049
absolute error = 2e-31
relative error = 1.9732006894061440152417018988730e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.162
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.166
y[1] (closed_form) = 1.0137463901664039643920869144861
y[1] (numeric) = 1.0137463901664039643920869144859
absolute error = 2e-31
relative error = 1.9728800214733242533735614917559e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.163
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.167
y[1] (closed_form) = 1.0139121219326832764376716571557
y[1] (numeric) = 1.0139121219326832764376716571555
absolute error = 2e-31
relative error = 1.9725575389982230733834052061891e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1639
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.168
y[1] (closed_form) = 1.014078839786758481812880152039
y[1] (numeric) = 1.0140788397867584818128801520388
absolute error = 2e-31
relative error = 1.9722332441337223949946372446596e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1649
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.169
y[1] (closed_form) = 1.0142465435619117403356610670895
y[1] (numeric) = 1.0142465435619117403356610670894
absolute error = 1e-31
relative error = 9.8595356952178550719482837862528e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1658
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (closed_form) = 1.0144152330904392908280700097875
y[1] (numeric) = 1.0144152330904392908280700097874
absolute error = 1e-31
relative error = 9.8578961295117488293772312119487e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1667
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.171
y[1] (closed_form) = 1.0145849082036516188200167297711
y[1] (numeric) = 1.014584908203651618820016729771
absolute error = 1e-31
relative error = 9.8562475344771826963869278141901e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1677
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.172
y[1] (closed_form) = 1.0147555687318736252387655314679
y[1] (numeric) = 1.0147555687318736252387655314678
absolute error = 1e-31
relative error = 9.8545899210948557704360460710775e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1686
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.173
y[1] (closed_form) = 1.0149272145044447960840202072392
y[1] (numeric) = 1.0149272145044447960840202072391
absolute error = 1e-31
relative error = 9.8529233003991004569699954796845e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1696
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.174
y[1] (closed_form) = 1.0150998453497193730884238159675
y[1] (numeric) = 1.0150998453497193730884238159674
absolute error = 1e-31
relative error = 9.8512476834777054231501626204298e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1705
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.175
y[1] (closed_form) = 1.0152734610950665253633026466005
y[1] (numeric) = 1.0152734610950665253633026466004
absolute error = 1e-31
relative error = 9.8495630814717378508309276700903e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1714
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.176
y[1] (closed_form) = 1.0154480615668705220294827209227
y[1] (numeric) = 1.0154480615668705220294827209226
absolute error = 1e-31
relative error = 9.8478695055753649939721229594336e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1724
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.177
y[1] (closed_form) = 1.0156236465905309058330062047525
y[1] (numeric) = 1.0156236465905309058330062047524
absolute error = 1e-31
relative error = 9.8461669670356750456885280823934e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1733
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.178
y[1] (closed_form) = 1.0158002159904626677455741118622
y[1] (numeric) = 1.0158002159904626677455741118621
absolute error = 1e-31
relative error = 9.8444554771524973201516882819593e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1743
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.179
y[1] (closed_form) = 1.0159777695900964225495407001936
y[1] (numeric) = 1.0159777695900964225495407001935
absolute error = 1e-31
relative error = 9.8427350472782217545727981321633e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1752
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (closed_form) = 1.0161563072118785854072839753885
y[1] (numeric) = 1.0161563072118785854072839753884
absolute error = 1e-31
relative error = 9.8410056888176177365086106897088e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1761
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.181
y[1] (closed_form) = 1.0163358286772715494147757322793
y[1] (numeric) = 1.0163358286772715494147757322792
absolute error = 1e-31
relative error = 9.8392674132276522617453131020006e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1771
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.182
y[1] (closed_form) = 1.016516333806753864139173580784
y[1] (numeric) = 1.0165163338067538641391735807839
absolute error = 1e-31
relative error = 9.8375202320173074280280529450554e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.178
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.183
y[1] (closed_form) = 1.0166978224198204151402564186277
y[1] (numeric) = 1.0166978224198204151402564186276
absolute error = 1e-31
relative error = 9.8357641567473972699163051545140e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1789
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.184
y[1] (closed_form) = 1.0168802943349826044755238294719
y[1] (numeric) = 1.0168802943349826044755238294718
absolute error = 1e-31
relative error = 9.8339991990303839400575371504772e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1799
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.185
y[1] (closed_form) = 1.0170637493697685321887789013652
y[1] (numeric) = 1.0170637493697685321887789013651
absolute error = 1e-31
relative error = 9.8322253705301932421836595020925e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1808
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.186
y[1] (closed_form) = 1.0172481873407231787820129769491
y[1] (numeric) = 1.017248187340723178782012976949
absolute error = 1e-31
relative error = 9.8304426829620295211465411056019e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1817
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.187
y[1] (closed_form) = 1.0174336080634085886704098635492
y[1] (numeric) = 1.017433608063408588670409863549
absolute error = 2e-31
relative error = 1.9657302296184379830640842500215e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1827
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.188
y[1] (closed_form) = 1.0176200113524040546202860481617
y[1] (numeric) = 1.0176200113524040546202860481615
absolute error = 2e-31
relative error = 1.9653701555475755953420732047401e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1836
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.189
y[1] (closed_form) = 1.0178073970213063031697824794125
y[1] (numeric) = 1.0178073970213063031697824794123
absolute error = 2e-31
relative error = 1.9650083167534033328233986377926e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1845
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (closed_form) = 1.0179957648827296810321224958101
y[1] (numeric) = 1.0179957648827296810321224958099
absolute error = 2e-31
relative error = 1.9646447156196121429437055732874e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1855
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.191
y[1] (closed_form) = 1.0181851147483063424812494970519
y[1] (numeric) = 1.0181851147483063424812494970517
absolute error = 2e-31
relative error = 1.9642793545399616798883702114906e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1864
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.192
y[1] (closed_form) = 1.0183754464286864377196569727608
y[1] (numeric) = 1.0183754464286864377196569727606
absolute error = 2e-31
relative error = 1.9639122359182425335009128357783e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1873
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=52.8MB, alloc=44.3MB, time=0.39
x[1] = -0.193
y[1] (closed_form) = 1.0185667597335383022282225208382
y[1] (numeric) = 1.018566759733538302228222520838
absolute error = 2e-31
relative error = 1.9635433621682383371040430703671e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1882
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.194
y[1] (closed_form) = 1.0187590544715486470978565056148
y[1] (numeric) = 1.0187590544715486470978565056146
absolute error = 2e-31
relative error = 1.9631727357136877553137434357135e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1892
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.195
y[1] (closed_form) = 1.0189523304504227503427750241667
y[1] (numeric) = 1.0189523304504227503427750241664
absolute error = 3e-31
relative error = 2.9442005384823695293930893502394e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1901
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.196
y[1] (closed_form) = 1.0191465874768846491952058675394
y[1] (numeric) = 1.0191465874768846491952058675391
absolute error = 3e-31
relative error = 2.9436393516531725189692202542718e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.191
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.197
y[1] (closed_form) = 1.019341825356677333381335182191
y[1] (numeric) = 1.0193418253566773333813351821907
absolute error = 3e-31
relative error = 2.9430755467630023540344351978921e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1919
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.198
y[1] (closed_form) = 1.0195380438945629393783015557216
y[1] (numeric) = 1.0195380438945629393783015557213
absolute error = 3e-31
relative error = 2.9425091275066234931560992916623e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1929
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.199
y[1] (closed_form) = 1.0197352428943229456520432699139
y[1] (numeric) = 1.0197352428943229456520432699136
absolute error = 3e-31
relative error = 2.9419400975934452072103343354548e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1938
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (closed_form) = 1.0199334221587583688758034832518
y[1] (numeric) = 1.0199334221587583688758034832515
absolute error = 3e-31
relative error = 2.9413684607474635152303106787816e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1947
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.201
y[1] (closed_form) = 1.020132581489689961129097124429
y[1] (numeric) = 1.0201325814896899611290971244287
absolute error = 3e-31
relative error = 2.9407942207072029516653740880267e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1956
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.202
y[1] (closed_form) = 1.0203327206879584080769422978976
y[1] (numeric) = 1.0203327206879584080769422978972
absolute error = 4e-31
relative error = 3.9202898416342108889236836878855e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1965
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.203
y[1] (closed_form) = 1.0205338395534245281291580222406
y[1] (numeric) = 1.0205338395534245281291580222403
absolute error = 3e-31
relative error = 2.9396379460702353612259913677853e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
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) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.204
y[1] (closed_form) = 1.020735937884969472579529142089
y[1] (numeric) = 1.0207359378849694725795291420887
absolute error = 3e-31
relative error = 2.9390559190226935582662292122478e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1984
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.205
y[1] (closed_form) = 1.0209390154804949267246382744327
y[1] (numeric) = 1.0209390154804949267246382744324
absolute error = 3e-31
relative error = 2.9384713038790857122451789371906e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1993
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.206
y[1] (closed_form) = 1.0211430721369233119621636705127
y[1] (numeric) = 1.0211430721369233119621636705124
absolute error = 3e-31
relative error = 2.9378841044496996580100696569104e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2002
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.207
y[1] (closed_form) = 1.0213481076501979888684408950116
y[1] (numeric) = 1.0213481076501979888684408950113
absolute error = 3e-31
relative error = 2.9372943245589989011034152874538e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2011
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.208
y[1] (closed_form) = 1.0215541218152834612550852449989
y[1] (numeric) = 1.0215541218152834612550852449986
absolute error = 3e-31
relative error = 2.9367019680455632509921541846818e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2021
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.209
y[1] (closed_form) = 1.0217611144261655812044708520248
y[1] (numeric) = 1.0217611144261655812044708520244
absolute error = 4e-31
relative error = 3.9148093850160390652035741957096e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.203
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (closed_form) = 1.0219690852758517550838614319006
y[1] (numeric) = 1.0219690852758517550838614319003
absolute error = 3e-31
relative error = 2.9355095405750307419201022379575e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2039
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.211
y[1] (closed_form) = 1.0221780341563711505379866680538
y[1] (numeric) = 1.0221780341563711505379866680534
absolute error = 4e-31
relative error = 3.9132126364868514066824124866377e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2048
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.212
y[1] (closed_form) = 1.022387960858774904459857235895
y[1] (numeric) = 1.0223879608587749044598572358946
absolute error = 4e-31
relative error = 3.9124091373690680168495002128739e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2057
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.213
y[1] (closed_form) = 1.0225988651731363319396104974034
y[1] (numeric) = 1.022598865173136331939610497403
absolute error = 4e-31
relative error = 3.9116022286243780821418860913943e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2066
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.214
y[1] (closed_form) = 1.0228107468885511361911779170994
y[1] (numeric) = 1.0228107468885511361911779170991
absolute error = 3e-31
relative error = 2.9330939366116085468545717112037e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2075
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.215
y[1] (closed_form) = 1.0230236057931376194565642727558
y[1] (numeric) = 1.0230236057931376194565642727554
absolute error = 4e-31
relative error = 3.9099782031899930557270321717783e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2084
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.216
y[1] (closed_form) = 1.0232374416740368948875277565849
y[1] (numeric) = 1.0232374416740368948875277565845
absolute error = 4e-31
relative error = 3.9091610970137293798983887991401e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2093
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.217
y[1] (closed_form) = 1.0234522543174130994044490852411
y[1] (numeric) = 1.0234522543174130994044490852407
absolute error = 4e-31
relative error = 3.9083406022372602991166211196817e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2103
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.218
y[1] (closed_form) = 1.023668043508453607532176759785
y[1] (numeric) = 1.0236680435084536075321767597845
absolute error = 5e-31
relative error = 4.8843959052031394530737262558293e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2112
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.219
y[1] (closed_form) = 1.0238848090313692462126346397834
y[1] (numeric) = 1.0238848090313692462126346397829
absolute error = 5e-31
relative error = 4.8833618351366834472179516910616e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2121
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (closed_form) = 1.0241025506693945105939770189553
y[1] (numeric) = 1.0241025506693945105939770189548
absolute error = 5e-31
relative error = 4.8823235492693572701048247021677e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
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) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.221
y[1] (closed_form) = 1.0243212682047877807960754132258
y[1] (numeric) = 1.0243212682047877807960754132253
absolute error = 5e-31
relative error = 4.8812810542955291693200411856723e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2139
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.222
y[1] (closed_form) = 1.0245409614188315396521202957203
y[1] (numeric) = 1.0245409614188315396521202957198
absolute error = 5e-31
relative error = 4.8802343569316834082372308863116e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2148
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.223
y[1] (closed_form) = 1.024761630091832591426120037115
y[1] (numeric) = 1.0247616300918325914261200371145
absolute error = 5e-31
relative error = 4.8791834639163177279238018475873e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2157
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.224
y[1] (closed_form) = 1.0249832740031222815060783338625
y[1] (numeric) = 1.024983274003122281506078333862
absolute error = 5e-31
relative error = 4.8781283820098405917681100120785e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2166
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.225
y[1] (closed_form) = 1.0252058929310567170726304311345
y[1] (numeric) = 1.025205892931056717072630431134
absolute error = 5e-31
relative error = 4.8770691179944682156233268763619e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2175
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.226
y[1] (closed_form) = 1.0254294866530169887429174718627
y[1] (numeric) = 1.0254294866530169887429174718622
absolute error = 5e-31
relative error = 4.8760056786741213862645447735900e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2184
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.227
y[1] (closed_form) = 1.0256540549454093931894773280223
y[1] (numeric) = 1.0256540549454093931894773280218
absolute error = 5e-31
relative error = 4.8749380708743220709567106646145e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2193
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.228
y[1] (closed_form) = 1.0258795975836656567339292952864
y[1] (numeric) = 1.0258795975836656567339292952859
absolute error = 5e-31
relative error = 4.8738663014420898209319155011105e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2202
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.229
y[1] (closed_form) = 1.0261061143422431599152290573844
y[1] (numeric) = 1.0261061143422431599152290573838
absolute error = 6e-31
relative error = 5.8473484526950055658904650275272e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2211
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (closed_form) = 1.0263336049946251630322693519284
y[1] (numeric) = 1.0263336049946251630322693519278
absolute error = 6e-31
relative error = 5.8460523662103235705442934178423e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.222
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.231
y[1] (closed_form) = 1.0265620693133210326606007951267
y[1] (numeric) = 1.0265620693133210326606007951261
absolute error = 6e-31
relative error = 5.8447513105695282451819827948332e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2229
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.232
y[1] (closed_form) = 1.0267915070698664691430463486806
y[1] (numeric) = 1.02679150706986646914304634868
absolute error = 6e-31
relative error = 5.8434452940909834674658181676567e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2238
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.233
y[1] (closed_form) = 1.0270219180348237350539819382704
y[1] (numeric) = 1.0270219180348237350539819382698
absolute error = 6e-31
relative error = 5.8421343251182250446502246438608e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2247
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.234
y[1] (closed_form) = 1.027253301977781884637054759369
y[1] (numeric) = 1.0272533019777818846370547593684
absolute error = 6e-31
relative error = 5.8408184120198349844703359444626e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2256
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.235
y[1] (closed_form) = 1.0274856586673569942161098326828
y[1] (numeric) = 1.0274856586673569942161098326822
absolute error = 6e-31
relative error = 5.8394975631893155422493308276178e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2264
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.236
y[1] (closed_form) = 1.0277189878711923935790943983139
y[1] (numeric) = 1.0277189878711923935790943983133
absolute error = 6e-31
relative error = 5.8381717870449630475868202147989e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2273
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.237
y[1] (closed_form) = 1.0279532893559588983347087647578
y[1] (numeric) = 1.0279532893559588983347087647572
absolute error = 6e-31
relative error = 5.8368410920297415139904618326040e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2282
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.238
y[1] (closed_form) = 1.0281885628873550432415712561047
y[1] (numeric) = 1.0281885628873550432415712561041
absolute error = 6e-31
relative error = 5.8355054866111560348127382903551e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2291
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.239
y[1] (closed_form) = 1.0284248082301073165096639283
y[1] (numeric) = 1.0284248082301073165096639282993
absolute error = 7e-31
relative error = 6.8065258091613136303302022519064e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.23
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (closed_form) = 1.0286620251479703950738247530366
y[1] (numeric) = 1.0286620251479703950738247530359
absolute error = 7e-31
relative error = 6.8049561749818342388287101983891e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2309
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.241
y[1] (closed_form) = 1.0289002134037273808390509958078
y[1] (numeric) = 1.0289002134037273808390509958071
absolute error = 7e-31
relative error = 6.8033808418050049250864402537854e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2318
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.242
y[1] (closed_form) = 1.0291393727591900378973775428355
y[1] (numeric) = 1.0291393727591900378973775428348
absolute error = 7e-31
relative error = 6.8017998196226247742568377440358e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2327
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.243
y[1] (closed_form) = 1.0293795029751990307160929600163
y[1] (numeric) = 1.0293795029751990307160929600156
absolute error = 7e-31
relative error = 6.8002131184543820051901779840895e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2335
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.244
y[1] (closed_form) = 1.0296206038116241632970550956892
y[1] (numeric) = 1.0296206038116241632970550956885
absolute error = 7e-31
relative error = 6.7986207483477048521612533033574e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2344
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.245
y[1] (closed_form) = 1.0298626750273646193068670679285
y[1] (numeric) = 1.0298626750273646193068670679278
absolute error = 7e-31
relative error = 6.7970227193776122247212282858993e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2353
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.246
y[1] (closed_form) = 1.0301057163803492031776735062069
y[1] (numeric) = 1.0301057163803492031776735062062
absolute error = 7e-31
relative error = 6.7954190416465641495880599411617e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2362
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.247
y[1] (closed_form) = 1.0303497276275365821783359466519
y[1] (numeric) = 1.0303497276275365821783359466511
absolute error = 8e-31
relative error = 7.7643539717534994268436594708259e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2371
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.248
y[1] (closed_form) = 1.0305947085249155294557453097401
y[1] (numeric) = 1.0305947085249155294557453097393
absolute error = 8e-31
relative error = 7.7625083205117125781262657933861e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.238
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.249
y[1] (closed_form) = 1.0308406588275051680460284191387
y[1] (numeric) = 1.0308406588275051680460284191379
absolute error = 8e-31
relative error = 7.7606562483665800918069266501057e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2388
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (closed_form) = 1.0310875782893552158554045505058
y[1] (numeric) = 1.031087578289355215855404550505
absolute error = 8e-31
relative error = 7.7587977669875016158471270529634e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2397
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.251
y[1] (closed_form) = 1.0313354666635462316104470294153
y[1] (numeric) = 1.0313354666635462316104470294145
absolute error = 8e-31
relative error = 7.7569328880743798771515375637775e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2406
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.252
y[1] (closed_form) = 1.0315843237021898617775039281638
y[1] (numeric) = 1.031584323702189861777503928163
absolute error = 8e-31
relative error = 7.7550616233574483572474841781761e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2415
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.253
y[1] (closed_form) = 1.0318341491564290884510309420608
y[1] (numeric) = 1.03183414915642908845103094206
absolute error = 8e-31
relative error = 7.7531839845970987501173930603548e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2423
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.254
y[1] (closed_form) = 1.0320849427764384782105885568886
y[1] (numeric) = 1.0320849427764384782105885568877
absolute error = 9e-31
relative error = 8.7202124815316717324673153975729e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2432
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.255
y[1] (closed_form) = 1.0323367043114244319462546505563
y[1] (numeric) = 1.0323367043114244319462546505555
absolute error = 8e-31
relative error = 7.7494096321374663700737267580891e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2441
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.256
y[1] (closed_form) = 1.0325894335096254356522027035565
y[1] (numeric) = 1.0325894335096254356522027035557
absolute error = 8e-31
relative error = 7.7475129421082022070789763219158e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.245
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.257
y[1] (closed_form) = 1.032843130118312312188194824666
y[1] (numeric) = 1.0328431301183123121881948246651
absolute error = 9e-31
relative error = 8.7138111660471119684686832525291e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2458
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.258
y[1] (closed_form) = 1.0330977938837884740087378304194
y[1] (numeric) = 1.0330977938837884740087378304185
absolute error = 9e-31
relative error = 8.7116631680779638473259711851025e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2467
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.259
y[1] (closed_form) = 1.0333534245513901768596496492213
y[1] (numeric) = 1.0333534245513901768596496492204
absolute error = 9e-31
relative error = 8.7095080793942023070533545270306e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2476
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (closed_form) = 1.0336100218654867744417823535499
y[1] (numeric) = 1.033610021865486774441782353549
absolute error = 9e-31
relative error = 8.7073459134583093127849356624638e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2484
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.261
y[1] (closed_form) = 1.0338675855694809740416471565521
y[1] (numeric) = 1.0338675855694809740416471565511
absolute error = 1.0e-30
relative error = 9.6724185375168152408187164376675e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2493
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.262
y[1] (closed_form) = 1.0341261154058090931286857424248
y[1] (numeric) = 1.0341261154058090931286857424239
absolute error = 9e-31
relative error = 8.7030004038416951675361335403351e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2502
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.263
y[1] (closed_form) = 1.0343856111159413169189313333344
y[1] (numeric) = 1.0343856111159413169189313333335
absolute error = 9e-31
relative error = 8.7008170872469878243828780092364e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.251
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.264
y[1] (closed_form) = 1.0346460724403819569048019292326
y[1] (numeric) = 1.0346460724403819569048019292316
absolute error = 1.0e-30
relative error = 9.6651408306353154233444158876844e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2519
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.265
y[1] (closed_form) = 1.0349074991186697103507671907983
y[1] (numeric) = 1.0349074991186697103507671907973
absolute error = 1.0e-30
relative error = 9.6626993315982632271105829200894e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2528
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.266
y[1] (closed_form) = 1.0351698908893779207546294698607
y[1] (numeric) = 1.0351698908893779207546294698596
absolute error = 1.1e-30
relative error = 1.0626275065389726102810931923574e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2536
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.267
y[1] (closed_form) = 1.0354332474901148392741585260421
y[1] (numeric) = 1.0354332474901148392741585260411
absolute error = 1.0e-30
relative error = 9.6577930293816152898377436888564e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2545
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.268
y[1] (closed_form) = 1.0356975686575238871188185030108
y[1] (numeric) = 1.0356975686575238871188185030098
absolute error = 1.0e-30
relative error = 9.6553282566473990535440138605606e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2554
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.269
y[1] (closed_form) = 1.0359628541272839189063247726353
y[1] (numeric) = 1.0359628541272839189063247726342
absolute error = 1.1e-30
relative error = 1.0618141332168345641995759244107e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2562
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (closed_form) = 1.0362291036341094869837672905078
y[1] (numeric) = 1.0362291036341094869837672905067
absolute error = 1.1e-30
relative error = 1.0615413098727324439801275166044e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2571
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.271
y[1] (closed_form) = 1.0364963169117511067130361417346
y[1] (numeric) = 1.0364963169117511067130361417335
absolute error = 1.1e-30
relative error = 1.0612676398865155781361576241779e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2579
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.272
y[1] (closed_form) = 1.0367644936929955227202839915894
y[1] (numeric) = 1.0367644936929955227202839915883
absolute error = 1.1e-30
relative error = 1.0609931249494831173515173232049e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2588
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.273
y[1] (closed_form) = 1.0370336337096659761091591915901
y[1] (numeric) = 1.0370336337096659761091591915891
absolute error = 1.0e-30
relative error = 9.6428887886963738573922608101810e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2596
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.274
y[1] (closed_form) = 1.0373037366926224726375423277883
y[1] (numeric) = 1.0373037366926224726375423277873
absolute error = 1.0e-30
relative error = 9.6403778818770760064957740214658e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2605
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.275
y[1] (closed_form) = 1.0375748023717620518575180345561
y[1] (numeric) = 1.0375748023717620518575180345551
absolute error = 1.0e-30
relative error = 9.6378593400122005239704344416125e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2613
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.276
y[1] (closed_form) = 1.0378468304760190572183129339225
y[1] (numeric) = 1.0378468304760190572183129339215
absolute error = 1.0e-30
relative error = 9.6353331786092151809473763700876e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2622
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.277
y[1] (closed_form) = 1.0381198207333654071319295975428
y[1] (numeric) = 1.0381198207333654071319295975418
absolute error = 1.0e-30
relative error = 9.6327994132080419546488109498390e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.263
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.278
y[1] (closed_form) = 1.0383937728708108670012054656899
y[1] (numeric) = 1.0383937728708108670012054656889
absolute error = 1.0e-30
relative error = 9.6302580593808363383223637818245e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2639
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.279
y[1] (closed_form) = 1.0386686866144033222100246952314
y[1] (numeric) = 1.0386686866144033222100246952304
absolute error = 1.0e-30
relative error = 9.6277091327317665217239513830360e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2647
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (closed_form) = 1.0389445616892290520754099464035
y[1] (numeric) = 1.0389445616892290520754099464025
absolute error = 1.0e-30
relative error = 9.6251526488967924475421000352693e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2656
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.281
y[1] (closed_form) = 1.0392213978194130047612201563121
y[1] (numeric) = 1.0392213978194130047612201563111
absolute error = 1.0e-30
relative error = 9.6225886235434447491472622146679e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2664
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.282
y[1] (closed_form) = 1.0394991947281190731531793854871
y[1] (numeric) = 1.0394991947281190731531793854861
absolute error = 1.0e-30
relative error = 9.6200170723706035750401494866095e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2673
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.283
y[1] (closed_form) = 1.0397779521375503716949608624835
y[1] (numeric) = 1.0397779521375503716949608624826
absolute error = 9e-31
relative error = 8.6556942099974495748270397912375e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2681
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.284
y[1] (closed_form) = 1.0400576697689495141850493904688
y[1] (numeric) = 1.0400576697689495141850493904678
absolute error = 1.0e-30
relative error = 9.6148514555173811658308100343329e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.269
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=94.3MB, alloc=44.3MB, time=0.69
x[1] = -0.285
y[1] (closed_form) = 1.040338347342598892534104318956
y[1] (numeric) = 1.0403383473425988925341043189551
absolute error = 9e-31
relative error = 8.6510316792505641699770045501150e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2698
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.286
y[1] (closed_form) = 1.0406199845778209564825443233454
y[1] (numeric) = 1.0406199845778209564825443233444
absolute error = 1.0e-30
relative error = 9.6096559245467454161540018832242e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2707
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.287
y[1] (closed_form) = 1.0409025811929784942780742747098
y[1] (numeric) = 1.0409025811929784942780742747088
absolute error = 1.0e-30
relative error = 9.6070469808413766813193363134257e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2715
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.288
y[1] (closed_form) = 1.0411861369054749143128735223236
y[1] (numeric) = 1.0411861369054749143128735223226
absolute error = 1.0e-30
relative error = 9.6044306061557364223943091945524e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2723
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.289
y[1] (closed_form) = 1.0414706514317545277201639517677
y[1] (numeric) = 1.0414706514317545277201639517667
absolute error = 1.0e-30
relative error = 9.6018068164019500850284882950109e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2732
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (closed_form) = 1.0417561244873028319298752220681
y[1] (numeric) = 1.0417561244873028319298752220671
absolute error = 1.0e-30
relative error = 9.5991756275217197883411999648011e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.274
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.291
y[1] (closed_form) = 1.0420425557866467951831236262249
y[1] (numeric) = 1.0420425557866467951831236262239
absolute error = 1.0e-30
relative error = 9.5965370554861023698266984297313e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2748
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.292
y[1] (closed_form) = 1.0423299450433551420052200606774
y[1] (numeric) = 1.0423299450433551420052200606764
absolute error = 1.0e-30
relative error = 9.5938911162952873701334548230576e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2757
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.293
y[1] (closed_form) = 1.0426182919700386396369216307212
y[1] (numeric) = 1.0426182919700386396369216307202
absolute error = 1.0e-30
relative error = 9.5912378259783749629745863251189e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2765
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.294
y[1] (closed_form) = 1.0429075962783503854236404606493
y[1] (numeric) = 1.0429075962783503854236404606483
absolute error = 1.0e-30
relative error = 9.5885772005931538354147380659383e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2773
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.295
y[1] (closed_form) = 1.043197857678986095162322319432
y[1] (numeric) = 1.0431978576789860951623223194309
absolute error = 1.1e-30
relative error = 1.0544500181848466926143533894656e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2782
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.296
y[1] (closed_form) = 1.0434890758816843924057067150814
y[1] (numeric) = 1.0434890758816843924057067150804
absolute error = 1.0e-30
relative error = 9.5832340089910497103201788797554e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.279
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.297
y[1] (closed_form) = 1.0437812505952270987236791534653
y[1] (numeric) = 1.0437812505952270987236791534643
absolute error = 1.0e-30
relative error = 9.5805514750311869861087481017520e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2798
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.298
y[1] (closed_form) = 1.0440743815274395249214253002402
y[1] (numeric) = 1.0440743815274395249214253002393
absolute error = 9e-31
relative error = 8.6200755034649504264252515334243e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2807
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.299
y[1] (closed_form) = 1.0443684683851907632140958277764
y[1] (numeric) = 1.0443684683851907632140958277755
absolute error = 9e-31
relative error = 8.6176481504806994343358498007157e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2815
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (closed_form) = 1.044663510874393980357689772432
y[1] (numeric) = 1.044663510874393980357689772431
absolute error = 1.0e-30
relative error = 9.5724603146422701446362589810738e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2823
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.301
y[1] (closed_form) = 1.0449595087000067117358632713184
y[1] (numeric) = 1.0449595087000067117358632713175
absolute error = 9e-31
relative error = 8.6127739161841287844500232540184e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2831
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.302
y[1] (closed_form) = 1.0452564615660311564023695917739
y[1] (numeric) = 1.0452564615660311564023695917729
absolute error = 1.0e-30
relative error = 9.5670300712781366920612528090345e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.284
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.303
y[1] (closed_form) = 1.0455543691755144730788354111266
y[1] (numeric) = 1.0455543691755144730788354111256
absolute error = 1.0e-30
relative error = 9.5643041575022352524168739167245e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2848
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.304
y[1] (closed_form) = 1.0458532312305490771075773489994
y[1] (numeric) = 1.0458532312305490771075773489984
absolute error = 1.0e-30
relative error = 9.5615710707648888201758060356737e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2856
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.305
y[1] (closed_form) = 1.0461530474322729383591617993617
y[1] (numeric) = 1.0461530474322729383591617993606
absolute error = 1.1e-30
relative error = 1.0514713910167269934879846109229e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2864
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.306
y[1] (closed_form) = 1.0464538174808698800944101547946
y[1] (numeric) = 1.0464538174808698800944101547935
absolute error = 1.1e-30
relative error = 1.0511691788253321484318528162387e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2873
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.307
y[1] (closed_form) = 1.0467555410755698787805505609892
y[1] (numeric) = 1.0467555410755698787805505609882
absolute error = 1.0e-30
relative error = 9.5533289365009973138684284503944e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2881
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.308
y[1] (closed_form) = 1.0470582179146493648612163853508
y[1] (numeric) = 1.0470582179146493648612163853497
absolute error = 1.1e-30
relative error = 1.0505624053940295500868784502905e-28 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2889
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.309
y[1] (closed_form) = 1.0473618476954315244799906297348
y[1] (numeric) = 1.0473618476954315244799906297338
absolute error = 1.0e-30
relative error = 9.5477986161168231412251670940696e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2897
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.31
y[1] (closed_form) = 1.0476664301142866021571945637978
y[1] (numeric) = 1.0476664301142866021571945637968
absolute error = 1.0e-30
relative error = 9.5450228360463280020869203157647e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2905
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.311
y[1] (closed_form) = 1.0479719648666322044196179021966
y[1] (numeric) = 1.0479719648666322044196179021956
absolute error = 1.0e-30
relative error = 9.5422399980639057586246905449760e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2913
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.312
y[1] (closed_form) = 1.0482784516469336043828868959338
y[1] (numeric) = 1.0482784516469336043828868959328
absolute error = 1.0e-30
relative error = 9.5394501187057303640737947357185e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2921
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.313
y[1] (closed_form) = 1.0485858901487040472861657555049
y[1] (numeric) = 1.0485858901487040472861657555039
absolute error = 1.0e-30
relative error = 9.5366532145324414668925243395728e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.293
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.314
y[1] (closed_form) = 1.0488942800645050569788858711721
y[1] (numeric) = 1.0488942800645050569788858711711
absolute error = 1.0e-30
relative error = 9.5338493021289223805644764912666e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2938
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.315
y[1] (closed_form) = 1.0492036210859467433591963436608
y[1] (numeric) = 1.0492036210859467433591963436598
absolute error = 1.0e-30
relative error = 9.5310383981040781109270523261552e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2946
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.316
y[1] (closed_form) = 1.0495139129036881107638283868539
y[1] (numeric) = 1.0495139129036881107638283868529
absolute error = 1.0e-30
relative error = 9.5282205190906134459719856553781e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2954
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.317
y[1] (closed_form) = 1.0498251552074373673090652126448
y[1] (numeric) = 1.0498251552074373673090652126438
absolute error = 1.0e-30
relative error = 9.5253956817448111130483608719517e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2962
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.318
y[1] (closed_form) = 1.0501373476859522351825080570062
y[1] (numeric) = 1.0501373476859522351825080570052
absolute error = 1.0e-30
relative error = 9.5225639027463100083830285641095e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.297
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.319
y[1] (closed_form) = 1.0504504900270402618853280555329
y[1] (numeric) = 1.0504504900270402618853280555319
absolute error = 1.0e-30
relative error = 9.5197251987978835038176321326195e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2978
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (closed_form) = 1.0507645819175591324246927262339
y[1] (numeric) = 1.0507645819175591324246927262329
absolute error = 1.0e-30
relative error = 9.5168795866252178356456200121295e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2986
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.321
y[1] (closed_form) = 1.0510796230434169824560548671731
y[1] (numeric) = 1.0510796230434169824560548671721
absolute error = 1.0e-30
relative error = 9.5140270829766905804166371523713e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2994
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.322
y[1] (closed_form) = 1.0513956130895727123749907266948
y[1] (numeric) = 1.0513956130895727123749907266939
absolute error = 9e-31
relative error = 8.5600509341608343003036107467511e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3002
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.323
y[1] (closed_form) = 1.051712551740036302358273354424
y[1] (numeric) = 1.0517125517400363023582733544231
absolute error = 9e-31
relative error = 8.5574713215219208367933138189333e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.301
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.324
y[1] (closed_form) = 1.0520304386778691283538660919921
y[1] (numeric) = 1.0520304386778691283538660919912
absolute error = 9e-31
relative error = 8.5548855518958921868848521841012e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3018
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.325
y[1] (closed_form) = 1.0523492735851842790195202135225
y[1] (numeric) = 1.0523492735851842790195202135216
absolute error = 9e-31
relative error = 8.5522936404359849945544080566286e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3026
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.326
y[1] (closed_form) = 1.0526690561431468736096597773046
y[1] (numeric) = 1.0526690561431468736096597773037
absolute error = 9e-31
relative error = 8.5496956023148625774883329938773e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3034
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.327
y[1] (closed_form) = 1.0529897860319743808102358017967
y[1] (numeric) = 1.0529897860319743808102358017958
absolute error = 9e-31
relative error = 8.5470914527244161161034072818610e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3042
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.328
y[1] (closed_form) = 1.0533114629309369385212309311322
y[1] (numeric) = 1.0533114629309369385212309311313
absolute error = 9e-31
relative error = 8.5444812068755659510890883963197e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.305
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.329
y[1] (closed_form) = 1.0536340865183576745864948076487
y[1] (numeric) = 1.0536340865183576745864948076478
absolute error = 9e-31
relative error = 8.5418648799980629937328693657197e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3058
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (closed_form) = 1.0539576564716130284705894216338
y[1] (numeric) = 1.0539576564716130284705894216329
absolute error = 9e-31
relative error = 8.5392424873402902532743847386086e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3066
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.331
y[1] (closed_form) = 1.0542821724671330738823227614669
y[1] (numeric) = 1.054282172467133073882322761466
absolute error = 9e-31
relative error = 8.5366140441690644855183023035282e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.332
y[1] (closed_form) = 1.0546076341804018423446481406519
y[1] (numeric) = 1.054607634180401842344648140651
absolute error = 9e-31
relative error = 8.5339795657694379669203238991148e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3081
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.333
y[1] (closed_form) = 1.0549340412859576477106056318672
y[1] (numeric) = 1.0549340412859576477106056318662
absolute error = 1.0e-30
relative error = 9.4792656304938893314942108460157e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3089
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.334
y[1] (closed_form) = 1.0552613934573934116249810921192
y[1] (numeric) = 1.0552613934573934116249810921182
absolute error = 1.0e-30
relative error = 9.4763250716835343807515989590220e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3097
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.335
y[1] (closed_form) = 1.0555896903673569899313573173679
y[1] (numeric) = 1.0555896903673569899313573173669
absolute error = 1.0e-30
relative error = 9.4733778581333893338364730955202e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3105
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.336
y[1] (closed_form) = 1.0559189316875515000242309195995
y[1] (numeric) = 1.0559189316875515000242309195985
absolute error = 1.0e-30
relative error = 9.4704240069056928085196944615425e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3113
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.337
y[1] (closed_form) = 1.056249117088735649145867574257
y[1] (numeric) = 1.056249117088735649145867574256
absolute error = 1.0e-30
relative error = 9.4674635350818461109773237112162e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3121
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.338
y[1] (closed_form) = 1.0565802462407240636275673412012
y[1] (numeric) = 1.0565802462407240636275673412002
absolute error = 1.0e-30
relative error = 9.4644964597621939186030549610132e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3128
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.339
y[1] (closed_form) = 1.0569123188123876190750108179637
y[1] (numeric) = 1.0569123188123876190750108179627
absolute error = 1.0e-30
relative error = 9.4615227980658051345138984340886e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3136
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.34
y[1] (closed_form) = 1.0572453344716537714973559399734
y[1] (numeric) = 1.0572453344716537714973559399725
absolute error = 9e-31
relative error = 8.5126883104172285264587977702050e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3144
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.341
y[1] (closed_form) = 1.0575792928855068893797542986879
y[1] (numeric) = 1.057579292885506889379754298687
absolute error = 9e-31
relative error = 8.5100002057002608077062205050530e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3152
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.342
y[1] (closed_form) = 1.0579141937199885866989549051396
y[1] (numeric) = 1.0579141937199885866989549051388
absolute error = 8e-31
relative error = 7.5620499729465396513792217752284e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3159
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.343
y[1] (closed_form) = 1.0582500366401980568816623833228
y[1] (numeric) = 1.0582500366401980568816623833219
absolute error = 9e-31
relative error = 8.5046063674836175757933779054006e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3167
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.344
y[1] (closed_form) = 1.0585868213102924077053156350886
y[1] (numeric) = 1.0585868213102924077053156350878
absolute error = 8e-31
relative error = 7.5572450355066759727907003350981e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3175
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.345
y[1] (closed_form) = 1.0589245473934869971409520758003
y[1] (numeric) = 1.0589245473934869971409520757995
absolute error = 8e-31
relative error = 7.5548347799583786100844370842273e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3183
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.346
y[1] (closed_form) = 1.0592632145520557701378215979091
y[1] (numeric) = 1.0592632145520557701378215979083
absolute error = 8e-31
relative error = 7.5524193515802044254315084957218e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.319
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.347
y[1] (closed_form) = 1.0596028224473315963494134778678
y[1] (numeric) = 1.059602822447331596349413477867
absolute error = 8e-31
relative error = 7.5499987641809498695189740972415e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3198
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.348
y[1] (closed_form) = 1.0599433707397066088005585003816
y[1] (numeric) = 1.0599433707397066088005585003807
absolute error = 9e-31
relative error = 8.4910196605306721637873795537017e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3206
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.349
y[1] (closed_form) = 1.0602848590886325434952676329222
y[1] (numeric) = 1.0602848590886325434952676329213
absolute error = 9e-31
relative error = 8.4882849385739098967757897439703e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3213
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (closed_form) = 1.0606272871526210799649676426963
y[1] (numeric) = 1.0606272871526210799649676426955
absolute error = 8e-31
relative error = 7.5427061861447508053902688946191e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3221
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.351
y[1] (closed_form) = 1.0609706545892441827567931078597
y[1] (numeric) = 1.0609706545892441827567931078589
absolute error = 8e-31
relative error = 7.5402651010147003111954356517683e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3229
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.352
y[1] (closed_form) = 1.0613149610551344438615933347137
y[1] (numeric) = 1.0613149610551344438615933347129
absolute error = 8e-31
relative error = 7.5378189261052040757765185869925e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3236
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.353
y[1] (closed_form) = 1.0616602062059854260813117529063
y[1] (numeric) = 1.0616602062059854260813117529055
absolute error = 8e-31
relative error = 7.5353676753029057950047977180240e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3244
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.354
y[1] (closed_form) = 1.0620063896965520073353944212866
y[1] (numeric) = 1.0620063896965520073353944212858
absolute error = 8e-31
relative error = 7.5329113625068177149791846708154e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3252
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.355
y[1] (closed_form) = 1.062353511180650725905883338033
y[1] (numeric) = 1.0623535111806507259058833380322
absolute error = 8e-31
relative error = 7.5304500016281479967810024958902e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3259
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.356
y[1] (closed_form) = 1.0627015703111601266208493099901
y[1] (numeric) = 1.0627015703111601266208493099893
absolute error = 8e-31
relative error = 7.5279836065901282782274781308757e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3267
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.357
y[1] (closed_form) = 1.0630505667400211079758181978111
y[1] (numeric) = 1.0630505667400211079758181978103
absolute error = 8e-31
relative error = 7.5255121913278414359905841360239e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3274
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.358
y[1] (closed_form) = 1.0634005001182372701928434155077
y[1] (numeric) = 1.0634005001182372701928434155069
absolute error = 8e-31
relative error = 7.5230357697880495514316051474317e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3282
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.359
y[1] (closed_form) = 1.0637513700958752642168766253644
y[1] (numeric) = 1.0637513700958752642168766253636
absolute error = 8e-31
relative error = 7.5205543559290220834854695349540e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3289
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (closed_form) = 1.0641031763220651416490876318753
y[1] (numeric) = 1.0641031763220651416490876318745
absolute error = 8e-31
relative error = 7.5180679637203642519124790882004e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3297
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.361
y[1] (closed_form) = 1.064455918445000705616783541413
y[1] (numeric) = 1.0644559184450007056167835414123
absolute error = 7e-31
relative error = 6.5761295312499899299412664723033e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3304
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.362
y[1] (closed_form) = 1.0648095961119398625795763177395
y[1] (numeric) = 1.0648095961119398625795763177388
absolute error = 7e-31
relative error = 6.5739452626647003570877442593972e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3312
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.363
y[1] (closed_form) = 1.0651642089692049750714469272204
y[1] (numeric) = 1.0651642089692049750714469272197
absolute error = 7e-31
relative error = 6.5717566747517118373467278358136e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3319
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.364
y[1] (closed_form) = 1.0655197566621832153783533317088
y[1] (numeric) = 1.0655197566621832153783533317081
absolute error = 7e-31
relative error = 6.5695637797726062365726865878842e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3327
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.365
y[1] (closed_form) = 1.0658762388353269201510286515192
y[1] (numeric) = 1.0658762388353269201510286515185
absolute error = 7e-31
relative error = 6.5673665899981362497304246317692e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3334
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.366
y[1] (closed_form) = 1.0662336551321539459526148857234
y[1] (numeric) = 1.0662336551321539459526148857227
absolute error = 7e-31
relative error = 6.5651651177080764008189315004408e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3342
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.367
y[1] (closed_form) = 1.0665920051952480257407766421643
y[1] (numeric) = 1.0665920051952480257407766421636
absolute error = 7e-31
relative error = 6.5629593751910742467800719611367e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3349
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.368
y[1] (closed_form) = 1.0669512886662591262839383951033
y[1] (numeric) = 1.0669512886662591262839383951026
absolute error = 7e-31
relative error = 6.5607493747445017881780120379433e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3357
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.369
y[1] (closed_form) = 1.0673115051859038065112878542941
y[1] (numeric) = 1.0673115051859038065112878542934
absolute error = 7e-31
relative error = 6.5585351286743070894203911204083e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3364
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (closed_form) = 1.0676726543939655767961870955091
y[1] (numeric) = 1.0676726543939655767961870955084
absolute error = 7e-31
relative error = 6.5563166492948661112773085676387e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3371
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.371
y[1] (closed_form) = 1.0680347359292952591726321691378
y[1] (numeric) = 1.0680347359292952591726321691371
absolute error = 7e-31
relative error = 6.5540939489288347584391983987782e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3379
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.372
y[1] (closed_form) = 1.0683977494298113484844009704265
y[1] (numeric) = 1.0683977494298113484844009704258
absolute error = 7e-31
relative error = 6.5518670399070011448396184247882e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3386
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.373
y[1] (closed_form) = 1.0687616945325003744665282222431
y[1] (numeric) = 1.0687616945325003744665282222424
absolute error = 7e-31
relative error = 6.5496359345681380794538814518118e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3394
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.374
y[1] (closed_form) = 1.0691265708734172647587454889206
y[1] (numeric) = 1.0691265708734172647587454889199
absolute error = 7e-31
relative error = 6.5474006452588557752693069009104e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3401
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.375
y[1] (closed_form) = 1.0694923780876857088505232077704
y[1] (numeric) = 1.0694923780876857088505232077698
absolute error = 6e-31
relative error = 5.6101381580001041006637190879375e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3408
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.376
y[1] (closed_form) = 1.0698591158094985229573507932542
y[1] (numeric) = 1.0698591158094985229573507932536
absolute error = 6e-31
relative error = 5.6082150549889535656844539111283e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3416
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
memory used=135.8MB, alloc=44.3MB, time=0.97
TOP MAIN SOLVE Loop
x[1] = -0.377
y[1] (closed_form) = 1.070226783672118015827889937563
y[1] (numeric) = 1.0702267836721180158278899375624
absolute error = 6e-31
relative error = 5.6062883975049170173029340737589e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3423
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.378
y[1] (closed_form) = 1.0705953813078763554816353004824
y[1] (numeric) = 1.0705953813078763554816353004818
absolute error = 6e-31
relative error = 5.6043581961564157203791737397083e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.343
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.379
y[1] (closed_form) = 1.070964908348175936876715850913
y[1] (numeric) = 1.0709649083481759368767158509124
absolute error = 6e-31
relative error = 5.6024244615579604166787757948474e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3437
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (closed_form) = 1.0713353644234897505074691922754
y[1] (numeric) = 1.0713353644234897505074691922749
absolute error = 5e-31
relative error = 4.6670726702750218924585065309607e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3445
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.381
y[1] (closed_form) = 1.0717067491633617519314202742562
y[1] (numeric) = 1.0717067491633617519314202742557
absolute error = 5e-31
relative error = 4.6654553625824400200830432608577e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3452
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.382
y[1] (closed_form) = 1.0720790621964072322252949639468
y[1] (numeric) = 1.0720790621964072322252949639463
absolute error = 5e-31
relative error = 4.6638351370805794630572910653883e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3459
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.383
y[1] (closed_form) = 1.072452303150313189369698020393
y[1] (numeric) = 1.0724523031503131893696980203925
absolute error = 5e-31
relative error = 4.6622120026341237148393516165312e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3466
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.384
y[1] (closed_form) = 1.0728264716518387005620840879077
y[1] (numeric) = 1.0728264716518387005620840879072
absolute error = 5e-31
relative error = 4.6605859681123115190991481346414e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3473
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.385
y[1] (closed_form) = 1.0732015673268152954576493952072
y[1] (numeric) = 1.0732015673268152954576493952067
absolute error = 5e-31
relative error = 4.6589570423888335392890802491772e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3481
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.386
y[1] (closed_form) = 1.0735775898001473303377709195101
y[1] (numeric) = 1.0735775898001473303377709195096
absolute error = 5e-31
relative error = 4.6573252343417292098733741714458e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3488
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.387
y[1] (closed_form) = 1.0739545386958123632056188471909
y[1] (numeric) = 1.0739545386958123632056188471904
absolute error = 5e-31
relative error = 4.6556905528532837709980257121806e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3495
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.388
y[1] (closed_form) = 1.0743324136368615298085672354074
y[1] (numeric) = 1.0743324136368615298085672354069
absolute error = 5e-31
relative error = 4.6540530068099254883719762329684e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3502
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.389
y[1] (closed_form) = 1.0747112142454199205870268523226
y[1] (numeric) = 1.0747112142454199205870268523221
absolute error = 5e-31
relative error = 4.6524126051021230601188778881360e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3509
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (closed_form) = 1.0750909401426869585493232471189
y[1] (numeric) = 1.0750909401426869585493232471184
absolute error = 5e-31
relative error = 4.6507693566242832123474951383348e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3516
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.391
y[1] (closed_form) = 1.0754715909489367780722421749589
y[1] (numeric) = 1.0754715909489367780722421749584
absolute error = 5e-31
relative error = 4.6491232702746484851774551429075e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3523
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.392
y[1] (closed_form) = 1.0758531662835186046268635763786
y[1] (numeric) = 1.0758531662835186046268635763781
absolute error = 5e-31
relative error = 4.6474743549551952109457009080086e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3531
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.393
y[1] (closed_form) = 1.0762356657648571354293043853106
y[1] (numeric) = 1.0762356657648571354293043853102
absolute error = 4e-31
relative error = 3.7166580956572253490460948981034e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3538
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.394
y[1] (closed_form) = 1.0766190890104529210159895150267
y[1] (numeric) = 1.0766190890104529210159895150262
absolute error = 5e-31
relative error = 4.6441680730327965399354050949478e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3545
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.395
y[1] (closed_form) = 1.0770034356368827477430694467592
y[1] (numeric) = 1.0770034356368827477430694467587
absolute error = 5e-31
relative error = 4.6425107242515572975048132449958e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3552
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.396
y[1] (closed_form) = 1.0773887052598000212096019216175
y[1] (numeric) = 1.077388705259800021209601921617
absolute error = 5e-31
relative error = 4.6408505821437091456499638530972e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3559
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.397
y[1] (closed_form) = 1.0777748974939351506041143126486
y[1] (numeric) = 1.0777748974939351506041143126481
absolute error = 5e-31
relative error = 4.6391876556283738965544408419465e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3566
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.398
y[1] (closed_form) = 1.0781620119530959339741623305114
y[1] (numeric) = 1.0781620119530959339741623305109
absolute error = 5e-31
relative error = 4.6375219536277991548353959168032e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3573
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.399
y[1] (closed_form) = 1.0785500482501679444184997932385
y[1] (numeric) = 1.078550048250167944418499793238
absolute error = 5e-31
relative error = 4.6358534850672576883658770347565e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.358
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (closed_form) = 1.0789390059971149172014732679482
y[1] (numeric) = 1.0789390059971149172014732679477
absolute error = 5e-31
relative error = 4.6341822588749470046690645502216e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3587
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.401
y[1] (closed_form) = 1.0793288848049791377892544701431
y[1] (numeric) = 1.0793288848049791377892544701426
absolute error = 5e-31
relative error = 4.6325082839818891345065496178898e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3594
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.402
y[1] (closed_form) = 1.0797196842838818308075223843972
y[1] (numeric) = 1.0797196842838818308075223843966
absolute error = 6e-31
relative error = 5.5569978831861967491254665830446e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3601
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.403
y[1] (closed_form) = 1.0801114040430235499202061487794
y[1] (numeric) = 1.0801114040430235499202061487788
absolute error = 6e-31
relative error = 5.5549825485973712865405011663045e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3608
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.404
y[1] (closed_form) = 1.0805040436906845686288988243055
y[1] (numeric) = 1.0805040436906845686288988243049
absolute error = 6e-31
relative error = 5.5529639477384662512960447683373e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3615
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.405
y[1] (closed_form) = 1.0808976028342252719925512500355
y[1] (numeric) = 1.0808976028342252719925512500349
absolute error = 6e-31
relative error = 5.5509420913390682349184863278144e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3621
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.406
y[1] (closed_form) = 1.0812920810800865492670542641556
y[1] (numeric) = 1.081292081080086549267054264155
absolute error = 6e-31
relative error = 5.5489169901315557549995917337352e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3628
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.407
y[1] (closed_form) = 1.0816874780337901874643166514964
y[1] (numeric) = 1.0816874780337901874643166514958
absolute error = 6e-31
relative error = 5.5468886548509805273985931677782e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3635
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.408
y[1] (closed_form) = 1.0820837932999392658304452584406
y[1] (numeric) = 1.08208379329993926583044525844
absolute error = 6e-31
relative error = 5.5448570962349490003132824347130e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3642
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.409
y[1] (closed_form) = 1.0824810264822185512426327970737
y[1] (numeric) = 1.082481026482218551242632797073
absolute error = 7e-31
relative error = 6.4666260458607548440642613962938e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3649
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (closed_form) = 1.082879177183394894524357941723
y[1] (numeric) = 1.0828791771833948945243579417223
absolute error = 7e-31
relative error = 6.4642484106188421467405398069793e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3656
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.411
y[1] (closed_form) = 1.0832782450053176276785014027179
y[1] (numeric) = 1.0832782450053176276785014027172
absolute error = 7e-31
relative error = 6.4618670524170253201265672529558e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3663
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.412
y[1] (closed_form) = 1.0836782295489189620379807442877
y[1] (numeric) = 1.083678229548918962037980744287
absolute error = 7e-31
relative error = 6.4594819837930580537235078263134e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3669
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.413
y[1] (closed_form) = 1.084079130414214387333505795996
y[1] (numeric) = 1.0840791304142143873335057959953
absolute error = 7e-31
relative error = 6.4570932172869881639047274910276e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3676
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.414
y[1] (closed_form) = 1.0844809472003030716780555899898
y[1] (numeric) = 1.0844809472003030716780555899891
absolute error = 7e-31
relative error = 6.4547007654410212611319088820288e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3683
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.415
y[1] (closed_form) = 1.0848836795053682624676768396186
y[1] (numeric) = 1.0848836795053682624676768396179
absolute error = 7e-31
relative error = 6.4523046407993847373263758002968e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.369
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.416
y[1] (closed_form) = 1.0852873269266776881982030586595
y[1] (numeric) = 1.0852873269266776881982030586588
absolute error = 7e-31
relative error = 6.4499048559081920754215391591007e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3696
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.417
y[1] (closed_form) = 1.0856918890605839611974925044623
y[1] (numeric) = 1.0856918890605839611974925044616
absolute error = 7e-31
relative error = 6.4475014233153074831059069624547e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3703
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.418
y[1] (closed_form) = 1.0860973655025249812727822128099
y[1] (numeric) = 1.0860973655025249812727822128092
absolute error = 7e-31
relative error = 6.4450943555702108527496201475224e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.371
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.419
y[1] (closed_form) = 1.0865037558470243402727544771743
y[1] (numeric) = 1.0865037558470243402727544771736
absolute error = 7e-31
relative error = 6.4426836652238630494909846248502e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3717
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (closed_form) = 1.0869110596876917275639112103343
y[1] (numeric) = 1.0869110596876917275639112103336
absolute error = 7e-31
relative error = 6.4402693648285715294429684274424e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3723
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.421
y[1] (closed_form) = 1.087319276617223336420850712016
y[1] (numeric) = 1.0873192766172233364208507120153
absolute error = 7e-31
relative error = 6.4378514669378562899631223518439e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.373
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.422
y[1] (closed_form) = 1.0877284062274022713300404523114
y[1] (numeric) = 1.0877284062274022713300404523107
absolute error = 7e-31
relative error = 6.4354299841063161539138636583361e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3737
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.423
y[1] (closed_form) = 1.0881384481090989562066785671374
y[1] (numeric) = 1.0881384481090989562066785671368
absolute error = 6e-31
relative error = 5.5140042247624246198487452339175e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3743
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.424
y[1] (closed_form) = 1.088549401852271543524235848908
y[1] (numeric) = 1.0885494018522715435242358489073
absolute error = 7e-31
relative error = 6.4305763138437506698421266439618e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.375
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.425
y[1] (closed_form) = 1.0889612670459663243562691029099
y[1] (numeric) = 1.0889612670459663243562691029092
absolute error = 7e-31
relative error = 6.4281441515261183673689802581596e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3756
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.426
y[1] (closed_form) = 1.0893740432783181393300958276049
y[1] (numeric) = 1.0893740432783181393300958276042
absolute error = 7e-31
relative error = 6.4257084544941821962133106145516e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3763
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.427
y[1] (closed_form) = 1.089787730136550790491919265217
y[1] (numeric) = 1.0897877301365507904919192652163
absolute error = 7e-31
relative error = 6.4232692353059411931317559942262e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.428
y[1] (closed_form) = 1.0902023272069774540829919575135
y[1] (numeric) = 1.0902023272069774540829919575128
absolute error = 7e-31
relative error = 6.4208265065196780455706784384780e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3776
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.429
y[1] (closed_form) = 1.0906178340750010942264050306518
y[1] (numeric) = 1.0906178340750010942264050306511
absolute error = 7e-31
relative error = 6.4183802806938277664243497546595e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3783
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (closed_form) = 1.0910342503251148775240895223366
y[1] (numeric) = 1.0910342503251148775240895223358
absolute error = 8e-31
relative error = 7.3324920804421105344041278777554e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3789
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.431
y[1] (closed_form) = 1.09145157554090258856361515432
y[1] (numeric) = 1.0914515755409025885636151543193
absolute error = 7e-31
relative error = 6.4134773881570819841930419646587e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3796
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.432
y[1] (closed_form) = 1.0918698093050390463343710434825
y[1] (numeric) = 1.0918698093050390463343710434818
absolute error = 7e-31
relative error = 6.4110207465626411009580946133728e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3802
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.433
y[1] (closed_form) = 1.0922889511992905215527119353457
y[1] (numeric) = 1.0922889511992905215527119353451
absolute error = 6e-31
relative error = 5.4930519927096532568118320212465e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3809
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.434
y[1] (closed_form) = 1.0927090008045151548956526349088
y[1] (numeric) = 1.0927090008045151548956526349082
absolute error = 6e-31
relative error = 5.4909404018658720959286331350262e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3815
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.435
y[1] (closed_form) = 1.0931299577006633761426924011461
y[1] (numeric) = 1.0931299577006633761426924011454
absolute error = 7e-31
relative error = 6.4036301911660178302920145866264e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3822
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.436
y[1] (closed_form) = 1.0935518214667783242253501633781
y[1] (numeric) = 1.0935518214667783242253501633774
absolute error = 7e-31
relative error = 6.4011598376846169943572889204310e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3828
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.437
y[1] (closed_form) = 1.0939745916809962681839905100158
y[1] (numeric) = 1.093974591680996268183990510015
absolute error = 8e-31
relative error = 7.3127841001382282724065986886702e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3835
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.438
y[1] (closed_form) = 1.0943982679205470290315194928856
y[1] (numeric) = 1.0943982679205470290315194928849
absolute error = 7e-31
relative error = 6.3962089535289705011604352961960e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3841
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.439
y[1] (closed_form) = 1.0948228497617544025235283834771
y[1] (numeric) = 1.0948228497617544025235283834763
absolute error = 8e-31
relative error = 7.3071182262417054481847639681454e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3847
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (closed_form) = 1.0952483367800365828344626110016
y[1] (numeric) = 1.0952483367800365828344626110009
absolute error = 7e-31
relative error = 6.3912445834700591730008770364225e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3854
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.441
y[1] (closed_form) = 1.0956747285499065871393922061318
y[1] (numeric) = 1.095674728549906587139392206131
absolute error = 8e-31
relative error = 7.3014369972626508363000263752152e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.386
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.442
y[1] (closed_form) = 1.0961020246449726811009591686834
y[1] (numeric) = 1.0961020246449726811009591686826
absolute error = 8e-31
relative error = 7.2985906604735987728236533428131e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3866
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.443
y[1] (closed_form) = 1.0965302246379388052610762723304
y[1] (numeric) = 1.0965302246379388052610762723296
absolute error = 8e-31
relative error = 7.2957405279380279116797063489264e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3873
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.444
y[1] (closed_form) = 1.0969593281006050023369509146883
y[1] (numeric) = 1.0969593281006050023369509146875
absolute error = 8e-31
relative error = 7.2928866139933121797165526130335e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3879
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.445
y[1] (closed_form) = 1.0973893346038678454210067167782
y[1] (numeric) = 1.0973893346038678454210067167774
absolute error = 8e-31
relative error = 7.2900289329746537660332274055022e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3885
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.446
y[1] (closed_form) = 1.0978202437177208670842746719854
y[1] (numeric) = 1.0978202437177208670842746719846
absolute error = 8e-31
relative error = 7.2871674992149400763737854835065e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3892
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.447
y[1] (closed_form) = 1.0982520550112549893828247411573
y[1] (numeric) = 1.0982520550112549893828247411565
absolute error = 8e-31
relative error = 7.2843023270446011181356974187894e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3898
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.448
y[1] (closed_form) = 1.0986847680526589547668078874449
y[1] (numeric) = 1.0986847680526589547668078874441
absolute error = 8e-31
relative error = 7.2814334307914673177032971774928e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3904
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.449
y[1] (closed_form) = 1.0991183824092197578916776418816
y[1] (numeric) = 1.0991183824092197578916776418808
absolute error = 8e-31
relative error = 7.2785608247806277717984903762486e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.391
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (closed_form) = 1.0995528976473230783311593885136
y[1] (numeric) = 1.0995528976473230783311593885127
absolute error = 9e-31
relative error = 8.1851450887510750513374194488374e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3917
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.451
y[1] (closed_form) = 1.0999883133324537141915346561489
y[1] (numeric) = 1.0999883133324537141915346561481
absolute error = 8e-31
relative error = 7.2728045407716337417408650411322e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3923
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.452
y[1] (closed_form) = 1.1004246290291960166268068024775
y[1] (numeric) = 1.1004246290291960166268068024767
absolute error = 8e-31
relative error = 7.2699208914086811744549403516517e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3929
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.453
y[1] (closed_form) = 1.100861844301234325254313575431
y[1] (numeric) = 1.1008618443012343252543135754301
absolute error = 9e-31
relative error = 8.1754127882529145456104543675741e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3935
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.454
y[1] (closed_form) = 1.101299958711353404470351136208
y[1] (numeric) = 1.1012999587113534044703511362072
absolute error = 8e-31
relative error = 7.2641426495293005320345751979181e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3941
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.455
y[1] (closed_form) = 1.1017389718214388806653732283767
y[1] (numeric) = 1.1017389718214388806653732283759
absolute error = 8e-31
relative error = 7.2612480856278328928316440309588e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3948
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.456
y[1] (closed_form) = 1.1021788831924776803383282778904
y[1] (numeric) = 1.1021788831924776803383282778896
absolute error = 8e-31
relative error = 7.2583499121557109762049033255194e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3954
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.457
y[1] (closed_form) = 1.1026196923845584691096963097179
y[1] (numeric) = 1.1026196923845584691096963097172
absolute error = 7e-31
relative error = 6.3485171254846625513622047532051e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.396
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.458
y[1] (closed_form) = 1.1030613989568720916327866680871
y[1] (numeric) = 1.1030613989568720916327866680864
absolute error = 7e-31
relative error = 6.3459749444769471313047311952913e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3966
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.459
y[1] (closed_form) = 1.1035040024677120124028566290802
y[1] (numeric) = 1.1035040024677120124028566290794
absolute error = 8e-31
relative error = 7.2496338772763772451412835499067e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3972
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (closed_form) = 1.1039475024744747574636100964996
y[1] (numeric) = 1.1039475024744747574636100964988
absolute error = 8e-31
relative error = 7.2467214084620607414659585637532e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3978
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.461
y[1] (closed_form) = 1.104391898533660357010634674543
y[1] (numeric) = 1.1043918985336603570106346745422
absolute error = 8e-31
relative error = 7.2438054015262870239798859960492e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3984
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.462
y[1] (closed_form) = 1.1048371902008727888913345138855
y[1] (numeric) = 1.1048371902008727888913345138847
absolute error = 8e-31
relative error = 7.2408858707458092183694777465704e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.399
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.463
y[1] (closed_form) = 1.1052833770308204230009154312754
y[1] (numeric) = 1.1052833770308204230009154312746
absolute error = 8e-31
relative error = 7.2379628303927011144241553521489e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3996
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.464
y[1] (closed_form) = 1.1057304585773164665739779066934
y[1] (numeric) = 1.1057304585773164665739779066926
absolute error = 8e-31
relative error = 7.2350362947342221179816261245519e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4002
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.465
y[1] (closed_form) = 1.1061784343932794103712726665209
y[1] (numeric) = 1.1061784343932794103712726665201
absolute error = 8e-31
relative error = 7.2321062780326826614239771192196e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4008
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.466
y[1] (closed_form) = 1.1066273040307334757611726659979
y[1] (numeric) = 1.106627304030733475761172665997
absolute error = 9e-31
relative error = 8.1328193938634738333626927692566e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4014
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.467
y[1] (closed_form) = 1.1070770670408090626954143895363
y[1] (numeric) = 1.1070770670408090626954143895354
absolute error = 9e-31
relative error = 8.1295153408396292782861362340454e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.402
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.468
y[1] (closed_form) = 1.107527722973743198578660493185
y[1] (numeric) = 1.1075277229737431985786604931841
absolute error = 9e-31
relative error = 8.1262074197427274825235236962250e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4026
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=177.2MB, alloc=44.3MB, time=1.27
TOP MAIN SOLVE Loop
x[1] = -0.469
y[1] (closed_form) = 1.1079792713788799880314349197206
y[1] (numeric) = 1.1079792713788799880314349197197
absolute error = 9e-31
relative error = 8.1228956465940935411578065757024e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4032
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (closed_form) = 1.1084317118046710635459807234666
y[1] (numeric) = 1.1084317118046710635459807234657
absolute error = 9e-31
relative error = 8.1195800374087356796593838265721e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4038
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.471
y[1] (closed_form) = 1.1088850437986760370345899490213
y[1] (numeric) = 1.1088850437986760370345899490204
absolute error = 9e-31
relative error = 8.1162606081951969676866759963436e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4044
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.472
y[1] (closed_form) = 1.109339266907562952269954015601
y[1] (numeric) = 1.1093392669075629522699540156001
absolute error = 9e-31
relative error = 8.1129373749554075591553246476008e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.405
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.473
y[1] (closed_form) = 1.1097943806771087382170821666872
y[1] (numeric) = 1.1097943806771087382170821666863
absolute error = 9e-31
relative error = 8.1096103536845374599792777863886e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4055
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.474
y[1] (closed_form) = 1.1102503846521996632563346530956
y[1] (numeric) = 1.1102503846521996632563346530947
absolute error = 9e-31
relative error = 8.1062795603708498248665530118788e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4061
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.475
y[1] (closed_form) = 1.1107072783768317902971164264731
y[1] (numeric) = 1.1107072783768317902971164264722
absolute error = 9e-31
relative error = 8.1029450109955547845320388212372e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4067
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.476
y[1] (closed_form) = 1.1111650613941114327817762295659
y[1] (numeric) = 1.1111650613941114327817762295651
absolute error = 8e-31
relative error = 7.1996504191401456041504903369094e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4073
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.477
y[1] (closed_form) = 1.1116237332462556115792550793985
y[1] (numeric) = 1.1116237332462556115792550793976
absolute error = 9e-31
relative error = 8.0962647079488445780030123425456e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4079
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.478
y[1] (closed_form) = 1.1120832934745925127680272497516
y[1] (numeric) = 1.1120832934745925127680272497507
absolute error = 9e-31
relative error = 8.0929189862032764507232925179684e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4084
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.479
y[1] (closed_form) = 1.1125437416195619463078759700387
y[1] (numeric) = 1.1125437416195619463078759700378
absolute error = 9e-31
relative error = 8.0895695722475063845830069448650e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.409
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (closed_form) = 1.1130050772207158056000451688413
y[1] (numeric) = 1.1130050772207158056000451688404
absolute error = 9e-31
relative error = 8.0862164820253054559187977016585e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4096
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.481
y[1] (closed_form) = 1.1134672998167185279353077019906
y[1] (numeric) = 1.1134672998167185279353077019898
absolute error = 8e-31
relative error = 7.1847642057533563491879689037528e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4102
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.482
y[1] (closed_form) = 1.1139304089453475558294896171662
y[1] (numeric) = 1.1139304089453475558294896171653
absolute error = 9e-31
relative error = 8.0794993365169586517811533797007e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4107
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.483
y[1] (closed_form) = 1.1143944041434937992459891195241
y[1] (numeric) = 1.1143944041434937992459891195232
absolute error = 9e-31
relative error = 8.0761353130781915346926979882929e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4113
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.484
y[1] (closed_form) = 1.1148592849471620987048280158762
y[1] (numeric) = 1.1148592849471620987048280158754
absolute error = 8e-31
relative error = 7.1757934907266380870457133284104e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4119
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.485
y[1] (closed_form) = 1.1153250508914716892777725284065
y[1] (numeric) = 1.1153250508914716892777725284057
absolute error = 8e-31
relative error = 7.1727968394555960925330709617309e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.486
y[1] (closed_form) = 1.115791701510656665469059482842
y[1] (numeric) = 1.1157917015106566654690594828412
absolute error = 8e-31
relative error = 7.1697970052733842382262394298523e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.413
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.487
y[1] (closed_form) = 1.1162592363380664469812629903921
y[1] (numeric) = 1.1162592363380664469812629903913
absolute error = 8e-31
relative error = 7.1667940023003289312946856184802e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4136
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.488
y[1] (closed_form) = 1.1167276549061662453658358576272
y[1] (numeric) = 1.1167276549061662453658358576264
absolute error = 8e-31
relative error = 7.1637878446488415394942350451994e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4141
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.489
y[1] (closed_form) = 1.117196956746537531557859073795
y[1] (numeric) = 1.1171969567465375315578590737942
absolute error = 8e-31
relative error = 7.1607785464232951776147509031169e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4147
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (closed_form) = 1.1176671413898785042945318408633
y[1] (numeric) = 1.1176671413898785042945318408625
absolute error = 8e-31
relative error = 7.1577661217199019814198623525233e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4152
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.491
y[1] (closed_form) = 1.1181382083660045594169337278386
y[1] (numeric) = 1.1181382083660045594169337278378
absolute error = 8e-31
relative error = 7.1547505846265908700042343924150e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4158
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.492
y[1] (closed_form) = 1.1186101572038487600545896476376
y[1] (numeric) = 1.1186101572038487600545896476368
absolute error = 8e-31
relative error = 7.1517319492228857974763778579352e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4164
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.493
y[1] (closed_form) = 1.1190829874314623076923674719854
y[1] (numeric) = 1.1190829874314623076923674719846
absolute error = 8e-31
relative error = 7.1487102295797844948575490332922e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4169
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.494
y[1] (closed_form) = 1.1195566985760150141192372174827
y[1] (numeric) = 1.1195566985760150141192372174818
absolute error = 9e-31
relative error = 8.0388961197295924159536201920532e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4175
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.495
y[1] (closed_form) = 1.1200312901637957742584198541208
y[1] (numeric) = 1.1200312901637957742584198541199
absolute error = 9e-31
relative error = 8.0354897930430325101032548604898e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.418
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.496
y[1] (closed_form) = 1.1205067617202130398784529061372
y[1] (numeric) = 1.1205067617202130398784529061364
absolute error = 8e-31
relative error = 7.1396267057936545075634464215004e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4186
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.497
y[1] (closed_form) = 1.1209831127697952941846991341835
y[1] (numeric) = 1.1209831127697952941846991341827
absolute error = 8e-31
relative error = 7.1365927897282046243304814674481e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4191
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.498
y[1] (closed_form) = 1.1214603428361915272908237073372
y[1] (numeric) = 1.1214603428361915272908237073364
absolute error = 8e-31
relative error = 7.1335558596462442099517436281008e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4197
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.499
y[1] (closed_form) = 1.1219384514421717125697643935207
y[1] (numeric) = 1.12193845144217171256976439352
absolute error = 7e-31
relative error = 6.2392014383694579471440536869640e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4202
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (closed_form) = 1.1224174381096272838837184173962
y[1] (numeric) = 1.1224174381096272838837184173954
absolute error = 8e-31
relative error = 7.1274730134927166844108599443208e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4207
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.501
y[1] (closed_form) = 1.1228973023595716136926687557886
y[1] (numeric) = 1.1228973023595716136926687557878
absolute error = 8e-31
relative error = 7.1244271254275916337308819082705e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4213
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.502
y[1] (closed_form) = 1.1233780437121404920409717621522
y[1] (numeric) = 1.1233780437121404920409717621514
absolute error = 8e-31
relative error = 7.1213782793586060575403941918520e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4218
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.503
y[1] (closed_form) = 1.1238596616865926064215271335312
y[1] (numeric) = 1.1238596616865926064215271335305
absolute error = 7e-31
relative error = 6.2285356781068178712565838599998e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4223
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.504
y[1] (closed_form) = 1.1243421558013100225170503558855
y[1] (numeric) = 1.1243421558013100225170503558848
absolute error = 7e-31
relative error = 6.2258627979764342653908919104168e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4229
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.505
y[1] (closed_form) = 1.1248255255737986658179668865485
y[1] (numeric) = 1.1248255255737986658179668865477
absolute error = 8e-31
relative error = 7.1122141328709810524142780313895e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4234
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.506
y[1] (closed_form) = 1.1253097705206888041164464559634
y[1] (numeric) = 1.1253097705206888041164464559626
absolute error = 8e-31
relative error = 7.1091535944794501487446948572178e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4239
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.507
y[1] (closed_form) = 1.1257948901577355308760949947039
y[1] (numeric) = 1.1257948901577355308760949947032
absolute error = 7e-31
relative error = 6.2178288968954437677821339624381e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4245
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.508
y[1] (closed_form) = 1.1262808839998192494768208161278
y[1] (numeric) = 1.126280883999819249476820816127
absolute error = 8e-31
relative error = 7.1030238670030413792232267252906e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.425
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.509
y[1] (closed_form) = 1.126767751560946158334390809836
y[1] (numeric) = 1.1267677515609461583343908098352
absolute error = 8e-31
relative error = 7.0999547057655430568429878409082e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4255
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (closed_form) = 1.1272554923542487368941915264245
y[1] (numeric) = 1.1272554923542487368941915264237
absolute error = 8e-31
relative error = 7.0968826980759906276157120870085e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4261
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.511
y[1] (closed_form) = 1.1277441058919862324987091598053
y[1] (numeric) = 1.1277441058919862324987091598045
absolute error = 8e-31
relative error = 7.0938078578317383931906511930281e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4266
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.512
y[1] (closed_form) = 1.1282335916855451481282415596589
y[1] (numeric) = 1.1282335916855451481282415596581
absolute error = 8e-31
relative error = 7.0907301989194047276371165464530e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4271
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.513
y[1] (closed_form) = 1.1287239492454397310143545333464
y[1] (numeric) = 1.1287239492454397310143545333457
absolute error = 7e-31
relative error = 6.2016935183129156862000914129098e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4276
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.514
y[1] (closed_form) = 1.1292151780813124621255938238659
y[1] (numeric) = 1.1292151780813124621255938238652
absolute error = 7e-31
relative error = 6.1989956705097922437993942968066e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4281
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.515
y[1] (closed_form) = 1.1297072777019345465249632781811
y[1] (numeric) = 1.1297072777019345465249632781804
absolute error = 7e-31
relative error = 6.1962953927671355553667744305923e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4286
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.516
y[1] (closed_form) = 1.1302002476152064045986788484863
y[1] (numeric) = 1.1302002476152064045986788484855
absolute error = 8e-31
relative error = 7.0783916539396474934928001904649e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4292
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.517
y[1] (closed_form) = 1.1306940873281581641557071976931
y[1] (numeric) = 1.1306940873281581641557071976923
absolute error = 8e-31
relative error = 7.0753001096026625857663270184233e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4297
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.518
y[1] (closed_form) = 1.1311887963469501533975968096429
y[1] (numeric) = 1.1311887963469501533975968096421
absolute error = 8e-31
relative error = 7.0722058296856549687141558213228e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4302
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.519
y[1] (closed_form) = 1.1316843741768733947581086342535
y[1] (numeric) = 1.1316843741768733947581086342527
absolute error = 8e-31
relative error = 7.0691088279970036271594356286940e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4307
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (closed_form) = 1.1321808203223500996121524280115
y[1] (numeric) = 1.1321808203223500996121524280107
absolute error = 8e-31
relative error = 7.0660091183334754397666150525655e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4312
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.521
y[1] (closed_form) = 1.1326781342869341638535340809147
y[1] (numeric) = 1.1326781342869341638535340809139
absolute error = 8e-31
relative error = 7.0629067144801179392283878836105e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4317
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.522
y[1] (closed_form) = 1.1331763155733116643410183521593
y[1] (numeric) = 1.1331763155733116643410183521585
absolute error = 8e-31
relative error = 7.0598016302101525811248383138996e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4322
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.523
y[1] (closed_form) = 1.133675363683301356212210568549
y[1] (numeric) = 1.1336753636833013562122105685483
absolute error = 7e-31
relative error = 6.1746071443742599566146375781074e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4327
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.524
y[1] (closed_form) = 1.134175278117855171064759971788
y[1] (numeric) = 1.1341752781178551710647599717873
absolute error = 7e-31
relative error = 6.1718855410218272927041827975469e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4332
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.525
y[1] (closed_form) = 1.1346760583770587160043865334936
y[1] (numeric) = 1.1346760583770587160043865334929
absolute error = 7e-31
relative error = 6.1691616283965549553996710976545e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4337
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.526
y[1] (closed_form) = 1.135177703960131773559232189945
y[1] (numeric) = 1.1351777039601317735592321899443
absolute error = 7e-31
relative error = 6.1664354185076954643899838441283e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4342
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.527
y[1] (closed_form) = 1.1356802143654288024600365822581
y[1] (numeric) = 1.1356802143654288024600365822574
absolute error = 7e-31
relative error = 6.1637069233536932609483882249937e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4347
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.528
y[1] (closed_form) = 1.1361835890904394392856365218521
y[1] (numeric) = 1.1361835890904394392856365218513
absolute error = 8e-31
relative error = 7.0411156056252502804649358025984e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4352
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.529
y[1] (closed_form) = 1.1366878276317890009732875357502
y[1] (numeric) = 1.1366878276317890009732875357495
absolute error = 7e-31
relative error = 6.1582431251894542618216484212527e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4357
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.53
y[1] (closed_form) = 1.1371929294852389881933049814358
y[1] (numeric) = 1.1371929294852389881933049814351
absolute error = 7e-31
relative error = 6.1555078461212517800769527393182e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4362
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.531
y[1] (closed_form) = 1.1376988941456875895875213566629
y[1] (numeric) = 1.1376988941456875895875213566622
absolute error = 7e-31
relative error = 6.1527703296717960256578195323429e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4367
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.532
y[1] (closed_form) = 1.138205721107170186871055565808
y[1] (numeric) = 1.1382057211071701868710555658073
absolute error = 7e-31
relative error = 6.1500305877841393073128527081147e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4372
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.533
y[1] (closed_form) = 1.1387134098628598607968890410339
y[1] (numeric) = 1.1387134098628598607968890410332
absolute error = 7e-31
relative error = 6.1472886323899882928116782130902e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4376
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.534
y[1] (closed_form) = 1.1392219599050678979827427537335
y[1] (numeric) = 1.1392219599050678979827427537328
absolute error = 7e-31
relative error = 6.1445444754096159829899698154393e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4381
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.535
y[1] (closed_form) = 1.1397313707252442985997482894172
y[1] (numeric) = 1.1397313707252442985997482894165
absolute error = 7e-31
relative error = 6.1417981287517741342612803840597e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4386
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.536
y[1] (closed_form) = 1.1402416418139782849224052974161
y[1] (numeric) = 1.1402416418139782849224052974154
absolute error = 7e-31
relative error = 6.1390496043136061297617879301126e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4391
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.537
y[1] (closed_form) = 1.1407527726609988107393167654858
y[1] (numeric) = 1.1407527726609988107393167654851
absolute error = 7e-31
relative error = 6.1362989139805602992809458751891e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4396
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.538
y[1] (closed_form) = 1.1412647627551750716241927086173
y[1] (numeric) = 1.1412647627551750716241927086167
absolute error = 6e-31
relative error = 5.2573252025368317326725405878347e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.44
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.539
y[1] (closed_form) = 1.1417776115845170160666120010952
y[1] (numeric) = 1.1417776115845170160666120010946
absolute error = 6e-31
relative error = 5.2549637855251168071351778130157e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4405
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (closed_form) = 1.1422913186361758574620312210822
y[1] (numeric) = 1.1422913186361758574620312210816
absolute error = 6e-31
relative error = 5.2526005425337762620971303683586e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.441
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.541
y[1] (closed_form) = 1.1428058833964445869605285177651
y[1] (numeric) = 1.1428058833964445869605285177645
absolute error = 6e-31
relative error = 5.2502354837095046370314098066485e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4414
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.542
y[1] (closed_form) = 1.1433213053507584871737696523608
y[1] (numeric) = 1.1433213053507584871737696523603
absolute error = 5e-31
relative error = 4.3732238493238386898938446529760e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4419
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.543
y[1] (closed_form) = 1.1438375839836956467396825060591
y[1] (numeric) = 1.1438375839836956467396825060585
absolute error = 6e-31
relative error = 5.2454999590969240999866439216073e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4424
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.544
y[1] (closed_form) = 1.1443547187789774757443254902696
y[1] (numeric) = 1.144354718778977475744325490269
absolute error = 6e-31
relative error = 5.2431295135497664864212406470351e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4429
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.545
y[1] (closed_form) = 1.1448727092194692220004344373497
y[1] (numeric) = 1.1448727092194692220004344373491
absolute error = 6e-31
relative error = 5.2407572926518375714802702233059e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4433
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.546
y[1] (closed_form) = 1.1453915547871804881821316933069
y[1] (numeric) = 1.1453915547871804881821316933063
absolute error = 6e-31
relative error = 5.2383833064971656596539142487983e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4438
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.547
y[1] (closed_form) = 1.1459112549632657498152802778119
y[1] (numeric) = 1.1459112549632657498152802778113
absolute error = 6e-31
relative error = 5.2360075651690329299261524494922e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4442
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.548
y[1] (closed_form) = 1.1464318092280248741229651212096
y[1] (numeric) = 1.146431809228024874122965121209
absolute error = 6e-31
relative error = 5.2336300787399053754702378822324e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4447
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.549
y[1] (closed_form) = 1.1469532170609036397255825330915
y[1] (numeric) = 1.1469532170609036397255825330909
absolute error = 6e-31
relative error = 5.2312508572713631287322158726843e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4451
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (closed_form) = 1.1474754779404942571950182023822
y[1] (numeric) = 1.1474754779404942571950182023816
absolute error = 6e-31
relative error = 5.2288699108140311718919433406936e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4456
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.551
y[1] (closed_form) = 1.1479985913445358904623931748063
y[1] (numeric) = 1.1479985913445358904623931748057
absolute error = 6e-31
relative error = 5.2264872494075104326805218074122e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4461
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.552
y[1] (closed_form) = 1.1485225567499151790788564000321
y[1] (numeric) = 1.1485225567499151790788564000315
absolute error = 6e-31
relative error = 5.2241028830803092655225657222645e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4465
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.553
y[1] (closed_form) = 1.1490473736326667613289015877443
y[1] (numeric) = 1.1490473736326667613289015877437
absolute error = 6e-31
relative error = 5.2217168218497753179612879786377e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.447
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.554
y[1] (closed_form) = 1.1495730414679737981956852593716
y[1] (numeric) = 1.149573041467973798195685259371
absolute error = 6e-31
relative error = 5.2193290757220277823139967863256e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4474
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.555
y[1] (closed_form) = 1.150099559730168498177822030195
y[1] (numeric) = 1.1500995597301684981778220301944
absolute error = 6e-31
relative error = 5.2169396546918900324952626135123e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4478
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.556
y[1] (closed_form) = 1.1506269278927326429571323050854
y[1] (numeric) = 1.1506269278927326429571323050848
absolute error = 6e-31
relative error = 5.2145485687428226459347308749160e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4483
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.557
y[1] (closed_form) = 1.1511551454282981139168167201663
y[1] (numeric) = 1.1511551454282981139168167201657
absolute error = 6e-31
relative error = 5.2121558278468568105063255952322e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4487
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.558
y[1] (closed_form) = 1.1516842118086474195095308122717
y[1] (numeric) = 1.1516842118086474195095308122711
absolute error = 6e-31
relative error = 5.2097614419645281163754115839608e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4492
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.559
y[1] (closed_form) = 1.1522141265047142234748325481675
y[1] (numeric) = 1.1522141265047142234748325481669
absolute error = 6e-31
relative error = 5.2073654210448107326603578810569e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4496
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (closed_form) = 1.1527448889865838739054744961337
y[1] (numeric) = 1.1527448889865838739054744961331
absolute error = 6e-31
relative error = 5.2049677750250519687948735306967e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4501
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=218.7MB, alloc=44.3MB, time=1.55
x[1] = -0.561
y[1] (closed_form) = 1.153276498723493933162011573659
y[1] (numeric) = 1.1532764987234939331620115736584
absolute error = 6e-31
relative error = 5.2025685138309072204674682671903e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4505
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.562
y[1] (closed_form) = 1.1538089551838347086351944566842
y[1] (numeric) = 1.1538089551838347086351944566837
absolute error = 5e-31
relative error = 4.3334730394802294166703546693700e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4509
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.563
y[1] (closed_form) = 1.1543422578351497843556178880455
y[1] (numeric) = 1.154342257835149784355617888045
absolute error = 5e-31
relative error = 4.3314709879693617925439702026494e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4513
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.564
y[1] (closed_form) = 1.1548764061441365534500922755128
y[1] (numeric) = 1.1548764061441365534500922755122
absolute error = 6e-31
relative error = 5.1953611382819769474098058454359e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4518
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.565
y[1] (closed_form) = 1.1554113995766467514442061230971
y[1] (numeric) = 1.1554113995766467514442061230965
absolute error = 6e-31
relative error = 5.1929555154107485758361630690039e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4522
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.566
y[1] (closed_form) = 1.1559472375976869904105459931083
y[1] (numeric) = 1.1559472375976869904105459931077
absolute error = 6e-31
relative error = 5.1905483268157825026792116930072e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4526
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.567
y[1] (closed_form) = 1.1564839196714192939620398507875
y[1] (numeric) = 1.1564839196714192939620398507869
absolute error = 6e-31
relative error = 5.1881395823512380241244145293626e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4531
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.568
y[1] (closed_form) = 1.157021445261161633089888798216
y[1] (numeric) = 1.1570214452611616330898887982154
absolute error = 6e-31
relative error = 5.1857292918591378998822229834952e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4535
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.569
y[1] (closed_form) = 1.1575598138293884628455513596132
y[1] (numeric) = 1.1575598138293884628455513596125
absolute error = 7e-31
relative error = 6.0472037093641907651268103457614e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4539
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (closed_form) = 1.158099024837731259866243636084
y[1] (numeric) = 1.1580990248377312598662436360833
absolute error = 7e-31
relative error = 6.0443881307825254812398369839999e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4543
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.571
y[1] (closed_form) = 1.158639077746979060743417804361
y[1] (numeric) = 1.1586390777469790607434178043603
absolute error = 7e-31
relative error = 6.0415707828634482791587962381381e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4547
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.572
y[1] (closed_form) = 1.1591799720170790012336805911064
y[1] (numeric) = 1.1591799720170790012336805911057
absolute error = 7e-31
relative error = 6.0387516770319632063640246899754e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4551
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.573
y[1] (closed_form) = 1.1597217071071368563116125119018
y[1] (numeric) = 1.1597217071071368563116125119011
absolute error = 7e-31
relative error = 6.0359308246985579157805983804178e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4556
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.574
y[1] (closed_form) = 1.1602642824754175810639478221502
y[1] (numeric) = 1.1602642824754175810639478221495
absolute error = 7e-31
relative error = 6.0331082372591335837961135382660e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.456
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.575
y[1] (closed_form) = 1.1608076975793458524245742857562
y[1] (numeric) = 1.1608076975793458524245742857555
absolute error = 7e-31
relative error = 6.0302839260949352737401095989815e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4564
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.576
y[1] (closed_form) = 1.1613519518755066117498110266296
y[1] (numeric) = 1.1613519518755066117498110266289
absolute error = 7e-31
relative error = 6.0274579025724827445131170685059e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4568
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.577
y[1] (closed_form) = 1.1618970448196456082334218877795
y[1] (numeric) = 1.1618970448196456082334218877788
absolute error = 7e-31
relative error = 6.0246301780435017040426391221705e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4572
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.578
y[1] (closed_form) = 1.162442975866669943160820883031
y[1] (numeric) = 1.1624429758666699431608208830303
absolute error = 7e-31
relative error = 6.0218007638448555072327666657584e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4576
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.579
y[1] (closed_form) = 1.1629897444706486150019254872046
y[1] (numeric) = 1.1629897444706486150019254872039
absolute error = 7e-31
relative error = 6.0189696712984772980635820284332e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.458
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (closed_form) = 1.16353735008481306534211267195
y[1] (numeric) = 1.1635373500848130653421126719493
absolute error = 7e-31
relative error = 6.0161369117113025954860266050349e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4584
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.581
y[1] (closed_form) = 1.1640857921615577256507317563242
y[1] (numeric) = 1.1640857921615577256507317563235
absolute error = 7e-31
relative error = 6.0133024963752023227474927136189e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4588
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.582
y[1] (closed_form) = 1.1646350701524405648866273036464
y[1] (numeric) = 1.1646350701524405648866273036457
absolute error = 7e-31
relative error = 6.0104664365669162797730497745187e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4592
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.583
y[1] (closed_form) = 1.165185183508183637940124459152
y[1] (numeric) = 1.1651851835081836379401244591513
absolute error = 7e-31
relative error = 6.0076287435479870582169297370926e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4596
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.584
y[1] (closed_form) = 1.1657361316786736349109282865074
y[1] (numeric) = 1.1657361316786736349109282865067
absolute error = 7e-31
relative error = 6.0047894285646943987886765630965e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.585
y[1] (closed_form) = 1.1662879141129624312213878253303
y[1] (numeric) = 1.1662879141129624312213878253296
absolute error = 7e-31
relative error = 6.0019485028479899904482096008630e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4604
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.586
y[1] (closed_form) = 1.1668405302592676385645747564984
y[1] (numeric) = 1.1668405302592676385645747564978
absolute error = 6e-31
relative error = 5.1420908379543708951891093665538e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4608
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.587
y[1] (closed_form) = 1.1673939795649731566866257272142
y[1] (numeric) = 1.1673939795649731566866257272135
absolute error = 7e-31
relative error = 5.9962618640611243090382222703211e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4612
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.588
y[1] (closed_form) = 1.1679482614766297260027965535271
y[1] (numeric) = 1.1679482614766297260027965535265
absolute error = 6e-31
relative error = 5.1372138628934104505776097184393e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.589
y[1] (closed_form) = 1.1685033754399554810466756843086
y[1] (numeric) = 1.168503375439955481046675684308
absolute error = 6e-31
relative error = 5.1347733571937079921315488968371e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4619
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (closed_form) = 1.1690593208998365047520034775093
y[1] (numeric) = 1.1690593208998365047520034775087
absolute error = 6e-31
relative error = 5.1323315187990124785929213435834e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4623
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.591
y[1] (closed_form) = 1.1696160973003273835665430069271
y[1] (numeric) = 1.1696160973003273835665430069265
absolute error = 6e-31
relative error = 5.1298883572558714978739495550386e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4627
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.592
y[1] (closed_form) = 1.1701737040846517633974472856612
y[1] (numeric) = 1.1701737040846517633974472856606
absolute error = 6e-31
relative error = 5.1274438820973136768240090330838e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4631
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.593
y[1] (closed_form) = 1.1707321406952029063875669609314
y[1] (numeric) = 1.1707321406952029063875669609308
absolute error = 6e-31
relative error = 5.1249981028427958112373352553260e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4634
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.594
y[1] (closed_form) = 1.1712914065735442485221417040005
y[1] (numeric) = 1.1712914065735442485221417039998
absolute error = 7e-31
relative error = 5.9763095338311754329418237733815e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4638
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.595
y[1] (closed_form) = 1.1718515011604099580653176885558
y[1] (numeric) = 1.1718515011604099580653176885551
absolute error = 7e-31
relative error = 5.9734531150647889440279138986546e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4642
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.596
y[1] (closed_form) = 1.172412423895705494825932721079
y[1] (numeric) = 1.1724124238957054948259327210783
absolute error = 7e-31
relative error = 5.9705952080756014513378289800118e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4646
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.597
y[1] (closed_form) = 1.1729741742185081702520097574644
y[1] (numeric) = 1.1729741742185081702520097574637
absolute error = 7e-31
relative error = 5.9677358239057026029381231833274e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4649
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.598
y[1] (closed_form) = 1.1735367515670677083533987114403
y[1] (numeric) = 1.1735367515670677083533987114397
absolute error = 6e-31
relative error = 5.1127499773551826217646126660082e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4653
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.599
y[1] (closed_form) = 1.1741001553788068074520056321979
y[1] (numeric) = 1.1741001553788068074520056321973
absolute error = 6e-31
relative error = 5.1102965726669075094152614763491e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4657
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (closed_form) = 1.1746643850903217027590475010446
y[1] (numeric) = 1.174664385090321702759047501044
absolute error = 6e-31
relative error = 5.1078419301344962624760199534449e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.466
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.601
y[1] (closed_form) = 1.1752294401373827297787700698751
y[1] (numeric) = 1.1752294401373827297787700698744
absolute error = 7e-31
relative error = 5.9562837356948014177158104285391e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4664
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.602
y[1] (closed_form) = 1.1757953199549348885380653377883
y[1] (numeric) = 1.1757953199549348885380653377876
absolute error = 7e-31
relative error = 5.9534171306858845182116821346211e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4667
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.603
y[1] (closed_form) = 1.1763620239770984086414244362806
y[1] (numeric) = 1.1763620239770984086414244362799
absolute error = 7e-31
relative error = 5.9505491144078934021907045895995e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4671
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.604
y[1] (closed_form) = 1.1769295516371693151506608681084
y[1] (numeric) = 1.1769295516371693151506608681077
absolute error = 7e-31
relative error = 5.9476796977887430071202766638176e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4675
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.605
y[1] (closed_form) = 1.177497902367619995288838220145
y[1] (numeric) = 1.1774979023676199952888382201444
absolute error = 6e-31
relative error = 5.0955504786341213855092600908278e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4678
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.606
y[1] (closed_form) = 1.1780670756000997659678356463513
y[1] (numeric) = 1.1780670756000997659678356463507
absolute error = 6e-31
relative error = 5.0930886061336012802206322675593e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4682
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.607
y[1] (closed_form) = 1.1786370707654354421389835933405
y[1] (numeric) = 1.1786370707654354421389835933399
absolute error = 6e-31
relative error = 5.0906255613557570972035051588774e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4685
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.608
y[1] (closed_form) = 1.1792078872936319059662014179512
y[1] (numeric) = 1.1792078872936319059662014179506
absolute error = 6e-31
relative error = 5.0881613536103778483935949200309e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4689
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.609
y[1] (closed_form) = 1.1797795246138726768210677237362
y[1] (numeric) = 1.1797795246138726768210677237355
absolute error = 7e-31
relative error = 5.9333119908916997662156184936013e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4692
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (closed_form) = 1.1803519821545204820992534213452
y[1] (numeric) = 1.1803519821545204820992534213445
absolute error = 7e-31
relative error = 5.9304344007816699013542379816472e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4695
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.611
y[1] (closed_form) = 1.1809252593431178288577466964165
y[1] (numeric) = 1.1809252593431178288577466964158
absolute error = 7e-31
relative error = 5.9275554863596579494337409217164e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4699
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.612
y[1] (closed_form) = 1.1814993556063875762722982477992
y[1] (numeric) = 1.1814993556063875762722982477985
absolute error = 7e-31
relative error = 5.9246752584197141011951016121514e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4702
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.613
y[1] (closed_form) = 1.1820742703702335089145143387088
y[1] (numeric) = 1.1820742703702335089145143387081
absolute error = 7e-31
relative error = 5.9217937277389123181839160659857e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4706
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.614
y[1] (closed_form) = 1.1826500030597409108480243837716
y[1] (numeric) = 1.1826500030597409108480243837709
absolute error = 7e-31
relative error = 5.9189109050772977263522467860761e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4709
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.615
y[1] (closed_form) = 1.1832265530991771405431489758368
y[1] (numeric) = 1.1832265530991771405431489758361
absolute error = 7e-31
relative error = 5.9160268011778344349601067913698e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4712
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.616
y[1] (closed_form) = 1.1838039199119922066094934379379
y[1] (numeric) = 1.1838039199119922066094934379372
absolute error = 7e-31
relative error = 5.9131414267663537800885964733047e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4716
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.617
y[1] (closed_form) = 1.1843821029208193443458911678558
y[1] (numeric) = 1.1843821029208193443458911678551
absolute error = 7e-31
relative error = 5.9102547925515029920686558940489e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4719
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.618
y[1] (closed_form) = 1.1849611015474755931071202253905
y[1] (numeric) = 1.1849611015474755931071202253898
absolute error = 7e-31
relative error = 5.9073669092246942861214098627879e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4722
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.619
y[1] (closed_form) = 1.1855409152129623744868157956707
y[1] (numeric) = 1.1855409152129623744868157956701
absolute error = 6e-31
relative error = 5.0609809606800466075698544295062e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4726
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (closed_form) = 1.1861215433374660713160003456393
y[1] (numeric) = 1.1861215433374660713160003456387
absolute error = 6e-31
relative error = 5.0585035182123209197716445617588e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4729
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.621
y[1] (closed_form) = 1.1867029853403586074766524752305
y[1] (numeric) = 1.1867029853403586074766524752299
absolute error = 6e-31
relative error = 5.0560250324803374119581369023158e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4732
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.622
y[1] (closed_form) = 1.1872852406401980285297346497202
y[1] (numeric) = 1.1872852406401980285297346497196
absolute error = 6e-31
relative error = 5.0535455125886430844162295491896e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4735
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.623
y[1] (closed_form) = 1.1878683086547290831570991852689
y[1] (numeric) = 1.1878683086547290831570991852683
absolute error = 6e-31
relative error = 5.0510649676267993040679411865142e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4739
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.624
y[1] (closed_form) = 1.1884521888008838054166910457999
y[1] (numeric) = 1.1884521888008838054166910457993
absolute error = 6e-31
relative error = 5.0485834066693403313445680147629e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4742
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.625
y[1] (closed_form) = 1.1890368804947820978104651960589
y[1] (numeric) = 1.1890368804947820978104651960583
absolute error = 6e-31
relative error = 5.0461008387757322054025735526968e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4745
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.626
y[1] (closed_form) = 1.189622383151732315164435442986
y[1] (numeric) = 1.1896223831517323151644354429854
absolute error = 6e-31
relative error = 5.0436172729903319870250293655194e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4748
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.627
y[1] (closed_form) = 1.1902086961862318493202708853993
y[1] (numeric) = 1.1902086961862318493202708853988
absolute error = 5e-31
relative error = 4.2009439319519561321217375794984e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4751
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.628
y[1] (closed_form) = 1.1907958190119677146378552804441
y[1] (numeric) = 1.1907958190119677146378552804436
absolute error = 5e-31
relative error = 4.1988726532048304834413852704304e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4754
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.629
y[1] (closed_form) = 1.1913837510418171343082238242947
y[1] (numeric) = 1.1913837510418171343082238242942
absolute error = 5e-31
relative error = 4.1968005654162240014394489379628e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4757
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (closed_form) = 1.1919724916878481274762910342229
y[1] (numeric) = 1.1919724916878481274762910342225
absolute error = 4e-31
relative error = 3.3557821408579231533561443905488e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.476
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.631
y[1] (closed_form) = 1.1925620403613200971727826093538
y[1] (numeric) = 1.1925620403613200971727826093534
absolute error = 4e-31
relative error = 3.3541231941175050998369687084415e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4764
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.632
y[1] (closed_form) = 1.1931523964726844190547833382246
y[1] (numeric) = 1.1931523964726844190547833382242
absolute error = 4e-31
relative error = 3.3524636180803031989933789134888e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4767
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.633
y[1] (closed_form) = 1.1937435594315850309543123126502
y[1] (numeric) = 1.1937435594315850309543123126497
absolute error = 5e-31
relative error = 4.1885042733807992454438686999071e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.477
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.634
y[1] (closed_form) = 1.1943355286468590232343358993664
y[1] (numeric) = 1.194335528646859023234335899366
absolute error = 4e-31
relative error = 3.3491426019385541445917069095722e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4773
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.635
y[1] (closed_form) = 1.1949283035265372299516281134903
y[1] (numeric) = 1.1949283035265372299516281134899
absolute error = 4e-31
relative error = 3.3474811737197813578563813690646e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.636
y[1] (closed_form) = 1.1955218834778448208258872309833
y[1] (numeric) = 1.1955218834778448208258872309829
absolute error = 4e-31
relative error = 3.3458191399757235999857279459849e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4778
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.637
y[1] (closed_form) = 1.1961162679072018940145166710524
y[1] (numeric) = 1.1961162679072018940145166710519
absolute error = 5e-31
relative error = 4.1801956332792843825923999846451e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4781
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.638
y[1] (closed_form) = 1.1967114562202240696924773737563
y[1] (numeric) = 1.1967114562202240696924773737558
absolute error = 5e-31
relative error = 4.1781165994619492961691804054084e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4784
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.639
y[1] (closed_form) = 1.1973074478217230844366180930148
y[1] (numeric) = 1.1973074478217230844366180930144
absolute error = 4e-31
relative error = 3.3408294647103813659662718753411e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4787
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (closed_form) = 1.1979042421157073864138892207397
y[1] (numeric) = 1.1979042421157073864138892207392
absolute error = 5e-31
relative error = 4.1739563349146587473903684267929e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.641
y[1] (closed_form) = 1.198501838505382731372844953923
y[1] (numeric) = 1.1985018385053827313728449539225
absolute error = 5e-31
relative error = 4.1718751188862226488057071573710e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4793
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.642
y[1] (closed_form) = 1.1991002363931527794378378132311
y[1] (numeric) = 1.1991002363931527794378378132306
absolute error = 5e-31
relative error = 4.1697931901338014728052538196133e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4796
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.643
y[1] (closed_form) = 1.1996994351806196927053087189588
y[1] (numeric) = 1.1996994351806196927053087189584
absolute error = 4e-31
relative error = 3.3341684447803240984905863351428e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.644
y[1] (closed_form) = 1.2002994342685847336415750281037
y[1] (numeric) = 1.2002994342685847336415750281033
absolute error = 4e-31
relative error = 3.3325017789727133182456694023846e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4801
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.645
y[1] (closed_form) = 1.2009002330570488642815181348221
y[1] (numeric) = 1.2009002330570488642815181348217
absolute error = 4e-31
relative error = 3.3308345605175510622228717037482e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4804
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.646
y[1] (closed_form) = 1.2015018309452133462275714356296
y[1] (numeric) = 1.2015018309452133462275714356292
absolute error = 4e-31
relative error = 3.3291667952376128410255819872027e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.647
y[1] (closed_form) = 1.2021042273314803414484086604078
y[1] (numeric) = 1.2021042273314803414484086604074
absolute error = 4e-31
relative error = 3.3274984889450851791368164739087e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.481
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.648
y[1] (closed_form) = 1.2027074216134535138767317705792
y[1] (numeric) = 1.2027074216134535138767317705788
absolute error = 4e-31
relative error = 3.3258296474415435707381181270203e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.649
y[1] (closed_form) = 1.203311413187938631805556826712
y[1] (numeric) = 1.2033114131879386318055568267117
absolute error = 3e-31
relative error = 2.4931202073884479971242730956549e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (closed_form) = 1.2039162014509441710823954293201
y[1] (numeric) = 1.2039162014509441710823954293198
absolute error = 3e-31
relative error = 2.4918677864659009988563238366354e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.651
y[1] (closed_form) = 1.2045217857976819191007285387257
y[1] (numeric) = 1.2045217857976819191007285387254
absolute error = 3e-31
relative error = 2.4906149771407259896867440652539e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.482
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.652
y[1] (closed_form) = 1.2051281656225675795881686825627
y[1] (numeric) = 1.2051281656225675795881686825624
absolute error = 3e-31
relative error = 2.4893617837321095715845412331694e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4823
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=260.2MB, alloc=44.3MB, time=1.84
x[1] = -0.653
y[1] (closed_form) = 1.2057353403192213781907057628076
y[1] (numeric) = 1.2057353403192213781907057628073
absolute error = 3e-31
relative error = 2.4881082105511999573142106258838e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4826
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.654
y[1] (closed_form) = 1.2063433092804686688524308781435
y[1] (numeric) = 1.2063433092804686688524308781432
absolute error = 3e-31
relative error = 2.4868542619010914541696242539657e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4828
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.655
y[1] (closed_form) = 1.2069520718983405409901317819836
y[1] (numeric) = 1.2069520718983405409901317819833
absolute error = 3e-31
relative error = 2.4855999420768091157695019005571e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4831
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.656
y[1] (closed_form) = 1.207561627564074427462152801609
y[1] (numeric) = 1.2075616275640744274621528016087
absolute error = 3e-31
relative error = 2.4843452553652935615032641631607e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4833
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.657
y[1] (closed_form) = 1.2081719756681147133309112496125
y[1] (numeric) = 1.2081719756681147133309112496122
absolute error = 3e-31
relative error = 2.4830902060453859632137168297007e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4836
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.658
y[1] (closed_form) = 1.2087831156001133454184615651814
y[1] (numeric) = 1.2087831156001133454184615651811
absolute error = 3e-31
relative error = 2.4818347983878131987006919267213e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.659
y[1] (closed_form) = 1.2093950467489304426544976297072
y[1] (numeric) = 1.2093950467489304426544976297068
absolute error = 4e-31
relative error = 3.3074387155402308955032976106020e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4841
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (closed_form) = 1.2100077685026349072161829087698
y[1] (numeric) = 1.2100077685026349072161829087694
absolute error = 4e-31
relative error = 3.3057639001358937298794168667540e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4844
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.661
y[1] (closed_form) = 1.2106212802485050364591972807178
y[1] (numeric) = 1.2106212802485050364591972807174
absolute error = 4e-31
relative error = 3.3040886239658015395507994988072e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4846
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.662
y[1] (closed_form) = 1.2112355813730291356393886208484
y[1] (numeric) = 1.211235581373029135639388620848
absolute error = 4e-31
relative error = 3.3024128926807870690507009995025e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4849
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.663
y[1] (closed_form) = 1.2118506712619061314244164195866
y[1] (numeric) = 1.2118506712619061314244164195861
absolute error = 5e-31
relative error = 4.1259208899009604304314932453359e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4851
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.664
y[1] (closed_form) = 1.2124665493000461861947739230711
y[1] (numeric) = 1.2124665493000461861947739230706
absolute error = 5e-31
relative error = 4.1238251091434127503234496926931e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4853
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.665
y[1] (closed_form) = 1.2130832148715713131335744951767
y[1] (numeric) = 1.2130832148715713131335744951763
absolute error = 4e-31
relative error = 3.2973830244807060263625028056294e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4856
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.666
y[1] (closed_form) = 1.213700667359815992104487111237
y[1] (numeric) = 1.2137006673598159921044871112365
absolute error = 5e-31
relative error = 4.1196319112821996634337277647635e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4858
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.667
y[1] (closed_form) = 1.2143189061473277863172051055833
y[1] (numeric) = 1.2143189061473277863172051055829
absolute error = 4e-31
relative error = 3.2940276065459679210988262948356e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.486
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.668
y[1] (closed_form) = 1.2149379306158679597798315074841
y[1] (numeric) = 1.2149379306158679597798315074836
absolute error = 5e-31
relative error = 4.1154365782830028781219763072688e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4863
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.669
y[1] (closed_form) = 1.2155577401464120955375635131482
y[1] (numeric) = 1.2155577401464120955375635131477
absolute error = 5e-31
relative error = 4.1133381285513903641831371387316e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4865
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (closed_form) = 1.2161783341191507146970578551619
y[1] (numeric) = 1.2161783341191507146970578551614
absolute error = 5e-31
relative error = 4.1112391659413848060604802413298e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4867
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.671
y[1] (closed_form) = 1.2167997119134898962358580450436
y[1] (numeric) = 1.2167997119134898962358580450431
absolute error = 5e-31
relative error = 4.1091396973929281317933259715530e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.487
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.672
y[1] (closed_form) = 1.2174218729080518975962636795423
y[1] (numeric) = 1.2174218729080518975962636795418
absolute error = 5e-31
relative error = 4.1070397298321208244422740028576e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4872
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.673
y[1] (closed_form) = 1.2180448164806757760630212168607
y[1] (numeric) = 1.2180448164806757760630212168602
absolute error = 5e-31
relative error = 4.1049392701712012627775806832191e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4874
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.674
y[1] (closed_form) = 1.2186685420084180109242148451658
y[1] (numeric) = 1.2186685420084180109242148451653
absolute error = 5e-31
relative error = 4.1028383253085253284213071064361e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4876
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.675
y[1] (closed_form) = 1.219293048867553126414735282546
y[1] (numeric) = 1.2192930488675531264147352825455
absolute error = 5e-31
relative error = 4.1007369021285462786909151181636e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4879
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.676
y[1] (closed_form) = 1.2199183364335743154417035649992
y[1] (numeric) = 1.2199183364335743154417035649987
absolute error = 5e-31
relative error = 4.0986350075017948843888905423310e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4881
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.677
y[1] (closed_form) = 1.2205444040811940640912260970796
y[1] (numeric) = 1.2205444040811940640912260970791
absolute error = 5e-31
relative error = 4.0965326482848598317799168866004e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4883
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.678
y[1] (closed_form) = 1.2211712511843447769158564585004
y[1] (numeric) = 1.2211712511843447769158564584999
absolute error = 5e-31
relative error = 4.0944298313203683879941085350578e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4885
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.679
y[1] (closed_form) = 1.221798877116179403002138679282
y[1] (numeric) = 1.2217988771161794030021386792815
absolute error = 5e-31
relative error = 4.0923265634369673290918398294936e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4887
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (closed_form) = 1.2224272812490720628176059159557
y[1] (numeric) = 1.2224272812490720628176059159552
absolute error = 5e-31
relative error = 4.0902228514493041300227753432705e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4889
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.681
y[1] (closed_form) = 1.2230564629546186758366076818755
y[1] (numeric) = 1.2230564629546186758366076818751
absolute error = 4e-31
relative error = 3.2704949617264067325670535428890e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4891
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.682
y[1] (closed_form) = 1.223686421603637588944338005864
y[1] (numeric) = 1.2236864216036375889443380058635
absolute error = 5e-31
relative error = 4.0860141223496736724778346327066e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.683
y[1] (closed_form) = 1.2243171565661702056184361152149
y[1] (numeric) = 1.2243171565661702056184361152145
absolute error = 4e-31
relative error = 3.2671272950374713752577929542083e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4896
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.684
y[1] (closed_form) = 1.2249486672114816158875304615069
y[1] (numeric) = 1.2249486672114816158875304615064
absolute error = 5e-31
relative error = 4.0818036982579724364537033962239e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4898
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.685
y[1] (closed_form) = 1.2255809529080612270660961307334
y[1] (numeric) = 1.225580952908061227066096130733
absolute error = 4e-31
relative error = 3.2637582939819610044980463922126e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.49
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.686
y[1] (closed_form) = 1.2262140130236233952649949029474
y[1] (numeric) = 1.226214013023623395264994902947
absolute error = 4e-31
relative error = 3.2620733065484375221342519223891e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4902
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.687
y[1] (closed_form) = 1.2268478469251080576770664509304
y[1] (numeric) = 1.22684784692510805767706645093
absolute error = 4e-31
relative error = 3.2603880016787255202087889249232e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4903
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.688
y[1] (closed_form) = 1.2274824539786813656371383923497
y[1] (numeric) = 1.2274824539786813656371383923493
absolute error = 4e-31
relative error = 3.2587023847344306598434998897460e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4905
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.689
y[1] (closed_form) = 1.2281178335497363184558221354451
y[1] (numeric) = 1.2281178335497363184558221354447
absolute error = 4e-31
relative error = 3.2570164610658330547535159701685e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4907
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (closed_form) = 1.2287539850028933980264606845022
y[1] (numeric) = 1.2287539850028933980264606845019
absolute error = 3e-31
relative error = 2.4414976770089057130827812424009e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4909
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.691
y[1] (closed_form) = 1.2293909077020012042045937982186
y[1] (numeric) = 1.2293909077020012042045937982183
absolute error = 3e-31
relative error = 2.4402327861751084560165392656387e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4911
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.692
y[1] (closed_form) = 1.2300286010101370909593051215486
y[1] (numeric) = 1.2300286010101370909593051215483
absolute error = 3e-31
relative error = 2.4389676772851527887428003524982e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4913
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.693
y[1] (closed_form) = 1.2306670642896078032958151397345
y[1] (numeric) = 1.2306670642896078032958151397342
absolute error = 3e-31
relative error = 2.4377023543176762680284266950833e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4915
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.694
y[1] (closed_form) = 1.2313062969019501149486830319832
y[1] (numeric) = 1.2313062969019501149486830319829
absolute error = 3e-31
relative error = 2.4364368212427751031453144646550e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4917
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.695
y[1] (closed_form) = 1.2319462982079314668449797316401
y[1] (numeric) = 1.2319462982079314668449797316398
absolute error = 3e-31
relative error = 2.4351710820219951705205660616905e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4919
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.696
y[1] (closed_form) = 1.2325870675675506063367937297397
y[1] (numeric) = 1.2325870675675506063367937297394
absolute error = 3e-31
relative error = 2.4339051406083231779370170704378e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.492
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.697
y[1] (closed_form) = 1.2332286043400382272024303894814
y[1] (numeric) = 1.2332286043400382272024303894811
absolute error = 3e-31
relative error = 2.4326390009461779777975132480580e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4922
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.698
y[1] (closed_form) = 1.2338709078838576104156647704838
y[1] (numeric) = 1.2338709078838576104156647704835
absolute error = 3e-31
relative error = 2.4313726669714020289650080085344e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4924
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.699
y[1] (closed_form) = 1.234513977556705265682407193618
y[1] (numeric) = 1.2345139775567052656824071936177
absolute error = 3e-31
relative error = 2.4301061426112530066892492461070e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4926
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (closed_form) = 1.2351578127155115737441400098081
y[1] (numeric) = 1.2351578127155115737441400098078
absolute error = 3e-31
relative error = 2.4288394317843955601295458894180e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4927
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.701
y[1] (closed_form) = 1.2358024127164414294474832694162
y[1] (numeric) = 1.2358024127164414294474832694158
absolute error = 4e-31
relative error = 3.2367633845345242893091322568919e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4929
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.702
y[1] (closed_form) = 1.2364477769148948855792462226979
y[1] (numeric) = 1.2364477769148948855792462226976
absolute error = 3e-31
relative error = 2.4263054663622004347171513602455e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4931
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.703
y[1] (closed_form) = 1.2370939046655077974663208163335
y[1] (numeric) = 1.2370939046655077974663208163332
absolute error = 3e-31
relative error = 2.4250382195611547979369945722918e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4932
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.704
y[1] (closed_form) = 1.2377407953221524683397725861917
y[1] (numeric) = 1.2377407953221524683397725861914
absolute error = 3e-31
relative error = 2.4237708018819693613506967360231e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4934
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.705
y[1] (closed_form) = 1.2383884482379382954624835822915
y[1] (numeric) = 1.2383884482379382954624835822912
absolute error = 3e-31
relative error = 2.4225032172002251378777362360165e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4936
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.706
y[1] (closed_form) = 1.2390368627652124170197011983717
y[1] (numeric) = 1.2390368627652124170197011983714
absolute error = 3e-31
relative error = 2.4212354693828637313775965007924e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4937
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.707
y[1] (closed_form) = 1.2396860382555603597718460155734
y[1] (numeric) = 1.2396860382555603597718460155731
absolute error = 3e-31
relative error = 2.4199675622881801135082522466597e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4939
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.708
y[1] (closed_form) = 1.2403359740598066874689310074817
y[1] (numeric) = 1.2403359740598066874689310074814
absolute error = 3e-31
relative error = 2.4186994997658155442133827066011e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.494
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.709
y[1] (closed_form) = 1.2409866695280156500259436921618
y[1] (numeric) = 1.2409866695280156500259436921615
absolute error = 3e-31
relative error = 2.4174312856567506353373229050352e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4942
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (closed_form) = 1.2416381240094918334585420558604
y[1] (numeric) = 1.2416381240094918334585420558602
absolute error = 2e-31
relative error = 1.6107752825288657045771413341951e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4943
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.711
y[1] (closed_form) = 1.2422903368527808105784143127322
y[1] (numeric) = 1.242290336852780810578414312732
absolute error = 2e-31
relative error = 1.6099296119993989235258451985661e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.712
y[1] (closed_form) = 1.2429433074056697924476518052839
y[1] (numeric) = 1.2429433074056697924476518052837
absolute error = 2e-31
relative error = 1.6090838480594057290554057304349e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4946
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.713
y[1] (closed_form) = 1.2435970350151882805914835912195
y[1] (numeric) = 1.2435970350151882805914835912193
absolute error = 2e-31
relative error = 1.6082379932464004548713717197937e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4948
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.714
y[1] (closed_form) = 1.2442515190276087199687205040045
y[1] (numeric) = 1.2442515190276087199687205040043
absolute error = 2e-31
relative error = 1.6073920500921019675356004895992e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4949
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.715
y[1] (closed_form) = 1.2449067587884471526992557167609
y[1] (numeric) = 1.2449067587884471526992557167607
absolute error = 2e-31
relative error = 1.6065460211224296076684178808225e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4951
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.716
y[1] (closed_form) = 1.2455627536424638725479680820458
y[1] (numeric) = 1.2455627536424638725479680820456
absolute error = 2e-31
relative error = 1.6056999088574992242125047334148e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4952
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.717
y[1] (closed_form) = 1.2462195029336640801643737636656
y[1] (numeric) = 1.2462195029336640801643737636654
absolute error = 2e-31
relative error = 1.6048537158116193014193154282940e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4953
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.718
y[1] (closed_form) = 1.2468770060052985390773709209283
y[1] (numeric) = 1.2468770060052985390773709209281
absolute error = 2e-31
relative error = 1.6040074444932871782182487768900e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4955
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.719
y[1] (closed_form) = 1.2475352621998642324444214506442
y[1] (numeric) = 1.2475352621998642324444214506441
absolute error = 1e-31
relative error = 8.0158054870259267981411023825437e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4956
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (closed_form) = 1.248194270859105020554513037748
y[1] (numeric) = 1.2481942708591050205545130377479
absolute error = 1e-31
relative error = 8.0115733852208895993536471220539e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4957
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.721
y[1] (closed_form) = 1.2488540313240122990842440116342
y[1] (numeric) = 1.248854031324012299084244011634
absolute error = 2e-31
relative error = 1.6014681859013069968429673334363e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4959
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.722
y[1] (closed_form) = 1.249514542934825658106372752177
y[1] (numeric) = 1.2495145429348256581063727521768
absolute error = 2e-31
relative error = 1.6006216264617893776089922494223e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.496
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.723
y[1] (closed_form) = 1.2501758050310335418501726369398
y[1] (numeric) = 1.2501758050310335418501726369396
absolute error = 2e-31
relative error = 1.5997750012050131745664716675242e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4961
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.724
y[1] (closed_form) = 1.2508378169513739092129327692739
y[1] (numeric) = 1.2508378169513739092129327692738
absolute error = 1e-31
relative error = 7.9946415630226729597299995631939e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4962
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.725
y[1] (closed_form) = 1.2515005780338348950219439758613
y[1] (numeric) = 1.2515005780338348950219439758612
absolute error = 1e-31
relative error = 7.9904078156403739114975360999916e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4964
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.726
y[1] (closed_form) = 1.2521640876156554720463088117698
y[1] (numeric) = 1.2521640876156554720463088117697
absolute error = 1e-31
relative error = 7.9861737761875839631690222852184e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4965
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.727
y[1] (closed_form) = 1.2528283450333261137579135612673
y[1] (numeric) = 1.2528283450333261137579135612672
absolute error = 1e-31
relative error = 7.9819394569445129992242379904209e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4966
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.728
y[1] (closed_form) = 1.2534933496225894578408994734763
y[1] (numeric) = 1.2534933496225894578408994734762
absolute error = 1e-31
relative error = 7.9777048701621511755392991501229e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4967
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.729
y[1] (closed_form) = 1.2541591007184409704489697234547
y[1] (numeric) = 1.2541591007184409704489697234546
absolute error = 1e-31
relative error = 7.9734700280622549843900823070646e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4968
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (closed_form) = 1.2548255976551296112098678414497
y[1] (numeric) = 1.2548255976551296112098678414496
absolute error = 1e-31
relative error = 7.9692349428373337607798927945875e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4969
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.731
y[1] (closed_form) = 1.2554928397661584989763626059028
y[1] (numeric) = 1.2554928397661584989763626059028
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.497
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.732
y[1] (closed_form) = 1.2561608263842855783230736492765
y[1] (numeric) = 1.2561608263842855783230736492764
absolute error = 1e-31
relative error = 7.9607640916361398832159154700270e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4972
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.733
y[1] (closed_form) = 1.2568295568415242867884712799312
y[1] (numeric) = 1.2568295568415242867884712799311
absolute error = 1e-31
relative error = 7.9565283498985348137686405797286e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4973
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.734
y[1] (closed_form) = 1.2574990304691442228613832781104
y[1] (numeric) = 1.2574990304691442228613832781103
absolute error = 1e-31
relative error = 7.9522924135132159550817850781091e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4974
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.735
y[1] (closed_form) = 1.2581692465976718147113406795812
y[1] (numeric) = 1.2581692465976718147113406795811
absolute error = 1e-31
relative error = 7.9480562945262697758093113543968e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4975
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.736
y[1] (closed_form) = 1.2588402045568909896620938166407
y[1] (numeric) = 1.2588402045568909896620938166407
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4976
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.737
y[1] (closed_form) = 1.2595119036758438444076291430284
y[1] (numeric) = 1.2595119036758438444076291430284
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4977
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.738
y[1] (closed_form) = 1.2601843432828313159700166267826
y[1] (numeric) = 1.2601843432828313159700166267826
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4978
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.739
y[1] (closed_form) = 1.2608575227054138533984167532507
y[1] (numeric) = 1.2608575227054138533984167532507
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4978
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (closed_form) = 1.2615314412704120902085754393012
y[1] (numeric) = 1.2615314412704120902085754393012
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4979
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.741
y[1] (closed_form) = 1.2622060983039075175621344192991
y[1] (numeric) = 1.2622060983039075175621344192992
absolute error = 1e-31
relative error = 7.9226364168557924634634371286759e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.498
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.742
y[1] (closed_form) = 1.2628814931312431581850839235906
y[1] (numeric) = 1.2628814931312431581850839235907
absolute error = 1e-31
relative error = 7.9183993544838211204563225277695e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4981
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.743
y[1] (closed_form) = 1.2635576250770242410246837310994
y[1] (numeric) = 1.2635576250770242410246837310995
absolute error = 1e-31
relative error = 7.9141622048226076454782195269688e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4982
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.744
y[1] (closed_form) = 1.2642344934651188766441779391716
y[1] (numeric) = 1.2642344934651188766441779391718
absolute error = 2e-31
relative error = 1.5819849959308054695077199984045e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4983
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.745
y[1] (closed_form) = 1.2649120976186587333546280560096
y[1] (numeric) = 1.2649120976186587333546280560097
absolute error = 1e-31
relative error = 7.9056876907305577511251824482494e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4984
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
memory used=301.7MB, alloc=44.3MB, time=2.16
TOP MAIN SOLVE Loop
x[1] = -0.746
y[1] (closed_form) = 1.2655904368600397140831882839174
y[1] (numeric) = 1.2655904368600397140831882839175
absolute error = 1e-31
relative error = 7.9014503497752719271787915695189e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4984
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.747
y[1] (closed_form) = 1.266269510510922633977146125141
y[1] (numeric) = 1.2662695105109226339771461251411
absolute error = 1e-31
relative error = 7.8972129684818322357495484589859e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4985
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.748
y[1] (closed_form) = 1.2669493178922338987430507063167
y[1] (numeric) = 1.2669493178922338987430507063169
absolute error = 2e-31
relative error = 1.5785951117028968957158391775702e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4986
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.749
y[1] (closed_form) = 1.2676298583241661837202504824584
y[1] (numeric) = 1.2676298583241661837202504824586
absolute error = 2e-31
relative error = 1.5777476263016104919706956216424e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4987
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (closed_form) = 1.2683111311261791136881612469999
y[1] (numeric) = 1.2683111311261791136881612470001
absolute error = 2e-31
relative error = 1.5769001398135865906735341046468e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4987
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.751
y[1] (closed_form) = 1.2689931356169999434065846406836
y[1] (numeric) = 1.2689931356169999434065846406837
absolute error = 1e-31
relative error = 7.8802632727700910743475900236224e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4988
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.752
y[1] (closed_form) = 1.2696758711146242388883966190315
y[1] (numeric) = 1.2696758711146242388883966190317
absolute error = 2e-31
relative error = 1.5752051728322112108335423649853e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4989
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.753
y[1] (closed_form) = 1.270359336936316559403924605769
y[1] (numeric) = 1.2703593369363165594039246057692
absolute error = 2e-31
relative error = 1.5743576969515834832414745612493e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.499
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.754
y[1] (closed_form) = 1.2710435323986111402163313278786
y[1] (numeric) = 1.2710435323986111402163313278788
absolute error = 2e-31
relative error = 1.5735102292096643102170908596163e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.499
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.755
y[1] (closed_form) = 1.2717284568173125760473225969591
y[1] (numeric) = 1.2717284568173125760473225969593
absolute error = 2e-31
relative error = 1.5726627718980937379026817271109e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4991
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.756
y[1] (closed_form) = 1.2724141095074965052724955712377
y[1] (numeric) = 1.2724141095074965052724955712379
absolute error = 2e-31
relative error = 1.5718153273026220542012046446614e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4991
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.757
y[1] (closed_form) = 1.2731004897835102948456433029448
y[1] (numeric) = 1.273100489783510294845643302945
absolute error = 2e-31
relative error = 1.5709678977031093413377805979465e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4992
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.758
y[1] (closed_form) = 1.2737875969589737259513306468032
y[1] (numeric) = 1.2737875969589737259513306468034
absolute error = 2e-31
relative error = 1.5701204853735251068882593161607e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4992
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.759
y[1] (closed_form) = 1.274475430346779680385055877114
y[1] (numeric) = 1.2744754303467796803850558771141
absolute error = 1e-31
relative error = 7.8463654629097399646125930969973e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4993
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (closed_form) = 1.275163989259094827660311633333
y[1] (numeric) = 1.2751639892590948276603116333331
absolute error = 1e-31
relative error = 7.8421286079528278145505742503394e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.761
y[1] (closed_form) = 1.2758532730073603128418580871366
y[1] (numeric) = 1.2758532730073603128418580871367
absolute error = 1e-31
relative error = 7.8378918732783708301793211516232e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.762
y[1] (closed_form) = 1.2765432809022924451045204977583
y[1] (numeric) = 1.2765432809022924451045204977584
absolute error = 1e-31
relative error = 7.8336552701383943928645451698169e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4995
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.763
y[1] (closed_form) = 1.2772340122538833870168225968583
y[1] (numeric) = 1.2772340122538833870168225968583
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4995
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.764
y[1] (closed_form) = 1.277925466371401844548766519348
y[1] (numeric) = 1.277925466371401844548766519348
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4995
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.765
y[1] (closed_form) = 1.2786176425633937578030692724491
y[1] (numeric) = 1.2786176425633937578030692724492
absolute error = 1e-31
relative error = 7.8209463620037612773173805316877e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4996
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.766
y[1] (closed_form) = 1.2793105401376829924691650118068
y[1] (numeric) = 1.2793105401376829924691650118069
absolute error = 1e-31
relative error = 7.8167103969328447190667648922365e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4996
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.767
y[1] (closed_form) = 1.2800041584013720319992816707128
y[1] (numeric) = 1.2800041584013720319992816707128
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4997
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.768
y[1] (closed_form) = 1.2806984966608426705058997664195
y[1] (numeric) = 1.2806984966608426705058997664196
absolute error = 1e-31
relative error = 7.8082390399246494163976684910609e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4997
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.769
y[1] (closed_form) = 1.2813935542217567063799004861449
y[1] (numeric) = 1.2813935542217567063799004861449
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4997
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (closed_form) = 1.2820893303890566366287094346757
y[1] (numeric) = 1.2820893303890566366287094346757
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.771
y[1] (closed_form) = 1.2827858244669663519337417054856
y[1] (numeric) = 1.2827858244669663519337417054856
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.772
y[1] (closed_form) = 1.2834830357589918324264532179796
y[1] (numeric) = 1.2834830357589918324264532179796
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.773
y[1] (closed_form) = 1.2841809635679218441823025448716
y[1] (numeric) = 1.2841809635679218441823025448716
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.774
y[1] (closed_form) = 1.2848796071958286364319267357915
y[1] (numeric) = 1.2848796071958286364319267357915
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.775
y[1] (closed_form) = 1.2855789659440686394888339260045
y[1] (numeric) = 1.2855789659440686394888339260045
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.776
y[1] (closed_form) = 1.2862790391132831633929148026071
y[1] (numeric) = 1.2862790391132831633929148026071
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.777
y[1] (closed_form) = 1.2869798260033990972690742847478
y[1] (numeric) = 1.2869798260033990972690742847478
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.778
y[1] (closed_form) = 1.2876813259136296094002840592981
y[1] (numeric) = 1.2876813259136296094002840592981
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.779
y[1] (closed_form) = 1.28838353814247484801435589898
y[1] (numeric) = 1.28838353814247484801435589898
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (closed_form) = 1.2890864619877226427837349762354
y[1] (numeric) = 1.2890864619877226427837349762354
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.781
y[1] (closed_form) = 1.289790096746449207037611673102
y[1] (numeric) = 1.289790096746449207037611673102
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.782
y[1] (closed_form) = 1.2904944417150198406856496750424
y[1] (numeric) = 1.2904944417150198406856496750424
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.783
y[1] (closed_form) = 1.2911994961890896338526274250576
y[1] (numeric) = 1.2911994961890896338526274250577
absolute error = 1e-31
relative error = 7.7447366030690818914636765036904e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.784
y[1] (closed_form) = 1.2919052594636041712232893035015
y[1] (numeric) = 1.2919052594636041712232893035016
absolute error = 1e-31
relative error = 7.7405056808515316052132140084880e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.785
y[1] (closed_form) = 1.2926117308328002370967021888034
y[1] (numeric) = 1.2926117308328002370967021888035
absolute error = 1e-31
relative error = 7.7362751408400326279439671408954e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.786
y[1] (closed_form) = 1.293318909590206521149412344802
y[1] (numeric) = 1.2933189095902065211494123448022
absolute error = 2e-31
relative error = 1.5464089987161080968882824699771e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.787
y[1] (closed_form) = 1.2940267950286443249066968715924
y[1] (numeric) = 1.2940267950286443249066968715925
absolute error = 1e-31
relative error = 7.7278152495896670742214629320924e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.788
y[1] (closed_form) = 1.2947353864402282689212032486917
y[1] (numeric) = 1.2947353864402282689212032486918
absolute error = 1e-31
relative error = 7.7235859193546897781770404171349e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.789
y[1] (closed_form) = 1.2954446831163670006582697919461
y[1] (numeric) = 1.2954446831163670006582697919463
absolute error = 2e-31
relative error = 1.5438714026667121806154333466459e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (closed_form) = 1.296154684347763903087219138915
y[1] (numeric) = 1.2961546843477639030872191389152
absolute error = 2e-31
relative error = 1.5430257083909834924347890232619e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.791
y[1] (closed_form) = 1.2968653894244178039779161714986
y[1] (numeric) = 1.2968653894244178039779161714988
absolute error = 2e-31
relative error = 1.5421801031236182580348264960182e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.792
y[1] (closed_form) = 1.2975767976356236859018810793109
y[1] (numeric) = 1.2975767976356236859018810793111
absolute error = 2e-31
relative error = 1.5413345889386238981666771715301e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.793
y[1] (closed_form) = 1.2982889082699733969372475627432
y[1] (numeric) = 1.2982889082699733969372475627434
absolute error = 2e-31
relative error = 1.5404891679041510430865380406920e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.794
y[1] (closed_form) = 1.2990017206153563620768554708199
y[1] (numeric) = 1.2990017206153563620768554708201
absolute error = 2e-31
relative error = 1.5396438420824957540795887910841e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.795
y[1] (closed_form) = 1.2997152339589602953387664658126
y[1] (numeric) = 1.2997152339589602953387664658128
absolute error = 2e-31
relative error = 1.5387986135301018104650383893389e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.796
y[1] (closed_form) = 1.3004294475872719125784906041565
y[1] (numeric) = 1.3004294475872719125784906041568
absolute error = 3e-31
relative error = 2.3069302264463445926026656525316e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.797
y[1] (closed_form) = 1.3011443607860776450022110215024
y[1] (numeric) = 1.3011443607860776450022110215027
absolute error = 3e-31
relative error = 2.3056626846444387667216449696141e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.798
y[1] (closed_form) = 1.3018599728404643533802932087375
y[1] (numeric) = 1.3018599728404643533802932087378
absolute error = 3e-31
relative error = 2.3043952979477871956399047537339e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.799
y[1] (closed_form) = 1.3025762830348200429603646655274
y[1] (numeric) = 1.3025762830348200429603646655277
absolute error = 3e-31
relative error = 2.3031280694059781078326773965931e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (closed_form) = 1.3032932906528345790792500183577
y[1] (numeric) = 1.303293290652834579079250018358
absolute error = 3e-31
relative error = 2.3018610020598399164790633953528e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.801
y[1] (closed_form) = 1.3040109949775004034730459911998
y[1] (numeric) = 1.3040109949775004034730459912001
absolute error = 3e-31
relative error = 2.3005940989414452283805121047725e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4998
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.802
y[1] (closed_form) = 1.3047293952911132512846199187868
y[1] (numeric) = 1.3047293952911132512846199187871
absolute error = 3e-31
relative error = 2.2993273630741149474660243064065e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4997
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.803
y[1] (closed_form) = 1.3054484908752728687678147950589
y[1] (numeric) = 1.3054484908752728687678147950592
absolute error = 3e-31
relative error = 2.2980607974724224723669185533774e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4997
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.804
y[1] (closed_form) = 1.3061682810108837316876431526351
y[1] (numeric) = 1.3061682810108837316876431526354
absolute error = 3e-31
relative error = 2.2967944051421979875445714905155e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4997
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.805
y[1] (closed_form) = 1.3068887649781557644157513731752
y[1] (numeric) = 1.3068887649781557644157513731755
absolute error = 3e-31
relative error = 2.2955281890805328474551227668967e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4996
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.806
y[1] (closed_form) = 1.3076099420566050597204353332294
y[1] (numeric) = 1.3076099420566050597204353332297
absolute error = 3e-31
relative error = 2.2942621522757840532357276472933e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4996
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.807
y[1] (closed_form) = 1.3083318115250545992504875956188
y[1] (numeric) = 1.3083318115250545992504875956191
absolute error = 3e-31
relative error = 2.2929962977075788213975448872539e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4995
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.808
y[1] (closed_form) = 1.3090543726616349747121556625597
y[1] (numeric) = 1.30905437266163497471215566256
absolute error = 3e-31
relative error = 2.2917306283468192440112637601482e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4995
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.809
y[1] (closed_form) = 1.3097776247437851097384901136346
y[1] (numeric) = 1.3097776247437851097384901136348
absolute error = 2e-31
relative error = 1.5269767647704580265810681403019e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (closed_form) = 1.3105015670482529824503607593199
y[1] (numeric) = 1.3105015670482529824503607593201
absolute error = 2e-31
relative error = 1.5261332380584322640852319019757e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4994
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.811
y[1] (closed_form) = 1.311226198851096348708418249117
y[1] (numeric) = 1.3112261988510963487084182491172
absolute error = 2e-31
relative error = 1.5252898407249725999121098932256e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4993
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.812
y[1] (closed_form) = 1.3119515194276834660552778823829
y[1] (numeric) = 1.311951519427683466055277882383
absolute error = 1e-31
relative error = 7.6222328736372285304868412467331e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4993
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.813
y[1] (closed_form) = 1.3126775280526938183472016797382
y[1] (numeric) = 1.3126775280526938183472016797384
absolute error = 2e-31
relative error = 1.5236034420174179419586765042977e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4992
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.814
y[1] (closed_form) = 1.3134042240001188410745540834314
y[1] (numeric) = 1.3134042240001188410745540834316
absolute error = 2e-31
relative error = 1.5227604445406588196814588090870e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4992
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.815
y[1] (closed_form) = 1.3141316065432626473703059662622
y[1] (numeric) = 1.3141316065432626473703059662623
absolute error = 1e-31
relative error = 7.6095879211857226425612208664758e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4991
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.816
y[1] (closed_form) = 1.314859674954742754705860940622
y[1] (numeric) = 1.3148596749547427547058609406221
absolute error = 1e-31
relative error = 7.6053743152053075861019096794619e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4991
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.817
y[1] (closed_form) = 1.315588428506490812273477271886
y[1] (numeric) = 1.3155884285064908122734772718861
absolute error = 1e-31
relative error = 7.6011614144040506724468383603378e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.499
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.818
y[1] (closed_form) = 1.316317866469753329054558013794
y[1] (numeric) = 1.3163178664697533290545580137941
absolute error = 1e-31
relative error = 7.5969492283950416344975548666648e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4989
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.819
y[1] (closed_form) = 1.3170479881150924025730812975917
y[1] (numeric) = 1.3170479881150924025730812975918
absolute error = 1e-31
relative error = 7.5927377667624769708208496578401e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4989
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (closed_form) = 1.3177787927123864483334420215631
y[1] (numeric) = 1.3177787927123864483334420215631
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4988
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.821
y[1] (closed_form) = 1.3185102795308309299419755031717
y[1] (numeric) = 1.3185102795308309299419755031717
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4987
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.822
y[1] (closed_form) = 1.3192424478389390899114329723498
y[1] (numeric) = 1.3192424478389390899114329723498
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4987
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.823
y[1] (closed_form) = 1.3199752969045426811476781015192
y[1] (numeric) = 1.3199752969045426811476781015191
absolute error = 1e-31
relative error = 7.5758993546704041388525110206991e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4986
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.824
y[1] (closed_form) = 1.3207088259947926991178730857087
y[1] (numeric) = 1.3207088259947926991178730857086
absolute error = 1e-31
relative error = 7.5716916576730956719207948331230e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4985
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.825
y[1] (closed_form) = 1.3214430343761601146994221046441
y[1] (numeric) = 1.3214430343761601146994221046441
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4984
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.826
y[1] (closed_form) = 1.3221779213144366077089393179268
y[1] (numeric) = 1.3221779213144366077089393179268
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4984
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.827
y[1] (closed_form) = 1.3229134860747353011105078643946
y[1] (numeric) = 1.3229134860747353011105078643946
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4983
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.828
y[1] (closed_form) = 1.3236497279214914959024956574681
y[1] (numeric) = 1.3236497279214914959024956574681
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4982
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.829
y[1] (closed_form) = 1.3243866461184634066821930897261
y[1] (numeric) = 1.3243866461184634066821930897261
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4981
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (closed_form) = 1.3251242399287328978875370821356
y[1] (numeric) = 1.3251242399287328978875370821355
absolute error = 1e-31
relative error = 7.5464622098663099641874975272178e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.498
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.831
y[1] (closed_form) = 1.3258625086147062207151852362717
y[1] (numeric) = 1.3258625086147062207151852362716
absolute error = 1e-31
relative error = 7.5422601778281264669689501790369e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4979
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.832
y[1] (closed_form) = 1.3266014514381147507142031715169
y[1] (numeric) = 1.3266014514381147507142031715168
absolute error = 1e-31
relative error = 7.5380589921407112676144017566724e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4978
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.833
y[1] (closed_form) = 1.3273410676600157260546274536119
y[1] (numeric) = 1.3273410676600157260546274536118
absolute error = 1e-31
relative error = 7.5338586619858833955722422128176e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4977
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.834
y[1] (closed_form) = 1.3280813565407929864701658460576
y[1] (numeric) = 1.3280813565407929864701658460574
absolute error = 2e-31
relative error = 1.5059318393033767000661193207483e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4976
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.835
y[1] (closed_form) = 1.3288223173401577128742959417292
y[1] (numeric) = 1.328822317340157712874295941729
absolute error = 2e-31
relative error = 1.5050921209716793960686847694940e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4975
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.836
y[1] (closed_form) = 1.3295639493171491676490225586661
y[1] (numeric) = 1.329563949317149167649022558666
absolute error = 1e-31
relative error = 7.5212628961065773699241014504042e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4974
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.837
y[1] (closed_form) = 1.3303062517301354356055536113409
y[1] (numeric) = 1.3303062517301354356055536113408
absolute error = 1e-31
relative error = 7.5170660793290699824677727303106e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4973
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=343.2MB, alloc=44.3MB, time=2.47
x[1] = -0.838
y[1] (closed_form) = 1.3310492238368141656161534967937
y[1] (numeric) = 1.3310492238368141656161534967936
absolute error = 1e-31
relative error = 7.5128701635650358083668179374226e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4972
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.839
y[1] (closed_form) = 1.3317928648942133129164323638407
y[1] (numeric) = 1.3317928648942133129164323638406
absolute error = 1e-31
relative error = 7.5086751578251756659869248454979e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4971
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (closed_form) = 1.3325371741586918820773289631291
y[1] (numeric) = 1.332537174158691882077328963129
absolute error = 1e-31
relative error = 7.5044810710917546040743775356377e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.497
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.841
y[1] (closed_form) = 1.3332821508859406706460441061175
y[1] (numeric) = 1.3332821508859406706460441061173
absolute error = 2e-31
relative error = 1.5000575824637253107936707826411e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4969
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.842
y[1] (closed_form) = 1.3340277943309830134551810921098
y[1] (numeric) = 1.3340277943309830134551810921096
absolute error = 2e-31
relative error = 1.4992191380862518459990445338116e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4968
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.843
y[1] (closed_form) = 1.334774103748175527599348794266
y[1] (numeric) = 1.3347741037481755275993487942658
absolute error = 2e-31
relative error = 1.4983808828653518552850117216689e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4967
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.844
y[1] (closed_form) = 1.3355210783912088580784824280462
y[1] (numeric) = 1.335521078391208858078482428046
absolute error = 2e-31
relative error = 1.4975428185747795318747702424721e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4966
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.845
y[1] (closed_form) = 1.3362687175131084241071363588314
y[1] (numeric) = 1.3362687175131084241071363588312
absolute error = 2e-31
relative error = 1.4967049469826270604076329322539e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4965
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.846
y[1] (closed_form) = 1.3370170203662351660890026394896
y[1] (numeric) = 1.3370170203662351660890026394894
absolute error = 2e-31
relative error = 1.4958672698513297923304636038532e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4963
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.847
y[1] (closed_form) = 1.3377659862022862932559083034306
y[1] (numeric) = 1.3377659862022862932559083034304
absolute error = 2e-31
relative error = 1.4950297889376714693122983122070e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4962
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.848
y[1] (closed_form) = 1.3385156142722960319705437742155
y[1] (numeric) = 1.3385156142722960319705437742153
absolute error = 2e-31
relative error = 1.4941925059927894943615057985391e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4961
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.849
y[1] (closed_form) = 1.3392659038266363746921740890535
y[1] (numeric) = 1.3392659038266363746921740890533
absolute error = 2e-31
relative error = 1.4933554227621802503255190572510e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.496
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (closed_form) = 1.3400168541150178296045839705385
y[1] (numeric) = 1.3400168541150178296045839705383
absolute error = 2e-31
relative error = 1.4925185409857044654538531399221e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4958
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.851
y[1] (closed_form) = 1.3407684643864901709055071187424
y[1] (numeric) = 1.3407684643864901709055071187421
absolute error = 3e-31
relative error = 2.2375227935963889385587188973445e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4957
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.852
y[1] (closed_form) = 1.3415207338894431897567894342973
y[1] (numeric) = 1.341520733889443189756789434297
absolute error = 3e-31
relative error = 2.2362680830896756502274779670867e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4956
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.853
y[1] (closed_form) = 1.3422736618716074458945352223685
y[1] (numeric) = 1.3422736618716074458945352223682
absolute error = 3e-31
relative error = 2.2350136825428964687249766755909e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4954
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.854
y[1] (closed_form) = 1.3430272475800550198984847674316
y[1] (numeric) = 1.3430272475800550198984847674313
absolute error = 3e-31
relative error = 2.2337595945321104374774054113346e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4953
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.855
y[1] (closed_form) = 1.3437814902612002661198710095412
y[1] (numeric) = 1.343781490261200266119871009541
absolute error = 2e-31
relative error = 1.4883372144166429346472582727816e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4952
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.856
y[1] (closed_form) = 1.3445363891608005662670023942965
y[1] (numeric) = 1.3445363891608005662670023942963
absolute error = 2e-31
relative error = 1.4875015775871343144442998077784e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.495
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.857
y[1] (closed_form) = 1.3452919435239570836478183109831
y[1] (numeric) = 1.3452919435239570836478183109829
absolute error = 2e-31
relative error = 1.4866661542334463661245057972797e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4949
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.858
y[1] (closed_form) = 1.3460481525951155180686628763995
y[1] (numeric) = 1.3460481525951155180686628763992
absolute error = 3e-31
relative error = 2.2287464190758299263041596243199e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4947
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.859
y[1] (closed_form) = 1.3468050156180668613885221656564
y[1] (numeric) = 1.3468050156180668613885221656562
absolute error = 2e-31
relative error = 1.4849959547278439641737668517989e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4946
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (closed_form) = 1.3475625318359481537279693357761
y[1] (numeric) = 1.3475625318359481537279693357759
absolute error = 2e-31
relative error = 1.4841611819491278213010108011191e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4944
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.861
y[1] (closed_form) = 1.3483207004912432403320614332074
y[1] (numeric) = 1.3483207004912432403320614332072
absolute error = 2e-31
relative error = 1.4833266293926406530036395695712e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4943
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.862
y[1] (closed_form) = 1.3490795208257835290864310224247
y[1] (numeric) = 1.3490795208257835290864310224245
absolute error = 2e-31
relative error = 1.4824922987310505445301085990428e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4941
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.863
y[1] (closed_form) = 1.3498389920807487486858151195816
y[1] (numeric) = 1.3498389920807487486858151195814
absolute error = 2e-31
relative error = 1.4816581916314638176089016322089e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.494
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.864
y[1] (closed_form) = 1.3505991134966677074542632627533
y[1] (numeric) = 1.3505991134966677074542632627531
absolute error = 2e-31
relative error = 1.4808243097554310217670254468088e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4938
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.865
y[1] (closed_form) = 1.3513598843134190528162658986232
y[1] (numeric) = 1.351359884313419052816265898623
absolute error = 2e-31
relative error = 1.4799906547589529680078351138131e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4937
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.866
y[1] (closed_form) = 1.3521213037702320314180436145485
y[1] (numeric) = 1.3521213037702320314180436145483
absolute error = 2e-31
relative error = 1.4791572282924868045404909889931e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4935
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.867
y[1] (closed_form) = 1.3528833711056872498982370947791
y[1] (numeric) = 1.3528833711056872498982370947789
absolute error = 2e-31
relative error = 1.4783240320009521342541107484005e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4934
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.868
y[1] (closed_form) = 1.3536460855577174363072370302028
y[1] (numeric) = 1.3536460855577174363072370302025
absolute error = 3e-31
relative error = 2.2162366012856057604456690021540e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4932
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.869
y[1] (closed_form) = 1.3544094463636082021743925623504
y[1] (numeric) = 1.3544094463636082021743925623502
absolute error = 2e-31
relative error = 1.4766583364947049527896833042157e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.493
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (closed_form) = 1.3551734527599988052223361945172
y[1] (numeric) = 1.3551734527599988052223361945169
absolute error = 3e-31
relative error = 2.2137387608132993345471155421531e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4929
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.871
y[1] (closed_form) = 1.3559381039828829127276624557362
y[1] (numeric) = 1.355938103982882912727662455736
absolute error = 2e-31
relative error = 1.4749935812890524049002331244283e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4927
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.872
y[1] (closed_form) = 1.3567033992676093655271969569926
y[1] (numeric) = 1.3567033992676093655271969569923
absolute error = 3e-31
relative error = 2.2112423405288828647094674665260e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4925
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.873
y[1] (closed_form) = 1.3574693378488829426690918334692
y[1] (numeric) = 1.3574693378488829426690918334689
absolute error = 3e-31
relative error = 2.2099946690169497523478028007281e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4923
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.874
y[1] (closed_form) = 1.3582359189607651267079829217956
y[1] (numeric) = 1.3582359189607651267079829217953
absolute error = 3e-31
relative error = 2.2087473598072765463332705091521e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4922
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.875
y[1] (closed_form) = 1.359003141836674869643443377204
y[1] (numeric) = 1.3590031418366748696434433772037
absolute error = 3e-31
relative error = 2.2075004153011298137905334650689e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.492
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.876
y[1] (closed_form) = 1.3597710057093893595009677922045
y[1] (numeric) = 1.3597710057093893595009677922043
absolute error = 2e-31
relative error = 1.4708358919277034214260009067176e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4918
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.877
y[1] (closed_form) = 1.3605395098110447875547202358586
y[1] (numeric) = 1.3605395098110447875547202358583
absolute error = 3e-31
relative error = 2.2050076299633868664080138289995e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4916
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.878
y[1] (closed_form) = 1.3613086533731371161912789909656
y[1] (numeric) = 1.3613086533731371161912789909654
absolute error = 2e-31
relative error = 1.4691745292621720027878448440849e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4914
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.879
y[1] (closed_form) = 1.3620784356265228474136101254846
y[1] (numeric) = 1.3620784356265228474136101254844
absolute error = 2e-31
relative error = 1.4683442213664066984851710154645e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4913
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (closed_form) = 1.3628488558014197919845013942779
y[1] (numeric) = 1.3628488558014197919845013942777
absolute error = 2e-31
relative error = 1.4675141645284686419091464888454e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4911
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.881
y[1] (closed_form) = 1.3636199131274078392086873278103
y[1] (numeric) = 1.3636199131274078392086873278101
absolute error = 2e-31
relative error = 1.4666843603164167894128644487916e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4909
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.882
y[1] (closed_form) = 1.3643916068334297273528957257406
y[1] (numeric) = 1.3643916068334297273528957257404
absolute error = 2e-31
relative error = 1.4658548102928691171665588541626e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4907
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.883
y[1] (closed_form) = 1.3651639361477918147030451354242
y[1] (numeric) = 1.365163936147791814703045135424
absolute error = 2e-31
relative error = 1.4650255160150093654406914045141e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4905
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.884
y[1] (closed_form) = 1.3659369002981648512578222581931
y[1] (numeric) = 1.3659369002981648512578222581929
absolute error = 2e-31
relative error = 1.4641964790345938195361903374083e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4903
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.885
y[1] (closed_form) = 1.3667104985115847510578675899006
y[1] (numeric) = 1.3667104985115847510578675899004
absolute error = 2e-31
relative error = 1.4633677008979581270692734908410e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4901
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.886
y[1] (closed_form) = 1.3674847300144533651497969666091
y[1] (numeric) = 1.367484730014453365149796966609
absolute error = 1e-31
relative error = 7.3126959157301207565955955188616e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4899
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.887
y[1] (closed_form) = 1.3682595940325392551842860514642
y[1] (numeric) = 1.368259594032539255184286051464
absolute error = 2e-31
relative error = 1.4617109273143068603474819623637e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4897
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.888
y[1] (closed_form) = 1.3690350897909784676474441647341
y[1] (numeric) = 1.3690350897909784676474441647339
absolute error = 2e-31
relative error = 1.4608829349329212516001896785537e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4895
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.889
y[1] (closed_form) = 1.369811216514275308724703225707
y[1] (numeric) = 1.3698112165142753087247032257068
absolute error = 2e-31
relative error = 1.4600552075265893117012940598747e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (closed_form) = 1.3705879734263031197964469426198
y[1] (numeric) = 1.3705879734263031197964469426195
absolute error = 3e-31
relative error = 2.1888416199219705167272434660619e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4891
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.891
y[1] (closed_form) = 1.3713653597503050535646047550548
y[1] (numeric) = 1.3713653597503050535646047550545
absolute error = 3e-31
relative error = 2.1876008305665770004649582172637e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4889
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.892
y[1] (closed_form) = 1.3721433747088948508094344022757
y[1] (numeric) = 1.3721433747088948508094344022754
absolute error = 3e-31
relative error = 2.1863604454865810095593856053295e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4887
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.893
y[1] (closed_form) = 1.3729220175240576177757163607833
y[1] (numeric) = 1.372922017524057617775716360783
absolute error = 3e-31
relative error = 2.1851204669368128965944996185100e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4885
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.894
y[1] (closed_form) = 1.373701287417150604187582764963
y[1] (numeric) = 1.3737012874171506041875827649626
absolute error = 4e-31
relative error = 2.9118411962187552974892513795863e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4883
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.895
y[1] (closed_form) = 1.3744811836089039818912027960585
y[1] (numeric) = 1.3744811836089039818912027960582
absolute error = 3e-31
relative error = 2.1826417384071097570216600412951e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.488
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.896
y[1] (closed_form) = 1.3752617053194216241245458968532
y[1] (numeric) = 1.3752617053194216241245458968528
absolute error = 4e-31
relative error = 2.9085373238622610263004860163221e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4878
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.897
y[1] (closed_form) = 1.3760428517681818854134435423582
y[1] (numeric) = 1.3760428517681818854134435423578
absolute error = 4e-31
relative error = 2.9068862171407645102721113394391e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4876
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.898
y[1] (closed_form) = 1.3768246221740383820931696705131
y[1] (numeric) = 1.3768246221740383820931696705127
absolute error = 4e-31
relative error = 2.9052356673313309506301704223573e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4874
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.899
y[1] (closed_form) = 1.3776070157552207734547592513822
y[1] (numeric) = 1.3776070157552207734547592513817
absolute error = 5e-31
relative error = 3.6294820967204059451414841234870e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4872
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (closed_form) = 1.3783900317293355435152838485929
y[1] (numeric) = 1.3783900317293355435152838485924
absolute error = 5e-31
relative error = 3.6274203127593523887255078370614e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4869
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.901
y[1] (closed_form) = 1.3791736693133667834113024028072
y[1] (numeric) = 1.3791736693133667834113024028067
absolute error = 5e-31
relative error = 3.6253592359324058684051087425374e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4867
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.902
y[1] (closed_form) = 1.3799579277236769744147048438388
y[1] (numeric) = 1.3799579277236769744147048438383
absolute error = 5e-31
relative error = 3.6232988698777205810033886836812e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4865
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.903
y[1] (closed_form) = 1.380742806176007771570165515639
y[1] (numeric) = 1.3807428061760077715701655156385
absolute error = 5e-31
relative error = 3.6212392182202206273009331573891e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4862
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.904
y[1] (closed_form) = 1.3815283038854807879534227767624
y[1] (numeric) = 1.3815283038854807879534227767618
absolute error = 6e-31
relative error = 4.3430163414859423751135674680592e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.486
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.905
y[1] (closed_form) = 1.3823144200665983795496005180982
y[1] (numeric) = 1.3823144200665983795496005180977
absolute error = 5e-31
relative error = 3.6171220725304345239604607954907e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4858
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.906
y[1] (closed_form) = 1.3831011539332444307507867196122
y[1] (numeric) = 1.3831011539332444307507867196116
absolute error = 6e-31
relative error = 4.3380775028184170202404798636437e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4855
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.907
y[1] (closed_form) = 1.3838885046986851404720835485838
y[1] (numeric) = 1.3838885046986851404720835485832
absolute error = 6e-31
relative error = 4.3356093931182581325475660664411e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4853
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.908
y[1] (closed_form) = 1.3846764715755698088853428833566
y[1] (numeric) = 1.384676471575569808885342883356
absolute error = 6e-31
relative error = 4.3331421622069103489702809995156e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.485
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.909
y[1] (closed_form) = 1.3854650537759316247698005289301
y[1] (numeric) = 1.3854650537759316247698005289295
absolute error = 6e-31
relative error = 4.3306758143394986658160577799750e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4848
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (closed_form) = 1.3862542505111884534788217738253
y[1] (numeric) = 1.3862542505111884534788217738247
absolute error = 6e-31
relative error = 4.3282103537554303930413468077431e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4846
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.911
y[1] (closed_form) = 1.3870440609921436255219703215436
y[1] (numeric) = 1.387044060992143625521970321543
absolute error = 6e-31
relative error = 4.3257457846784181420327583877569e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4843
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.912
y[1] (closed_form) = 1.387834484428986725761612014616
y[1] (numeric) = 1.3878344844289867257616120146155
absolute error = 5e-31
relative error = 3.6027350927637524164364403558332e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4841
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.913
y[1] (closed_form) = 1.3886255200312943832232641547054
y[1] (numeric) = 1.3886255200312943832232641547049
absolute error = 5e-31
relative error = 3.6006827815517309902015277657393e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4838
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.914
y[1] (closed_form) = 1.3894171670080310615189006084766
y[1] (numeric) = 1.3894171670080310615189006084761
absolute error = 5e-31
relative error = 3.5986312237432569244038146562055e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4836
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.915
y[1] (closed_form) = 1.390209424567549849882422275997
y[1] (numeric) = 1.3902094245675498498824222759965
absolute error = 5e-31
relative error = 3.5965804228059680603534838277351e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4833
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.916
y[1] (closed_form) = 1.3910022919175932548165018862618
y[1] (numeric) = 1.3910022919175932548165018862614
absolute error = 4e-31
relative error = 2.8756243057556161376963976471312e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.483
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.917
y[1] (closed_form) = 1.3917957682652939923500114730661
y[1] (numeric) = 1.3917957682652939923500114730657
absolute error = 4e-31
relative error = 2.8739848842804852357444762263392e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4828
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.918
y[1] (closed_form) = 1.3925898528171757809052402738607
y[1] (numeric) = 1.3925898528171757809052402738603
absolute error = 4e-31
relative error = 2.8723460765623820960136023905637e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4825
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.919
y[1] (closed_form) = 1.3933845447791541347741101844421
y[1] (numeric) = 1.3933845447791541347741101844417
absolute error = 4e-31
relative error = 2.8707078853339685684165276694048e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4823
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (closed_form) = 1.3941798433565371582025952933256
y[1] (numeric) = 1.3941798433565371582025952933252
absolute error = 4e-31
relative error = 2.8690703133175838232272584725222e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.482
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.921
y[1] (closed_form) = 1.3949757477540263400825514114488
y[1] (numeric) = 1.3949757477540263400825514114484
absolute error = 4e-31
relative error = 2.8674333632252602279089342213723e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.922
y[1] (closed_form) = 1.3957722571757173492501609054418
y[1] (numeric) = 1.3957722571757173492501609054414
absolute error = 4e-31
relative error = 2.8657970377587392762142219961199e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.923
y[1] (closed_form) = 1.3965693708251008303901975360864
y[1] (numeric) = 1.396569370825100830390197536086
absolute error = 4e-31
relative error = 2.8641613396094875690397758281360e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.924
y[1] (closed_form) = 1.3973670879050632005453153977649
y[1] (numeric) = 1.3973670879050632005453153977645
absolute error = 4e-31
relative error = 2.8625262714587128465181383157311e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.925
y[1] (closed_form) = 1.3981654076178874462295654496762
y[1] (numeric) = 1.3981654076178874462295654496758
absolute error = 4e-31
relative error = 2.8608918359773800708322944464474e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.926
y[1] (closed_form) = 1.3989643291652539211453425253694
y[1] (numeric) = 1.3989643291652539211453425253689
absolute error = 5e-31
relative error = 3.5740725447827844490499028635236e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4804
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.927
y[1] (closed_form) = 1.3997638517482411445029651037137
y[1] (numeric) = 1.3997638517482411445029651037132
absolute error = 5e-31
relative error = 3.5720310920697289584952781350503e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4801
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.928
y[1] (closed_form) = 1.4005639745673265999420895217925
y[1] (numeric) = 1.4005639745673265999420895217921
absolute error = 4e-31
relative error = 2.8559923521063805182660482920099e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.929
y[1] (closed_form) = 1.4013646968223875350541597083728
y[1] (numeric) = 1.4013646968223875350541597083723
absolute error = 5e-31
relative error = 3.5679505922602191108973742572889e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4795
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=384.6MB, alloc=44.3MB, time=2.78
x[1] = -0.93
y[1] (closed_form) = 1.402166017712701761505092915567
y[1] (numeric) = 1.4021660177127017615050929155666
absolute error = 4e-31
relative error = 2.8527292413811615322941882236874e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4792
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.931
y[1] (closed_form) = 1.4029679364369484557574013260696
y[1] (numeric) = 1.4029679364369484557574013260692
absolute error = 4e-31
relative error = 2.8510986574351880586540321412164e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4789
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.932
y[1] (closed_form) = 1.4037704521932089603909488139114
y[1] (numeric) = 1.403770452193208960390948813911
absolute error = 4e-31
relative error = 2.8494687245699748565866752497968e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4787
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.933
y[1] (closed_form) = 1.4045735641789675860215415380431
y[1] (numeric) = 1.4045735641789675860215415380428
absolute error = 3e-31
relative error = 2.1358795840313471732216195383026e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4784
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.934
y[1] (closed_form) = 1.4053772715911124138165504502244
y[1] (numeric) = 1.405377271591112413816550450224
absolute error = 4e-31
relative error = 2.8462108224301639858543838039964e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4781
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.935
y[1] (closed_form) = 1.4061815736259360986067632016613
y[1] (numeric) = 1.4061815736259360986067632016609
absolute error = 4e-31
relative error = 2.8445828583045106533402137700699e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4778
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.936
y[1] (closed_form) = 1.4069864694791366725936623366093
y[1] (numeric) = 1.4069864694791366725936623366089
absolute error = 4e-31
relative error = 2.8429555555575394341468210758077e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4775
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.937
y[1] (closed_form) = 1.4077919583458183496513260657285
y[1] (numeric) = 1.4077919583458183496513260657282
absolute error = 3e-31
relative error = 2.1309966875539306372409730514911e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4772
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.938
y[1] (closed_form) = 1.4085980394204923302221473173594
y[1] (numeric) = 1.4085980394204923302221473173591
absolute error = 3e-31
relative error = 2.1297772082901820785738306201500e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4769
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.939
y[1] (closed_form) = 1.409404711897077606805566171065
y[1] (numeric) = 1.4094047118970776068055661710647
absolute error = 3e-31
relative error = 2.1285582307738703708583576151411e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4766
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (closed_form) = 1.410211974968901770039010184776
y[1] (numeric) = 1.4102119749689017700390101847757
absolute error = 3e-31
relative error = 2.1273397568944601402672531483574e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.941
y[1] (closed_form) = 1.4110198278287018153702365346646
y[1] (numeric) = 1.4110198278287018153702365346643
absolute error = 3e-31
relative error = 2.1261217885339317872984902964924e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.476
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.942
y[1] (closed_form) = 1.4118282696686249503202692954725
y[1] (numeric) = 1.4118282696686249503202692954722
absolute error = 3e-31
relative error = 2.1249043275667941378678592218864e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4757
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.943
y[1] (closed_form) = 1.4126372996802294023361245984231
y[1] (numeric) = 1.4126372996802294023361245984229
absolute error = 2e-31
relative error = 1.4157915839067314171538159893535e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4754
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.944
y[1] (closed_form) = 1.41344691705448522723251581406
y[1] (numeric) = 1.4134469170544852272325158140598
absolute error = 2e-31
relative error = 1.4149806235156296705822055344966e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4751
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.945
y[1] (closed_form) = 1.4142571209817751182217303183736
y[1] (numeric) = 1.4142571209817751182217303183734
absolute error = 2e-31
relative error = 1.4141700051060043990101513953748e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.946
y[1] (closed_form) = 1.4150679106518952155308688124071
y[1] (numeric) = 1.4150679106518952155308688124069
absolute error = 2e-31
relative error = 1.4133597299076887089109219766218e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4744
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.947
y[1] (closed_form) = 1.4158792852540559166056375781701
y[1] (numeric) = 1.4158792852540559166056375781699
absolute error = 2e-31
relative error = 1.4125497991455771358551665963546e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4741
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.948
y[1] (closed_form) = 1.4166912439768826868998834671338
y[1] (numeric) = 1.4166912439768826868998834671337
absolute error = 1e-31
relative error = 7.0587010701981710015565669499950e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4738
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.949
y[1] (closed_form) = 1.4175037860084168712500608318425
y[1] (numeric) = 1.4175037860084168712500608318424
absolute error = 1e-31
relative error = 7.0546548790245149145369811271292e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4735
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (closed_form) = 1.4183169105361165058338190262395
y[1] (numeric) = 1.4183169105361165058338190262395
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4732
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.951
y[1] (closed_form) = 1.4191306167468571307118985161905
y[1] (numeric) = 1.4191306167468571307118985161905
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4728
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.952
y[1] (closed_form) = 1.419944903826932602952523058373
y[1] (numeric) = 1.419944903826932602952523058373
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4725
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.953
y[1] (closed_form) = 1.4207597709620559103374748232099
y[1] (numeric) = 1.4207597709620559103374748232099
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4722
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.954
y[1] (closed_form) = 1.4215752173373599856490387558386
y[1] (numeric) = 1.4215752173373599856490387558387
absolute error = 1e-31
relative error = 7.0344501494125709695354772957629e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4718
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.955
y[1] (closed_form) = 1.4223912421373985215370018882395
y[1] (numeric) = 1.4223912421373985215370018882395
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4715
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.956
y[1] (closed_form) = 1.4232078445461467859648927355918
y[1] (numeric) = 1.4232078445461467859648927355918
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4712
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.957
y[1] (closed_form) = 1.4240250237470024382346453306867
y[1] (numeric) = 1.4240250237470024382346453306867
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4708
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.958
y[1] (closed_form) = 1.4248427789227863455888718718004
y[1] (numeric) = 1.4248427789227863455888718718005
absolute error = 1e-31
relative error = 7.0183181947696911447366640051319e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4705
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.959
y[1] (closed_form) = 1.4256611092557434003899273818234
y[1] (numeric) = 1.4256611092557434003899273818235
absolute error = 1e-31
relative error = 7.0142896759107298528142905540120e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4702
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (closed_form) = 1.4264800139275433378749491996481
y[1] (numeric) = 1.4264800139275433378749491996482
absolute error = 1e-31
relative error = 7.0102629566234779749643425416400e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4698
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.961
y[1] (closed_form) = 1.4272994921192815544860535488458
y[1] (numeric) = 1.4272994921192815544860535488459
absolute error = 1e-31
relative error = 7.0062380426912427116371897107466e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4695
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.962
y[1] (closed_form) = 1.4281195430114799267748708535018
y[1] (numeric) = 1.4281195430114799267748708535019
absolute error = 1e-31
relative error = 7.0022149398732897846972099849154e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.963
y[1] (closed_form) = 1.4289401657840876308806008967442
y[1] (numeric) = 1.4289401657840876308806008967442
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4688
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.964
y[1] (closed_form) = 1.4297613596164819625807683439772
y[1] (numeric) = 1.4297613596164819625807683439772
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4684
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.965
y[1] (closed_form) = 1.4305831236874691579138585801337
y[1] (numeric) = 1.4305831236874691579138585801337
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4681
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.966
y[1] (closed_form) = 1.4314054571752852143730132383785
y[1] (numeric) = 1.4314054571752852143730132383785
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4677
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.967
y[1] (closed_form) = 1.4322283592575967126699642266353
y[1] (numeric) = 1.4322283592575967126699642266354
absolute error = 1e-31
relative error = 6.9821267923947225030713399666178e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4674
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.968
y[1] (closed_form) = 1.4330518291115016390683844880724
y[1] (numeric) = 1.4330518291115016390683844880724
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.969
y[1] (closed_form) = 1.4338758659135302082858331622636
y[1] (numeric) = 1.4338758659135302082858331622637
absolute error = 1e-31
relative error = 6.9741044100975539787305325039587e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4667
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (closed_form) = 1.4347004688396456869634722451501
y[1] (numeric) = 1.4347004688396456869634722451502
absolute error = 1e-31
relative error = 6.9700960006570437358545324033530e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4663
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.971
y[1] (closed_form) = 1.4355256370652452177027312781524
y[1] (numeric) = 1.4355256370652452177027312781524
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4659
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.972
y[1] (closed_form) = 1.4363513697651606436680960298383
y[1] (numeric) = 1.4363513697651606436680960298383
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4656
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.973
y[1] (closed_form) = 1.4371776661136593337551965674268
y[1] (numeric) = 1.4371776661136593337551965674267
absolute error = 1e-31
relative error = 6.9580819656357984619361504950992e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4652
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.974
y[1] (closed_form) = 1.4380045252844450083233695501071
y[1] (numeric) = 1.4380045252844450083233695501071
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4648
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.975
y[1] (closed_form) = 1.4388319464506585654918690116816
y[1] (numeric) = 1.4388319464506585654918690116816
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4645
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.976
y[1] (closed_form) = 1.4396599287848789079988993363884
y[1] (numeric) = 1.4396599287848789079988993363885
absolute error = 1e-31
relative error = 6.9460848357711353338663165625435e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
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) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.977
y[1] (closed_form) = 1.4404884714591237706226435689417
y[1] (numeric) = 1.4404884714591237706226435689417
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4637
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.978
y[1] (closed_form) = 1.4413175736448505481634596378282
y[1] (numeric) = 1.4413175736448505481634596378282
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4634
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.979
y[1] (closed_form) = 1.4421472345129571239864165097351
y[1] (numeric) = 1.4421472345129571239864165097351
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.463
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (closed_form) = 1.4429774532337826991233417326401
y[1] (numeric) = 1.4429774532337826991233417326401
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4626
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.981
y[1] (closed_form) = 1.4438082289771086219335512655861
y[1] (numeric) = 1.4438082289771086219335512655861
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4622
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.982
y[1] (closed_form) = 1.4446395609121592183224319344801
y[1] (numeric) = 1.4446395609121592183224319344801
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4618
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.983
y[1] (closed_form) = 1.4454714482076026225170462954026
y[1] (numeric) = 1.4454714482076026225170462954025
absolute error = 1e-31
relative error = 6.9181580946480045841511094776152e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.984
y[1] (closed_form) = 1.4463038900315516083979291298914
y[1] (numeric) = 1.4463038900315516083979291298913
absolute error = 1e-31
relative error = 6.9141762453406985019674850747968e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4611
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.985
y[1] (closed_form) = 1.4471368855515644213862442404742
y[1] (numeric) = 1.4471368855515644213862442404741
absolute error = 1e-31
relative error = 6.9101963330777665568800804955532e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4607
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.986
y[1] (closed_form) = 1.4479704339346456108854696593607
y[1] (numeric) = 1.4479704339346456108854696593605
absolute error = 2e-31
relative error = 1.3812436726109770390807584317099e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4603
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.987
y[1] (closed_form) = 1.4488045343472468632767788286789
y[1] (numeric) = 1.4488045343472468632767788286788
absolute error = 1e-31
relative error = 6.9022423404448139294022707608052e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4599
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.988
y[1] (closed_form) = 1.4496391859552678354672847569453
y[1] (numeric) = 1.4496391859552678354672847569452
absolute error = 1e-31
relative error = 6.8982682703974411404068014346532e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4595
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.989
y[1] (closed_form) = 1.4504743879240569889903136035916
y[1] (numeric) = 1.4504743879240569889903136035915
absolute error = 1e-31
relative error = 6.8942961580398299380616553354598e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4591
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (closed_form) = 1.4513101394184124246568735913464
y[1] (numeric) = 1.4513101394184124246568735913462
absolute error = 2e-31
relative error = 1.3780652016952528143424110141293e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4587
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.991
y[1] (closed_form) = 1.4521464396025827177574845950707
y[1] (numeric) = 1.4521464396025827177574845950705
absolute error = 2e-31
relative error = 1.3772715653576587788311044450426e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4583
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.992
y[1] (closed_form) = 1.4529832876402677538135332052885
y[1] (numeric) = 1.4529832876402677538135332052884
absolute error = 1e-31
relative error = 6.8823916180347823765819967747718e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4579
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.993
y[1] (closed_form) = 1.4538206826946195648773175151265
y[1] (numeric) = 1.4538206826946195648773175151264
absolute error = 1e-31
relative error = 6.8784273872519511737327352825419e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4575
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.994
y[1] (closed_form) = 1.4546586239282431663799453306873
y[1] (numeric) = 1.4546586239282431663799453306872
absolute error = 1e-31
relative error = 6.8744651394534267383126073313572e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4571
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.995
y[1] (closed_form) = 1.4554971105031973945262489570286
y[1] (numeric) = 1.4554971105031973945262489570285
absolute error = 1e-31
relative error = 6.8705048796302864836950175261879e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4567
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.996
y[1] (closed_form) = 1.4563361415809957442358791649033
y[1] (numeric) = 1.4563361415809957442358791649031
absolute error = 2e-31
relative error = 1.3733093225502209987926566997728e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4563
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.997
y[1] (closed_form) = 1.4571757163226072076297403972349
y[1] (numeric) = 1.4571757163226072076297403972348
absolute error = 1e-31
relative error = 6.8625903437620002803368985375585e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4559
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.998
y[1] (closed_form) = 1.4580158338884571130609287289657
y[1] (numeric) = 1.4580158338884571130609287289656
absolute error = 1e-31
relative error = 6.8586360775866800830357006332495e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4555
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.999
y[1] (closed_form) = 1.4588564934384279646893335494061
y[1] (numeric) = 1.458856493438427964689333549406
absolute error = 1e-31
relative error = 6.8546838191264882176395577691515e-30 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4551
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sin ( x ) ;
Iterations = 900
Total Elapsed Time = 2 Seconds
Elapsed Time(since restart) = 2 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 2 Seconds
Time to Timeout = 2 Minutes 57 Seconds
Percent Done = 0 %
> quit
memory used=416.0MB, alloc=44.3MB, time=3.00