|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ 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
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number 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 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 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 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 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 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 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 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_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 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> 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 22
# Begin Function number 23
> 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 23
# Begin Function number 24
> 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 24
# Begin Function number 25
> 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 25
# Begin Function number 26
> 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 26
# Begin Function number 27
> 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 27
# Begin Function number 28
> 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 28
# Begin Function number 29
> 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> 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 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> 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 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c( x) + c(0.1)) /c( 0.3));
> end;
exact_soln_y := proc(x)
return
c(0.05)*c(x)*c(x) + c(0.2)*c(x) - cos(c(0.3)*c(x) + c(0.1))/c(0.3)
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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> 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)*29*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,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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
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)*29*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, 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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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 mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre add CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D3[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp4[1] + array_const_0D1[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp6[1] := sin(array_tmp5[1]);
> array_tmp6_g[1] := cos(array_tmp5[1]);
> #emit pre add LINEAR - FULL $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp3[1] + array_tmp6[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_tmp7[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 mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre add CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := array_const_0D3[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp6[2] := array_tmp6_g[1] * array_tmp5[2] / c(1);
> array_tmp6_g[2] := neg(array_tmp6[1]) * array_tmp5[2] / c(1);
> #emit pre add LINEAR - FULL $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp3[2] + array_tmp6[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_tmp7[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_tmp6[3] := array_tmp6_g[2] * array_tmp5[2] / c(2);
> array_tmp6_g[3] := neg(array_tmp6[2]) * array_tmp5[2] / c(2);
> #emit pre add LINEAR FULL $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp6[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_tmp7[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_tmp6[4] := array_tmp6_g[3] * array_tmp5[2] / c(3);
> array_tmp6_g[4] := neg(array_tmp6[3]) * array_tmp5[2] / c(3);
> #emit pre add LINEAR FULL $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp6[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_tmp7[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_tmp6[5] := array_tmp6_g[4] * array_tmp5[2] / c(4);
> array_tmp6_g[5] := neg(array_tmp6[4]) * array_tmp5[2] / c(4);
> #emit pre add LINEAR FULL $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp6[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_tmp7[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_tmp6[kkk] := array_tmp6_g[kkk - 1] * array_tmp5[2] / c(kkk - 1);
> array_tmp6_g[kkk] := neg(array_tmp6[kkk - 1]) * array_tmp5[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp7[kkk] := array_tmp6[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_tmp7[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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_0D3[1]*array_x[1];
array_tmp5[1] := array_tmp4[1] + array_const_0D1[1];
array_tmp6[1] := sin(array_tmp5[1]);
array_tmp6_g[1] := cos(array_tmp5[1]);
array_tmp7[1] := array_tmp3[1] + array_tmp6[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
array_tmp4[2] := array_const_0D3[1]*array_x[2];
array_tmp5[2] := array_tmp4[2];
array_tmp6[2] := array_tmp6_g[1]*array_tmp5[2]/c(1);
array_tmp6_g[2] := neg(array_tmp6[1])*array_tmp5[2]/c(1);
array_tmp7[2] := array_tmp3[2] + array_tmp6[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[3] := array_tmp6_g[2]*array_tmp5[2]/c(2);
array_tmp6_g[3] := neg(array_tmp6[2])*array_tmp5[2]/c(2);
array_tmp7[3] := array_tmp6[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[4] := array_tmp6_g[3]*array_tmp5[2]/c(3);
array_tmp6_g[4] := neg(array_tmp6[3])*array_tmp5[2]/c(3);
array_tmp7[4] := array_tmp6[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[5] := array_tmp6_g[4]*array_tmp5[2]/c(4);
array_tmp6_g[5] := neg(array_tmp6[4])*array_tmp5[2]/c(4);
array_tmp7[5] := array_tmp6[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[kkk] := array_tmp6_g[kkk - 1]*array_tmp5[2]/c(kkk - 1);
array_tmp6_g[kkk] :=
neg(array_tmp6[kkk - 1])*array_tmp5[2]/c(kkk - 1);
array_tmp7[kkk] := array_tmp6[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_tmp7[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,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #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,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_tmp6_g:= Array(0..(40),[]);
> array_tmp6:= Array(0..(40),[]);
> array_tmp7:= 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[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp7[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);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6_g);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_const_0D3);
> array_const_0D3[1] := c(0.3);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_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,"##############temp/add_lin_fullpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(-5.0);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> 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,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c( x) + c(0.1)) /c( 0.3));");
> 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(-5.0);
> x_end := c(5.0) ;
> 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:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> 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 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
> 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,"2015-05-01T21:36:52-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"add_lin_full")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ")
> ;
> 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," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"add_lin_full diffeq.mxt")
> ;
> logitem_str(html_log_file,"add_lin_full maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> 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_const_0D1,
array_const_0D2, array_const_0D3, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_tmp6_g := Array(0 .. 40, []);
array_tmp6 := Array(0 .. 40, []);
array_tmp7 := 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[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp6_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp7[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);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6_g);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_const_0D3);
array_const_0D3[1] := c(0.3);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_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,
"##############temp/add_lin_fullpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.1 * x + \
0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(-5.0);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
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, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - c\
os(c(0.3) * c( x) + c(0.1)) /c( 0.3));");
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(-5.0);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
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 ) = ( 0.1 * x +\
0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
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, "2015-05-01T21:36:52-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"add_lin_full");
logitem_str(html_log_file, "diff ( y , x , 1 ) = (\
0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; \
");
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, " 308.maple.seems.ok | ");
logitem_str(html_log_file, "add_lin_full diffeq.mxt");
logitem_str(html_log_file, "add_lin_full maple results");
logitem_str(html_log_file, "OK");
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#################
##############temp/add_lin_fullpostode.ode#################
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-5.0);
x_end := c(5.0) ;
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:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c( x) + c(0.1)) /c( 0.3));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (closed_form) = -0.31655714300080312872249345067883
y[1] (numeric) = -0.31655714300080312872249345067883
absolute error = 0
relative error = 0 %
Desired digits = 8
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 = 0.5583
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
memory used=3.9MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = -4.99
y[1] (closed_form) = -0.3294040760137170586563469704566
y[1] (numeric) = -0.32940407601371705865634697045658
absolute error = 2e-32
relative error = 6.0715702859630550359410592876472e-30 %
Desired digits = 8
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 = 0.5677
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.98
y[1] (closed_form) = -0.34223582134883762523253698192003
y[1] (numeric) = -0.34223582134883762523253698192001
absolute error = 2e-32
relative error = 5.8439236200275469187349027883322e-30 %
Desired digits = 8
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 = 0.5771
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.97
y[1] (closed_form) = -0.3550522903855232778770367070844
y[1] (numeric) = -0.35505229038552327787703670708438
absolute error = 2e-32
relative error = 5.6329730976481175412262023601340e-30 %
Desired digits = 8
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 = 0.5865
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.96
y[1] (closed_form) = -0.3678533945506191163150410020111
y[1] (numeric) = -0.36785339455061911631504100201109
absolute error = 1e-32
relative error = 2.7184743020290199690032849072161e-30 %
Desired digits = 8
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 = 0.5958
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.95
y[1] (closed_form) = -0.38063904531925404836720021383773
y[1] (numeric) = -0.38063904531925404836720021383773
absolute error = 0
relative error = 0 %
Desired digits = 8
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 = 0.6052
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.94
y[1] (closed_form) = -0.39340915421563751319190709431563
y[1] (numeric) = -0.39340915421563751319190709431563
absolute error = 0
relative error = 0 %
Desired digits = 8
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 = 0.6145
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.93
y[1] (closed_form) = -0.4061636328138557628031329671528
y[1] (numeric) = -0.40616363281385576280313296715281
absolute error = 1e-32
relative error = 2.4620618864178286286372817419124e-30 %
Desired digits = 8
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 = 0.6238
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.92
y[1] (closed_form) = -0.4189023927386676946972848635356
y[1] (numeric) = -0.41890239273866769469728486353559
absolute error = 1e-32
relative error = 2.3871909479014365850444214796872e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.633
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.91
y[1] (closed_form) = -0.4316253456663002284265953559833
y[1] (numeric) = -0.43162534566630022842659535598329
absolute error = 1e-32
relative error = 2.3168240930251664845888323885747e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6423
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
memory used=44.5MB, alloc=44.3MB, time=0.55
TOP MAIN SOLVE Loop
x[1] = -4.9
y[1] (closed_form) = -0.4443324033252432189606612988177
y[1] (numeric) = -0.4443324033252432189606612988177
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6515
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.89
y[1] (closed_form) = -0.45702347749704389968191658706207
y[1] (numeric) = -0.45702347749704389968191658706209
absolute error = 2e-32
relative error = 4.3761427989504900590581935271750e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6607
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.88
y[1] (closed_form) = -0.4696984800171008478650573370039
y[1] (numeric) = -0.46969848001710084786505733700392
absolute error = 2e-32
relative error = 4.2580508242802568163565301215870e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6698
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.87
y[1] (closed_form) = -0.4823573227754574654947355328597
y[1] (numeric) = -0.48235732277545746549473553285971
absolute error = 1e-32
relative error = 2.0731518996043329105870348711950e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.679
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.86
y[1] (closed_form) = -0.49499991771759496828019913629313
y[1] (numeric) = -0.49499991771759496828019913629315
absolute error = 2e-32
relative error = 4.0404047120287212266998878419211e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6881
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.85
y[1] (closed_form) = -0.50762617684522487572998287969983
y[1] (numeric) = -0.50762617684522487572998287969985
absolute error = 2e-32
relative error = 3.9399071427512289572719366360611e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6972
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.84
y[1] (closed_form) = -0.52023601221708099515424442034797
y[1] (numeric) = -0.52023601221708099515424442034798
absolute error = 1e-32
relative error = 1.9222044927999446832085671809316e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7063
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.83
y[1] (closed_form) = -0.5328293359497108924668951802397
y[1] (numeric) = -0.53282933594971089246689518023971
absolute error = 1e-32
relative error = 1.8767735417900887995745935578671e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7153
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.82
y[1] (closed_form) = -0.54540606021826684266429399494227
y[1] (numeric) = -0.54540606021826684266429399494229
absolute error = 2e-32
relative error = 3.6669926241736608094313455479576e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7243
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.81
y[1] (closed_form) = -0.55796609725729625286195460206003
y[1] (numeric) = -0.55796609725729625286195460206007
absolute error = 4e-32
relative error = 7.1688943462015943014528315981554e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7333
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
memory used=85.2MB, alloc=44.3MB, time=0.97
TOP MAIN SOLVE Loop
x[1] = -4.8
y[1] (closed_form) = -0.5705093593615315507754649743338
y[1] (numeric) = -0.57050935936153155077546497433386
absolute error = 6e-32
relative error = 1.0516917735959178930035196780200e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7423
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.79
y[1] (closed_form) = -0.5830357588866795315366275008394
y[1] (numeric) = -0.58303575888667953153662750083945
absolute error = 5e-32
relative error = 8.5758033255929574129362136273837e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7512
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.78
y[1] (closed_form) = -0.59554520825021015574070399911277
y[1] (numeric) = -0.59554520825021015574070399911283
absolute error = 6e-32
relative error = 1.0074801907362811398361565283097e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7601
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.77
y[1] (closed_form) = -0.6080376199321447916255884573825
y[1] (numeric) = -0.60803761993214479162558845738255
absolute error = 5e-32
relative error = 8.2231754024660271521253368714138e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.769
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.76
y[1] (closed_form) = -0.62051290647584389428873321498723
y[1] (numeric) = -0.62051290647584389428873321498728
absolute error = 5e-32
relative error = 8.0578501233715213293242057240047e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7779
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.75
y[1] (closed_form) = -0.63297098048879411485272094547633
y[1] (numeric) = -0.63297098048879411485272094547638
absolute error = 5e-32
relative error = 7.8992562915584060630598292763073e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7867
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.74
y[1] (closed_form) = -0.64541175464339483249550526523063
y[1] (numeric) = -0.64541175464339483249550526523068
absolute error = 5e-32
relative error = 7.7469924649305737321326380211473e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7955
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.73
y[1] (closed_form) = -0.65783514167774410226653700452773
y[1] (numeric) = -0.65783514167774410226653700452778
absolute error = 5e-32
relative error = 7.6006885057067484816719347747492e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8043
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.72
y[1] (closed_form) = -0.67024105439642401161525110106147
y[1] (numeric) = -0.67024105439642401161525110106149
absolute error = 2e-32
relative error = 2.9840010349725165284371461386156e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.813
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
memory used=126.0MB, alloc=44.3MB, time=1.39
TOP MAIN SOLVE Loop
x[1] = -4.71
y[1] (closed_form) = -0.68262940567128543856371066068827
y[1] (numeric) = -0.68262940567128543856371066068832
absolute error = 5e-32
relative error = 7.3246185389319556660193630725133e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8218
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.7
y[1] (closed_form) = -0.69500010844223220446058992872067
y[1] (numeric) = -0.69500010844223220446058992872069
absolute error = 2e-32
relative error = 2.8776973927137714031113458391868e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8304
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.69
y[1] (closed_form) = -0.70735307571800461425912667894947
y[1] (numeric) = -0.7073530757180046142591266789495
absolute error = 3e-32
relative error = 4.2411634344769407897441758356687e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8391
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.68
y[1] (closed_form) = -0.71968822057696237726718680771983
y[1] (numeric) = -0.71968822057696237726718680771987
absolute error = 4e-32
relative error = 5.5579623031668697547994241081384e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8477
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.67
y[1] (closed_form) = -0.7320054561678669013231596671921
y[1] (numeric) = -0.73200545616786690132315966719214
absolute error = 4e-32
relative error = 5.4644401435755164175061781798107e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8563
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.66
y[1] (closed_form) = -0.74430469571066295335704183521437
y[1] (numeric) = -0.7443046957106629533570418352144
absolute error = 3e-32
relative error = 4.0306073806716974357244393313708e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8649
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.65
y[1] (closed_form) = -0.7565858524972596793017695482596
y[1] (numeric) = -0.75658585249725967930176954825963
absolute error = 3e-32
relative error = 3.9651812019718751853346317110698e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8734
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.64
y[1] (closed_form) = -0.76884883989231097632562586731847
y[1] (numeric) = -0.76884883989231097632562586731849
absolute error = 2e-32
relative error = 2.6012915624352513150062624223268e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8819
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.63
y[1] (closed_form) = -0.78109357133399521036237775259417
y[1] (numeric) = -0.78109357133399521036237775259418
absolute error = 1e-32
relative error = 1.2802563440538169697084560092968e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8904
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.62
y[1] (closed_form) = -0.7933199603347942719216905388575
y[1] (numeric) = -0.79331996033479427192169053885751
absolute error = 1e-32
relative error = 1.2605254500063042655908695865126e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8988
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
memory used=166.7MB, alloc=44.3MB, time=1.81
TOP MAIN SOLVE Loop
x[1] = -4.61
y[1] (closed_form) = -0.80552792048227196316832277635707
y[1] (numeric) = -0.80552792048227196316832277635706
absolute error = 1e-32
relative error = 1.2414218980780914758283403958782e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9072
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.6
y[1] (closed_form) = -0.81771736543985170926462297864197
y[1] (numeric) = -0.81771736543985170926462297864196
absolute error = 1e-32
relative error = 1.2229164284191251321562186152397e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9156
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.59
y[1] (closed_form) = -0.82988820894759358697693144437667
y[1] (numeric) = -0.82988820894759358697693144437668
absolute error = 1e-32
relative error = 1.2049815736846416166345417311212e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9239
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.58
y[1] (closed_form) = -0.8420403648229706635526349404728
y[1] (numeric) = -0.8420403648229706635526349404728
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9322
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.57
y[1] (closed_form) = -0.8541737469616446388808295933317
y[1] (numeric) = -0.85417374696164463888082959333171
absolute error = 1e-32
relative error = 1.1707220030550803912700165537759e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9405
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.56
y[1] (closed_form) = -0.86628826933824078395581777781493
y[1] (numeric) = -0.86628826933824078395581777781494
absolute error = 1e-32
relative error = 1.1543501573256923531382095054805e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9487
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.55
y[1] (closed_form) = -0.8783838460071221686689980633033
y[1] (numeric) = -0.87838384600712216866899806330331
absolute error = 1e-32
relative error = 1.1384544519411525418368217144737e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.957
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.54
y[1] (closed_form) = -0.8904603911031631719611033158716
y[1] (numeric) = -0.89046039110316317196110331587154
absolute error = 6e-32
relative error = 6.7380874657061276564814705058605e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9651
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.53
y[1] (closed_form) = -0.9025178188425222673732008076271
y[1] (numeric) = -0.90251781884252226737320080762711
absolute error = 1e-32
relative error = 1.1080113645650769333080991615438e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9733
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.52
y[1] (closed_form) = -0.9145560435234140770413895905135
y[1] (numeric) = -0.91455604352341407704138959051347
absolute error = 3e-32
relative error = 3.2802801110385918834757603448096e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9814
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
memory used=207.4MB, alloc=44.3MB, time=2.23
TOP MAIN SOLVE Loop
x[1] = -4.51
y[1] (closed_form) = -0.9265749795268806871867143936641
y[1] (numeric) = -0.92657497952688068718671439366404
absolute error = 6e-32
relative error = 6.4754608451262795647638608162435e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9894
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.5
y[1] (closed_form) = -0.9385745413175622181584618414601
y[1] (numeric) = -0.93857454131756221815846184146012
absolute error = 2e-32
relative error = 2.1308909542681805407172184485040e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9975
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.49
y[1] (closed_form) = -0.9505546434444666420957138039725
y[1] (numeric) = -0.95055464344446664209571380397253
absolute error = 3e-32
relative error = 3.1560521225051131656311334952487e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.48
y[1] (closed_form) = -0.9625152005417388412788041220751
y[1] (numeric) = -0.96251520054173884127880412207514
absolute error = 4e-32
relative error = 4.1557785245870957232455638895332e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.013
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.47
y[1] (closed_form) = -0.9744561273294289002491587352614
y[1] (numeric) = -0.97445612732942890024915873526136
absolute error = 4e-32
relative error = 4.1048538644446765387852919720769e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.021
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.46
y[1] (closed_form) = -0.9863773386142596247828953195733
y[1] (numeric) = -0.98637733861425962478289531957331
absolute error = 1e-32
relative error = 1.0138108012546988966006051898019e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.45
y[1] (closed_form) = -0.998278749290393280810516853998
y[1] (numeric) = -0.99827874929039328081051685399802
absolute error = 2e-32
relative error = 2.0034484370439223237758346471557e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.037
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.44
y[1] (closed_form) = -1.010160274340197546382054013575
y[1] (numeric) = -1.010160274340197546382054013575
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.045
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.43
y[1] (closed_form) = -1.0220218288350106697840938731076
y[1] (numeric) = -1.0220218288350106697840938731077
absolute error = 1e-31
relative error = 9.7845268250276702527660804363615e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.053
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
memory used=248.1MB, alloc=44.3MB, time=2.66
TOP MAIN SOLVE Loop
x[1] = -4.42
y[1] (closed_form) = -1.0338633279359058269222770330361
y[1] (numeric) = -1.0338633279359058269222770330361
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.41
y[1] (closed_form) = -1.0456846868944546710900518844077
y[1] (numeric) = -1.0456846868944546710900518844077
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.068
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.4
y[1] (closed_form) = -1.0574858210534900682517432481173
y[1] (numeric) = -1.0574858210534900682517432481173
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.076
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.39
y[1] (closed_form) = -1.0692666458478680109753229892593
y[1] (numeric) = -1.0692666458478680109753229892591
absolute error = 2e-31
relative error = 1.8704408369664547498479517484141e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.083
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.38
y[1] (closed_form) = -1.0810270768052287041576623545753
y[1] (numeric) = -1.081027076805228704157662354575
absolute error = 3e-31
relative error = 2.7751386291506529460795376201380e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.091
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.37
y[1] (closed_form) = -1.0927670295467568156924996430527
y[1] (numeric) = -1.0927670295467568156924996430524
absolute error = 3e-31
relative error = 2.7453244093979478656787747792247e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.098
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.36
y[1] (closed_form) = -1.1044864197879408852388723296547
y[1] (numeric) = -1.1044864197879408852388723296545
absolute error = 2e-31
relative error = 1.8107963703021318046616935368074e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.106
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.35
y[1] (closed_form) = -1.1161851633393318842553398523028
y[1] (numeric) = -1.1161851633393318842553398523027
absolute error = 1e-31
relative error = 8.9590870121249731420843927360134e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.113
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.34
y[1] (closed_form) = -1.1278631761073009204729618743818
y[1] (numeric) = -1.1278631761073009204729618743818
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.121
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.33
y[1] (closed_form) = -1.1395203740947960799876968804703
y[1] (numeric) = -1.1395203740947960799876968804702
absolute error = 1e-31
relative error = 8.7756219435249039613045349971167e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.128
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
memory used=288.9MB, alloc=44.3MB, time=3.08
TOP MAIN SOLVE Loop
x[1] = -4.32
y[1] (closed_form) = -1.1511566734020984001606473823892
y[1] (numeric) = -1.151156673402098400160647382389
absolute error = 2e-31
relative error = 1.7373829698517510894507550871134e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.136
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.31
y[1] (closed_form) = -1.162771990227576966522400736178
y[1] (numeric) = -1.162771990227576966522400736178
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.143
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.3
y[1] (closed_form) = -1.1743662408684431268855985278349
y[1] (numeric) = -1.1743662408684431268855985278348
absolute error = 1e-31
relative error = 8.5152311536178066825205138573725e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.15
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.29
y[1] (closed_form) = -1.1859393417215038158778126056374
y[1] (numeric) = -1.1859393417215038158778126056374
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.157
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.28
y[1] (closed_form) = -1.1974912092839139831148120481017
y[1] (numeric) = -1.1974912092839139831148120481018
absolute error = 1e-31
relative error = 8.3507919911828708745201307919258e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.165
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.27
y[1] (closed_form) = -1.2090217601539281182423725870636
y[1] (numeric) = -1.2090217601539281182423725870637
absolute error = 1e-31
relative error = 8.2711497258137334823523573549843e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.172
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.26
y[1] (closed_form) = -1.2205309110316508660829081823907
y[1] (numeric) = -1.2205309110316508660829081823909
absolute error = 2e-31
relative error = 1.6386311742891498994106963170643e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.179
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.25
y[1] (closed_form) = -1.2320185787197867251313934952919
y[1] (numeric) = -1.2320185787197867251313934952921
absolute error = 2e-31
relative error = 1.6233521430157627681842104344885e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.186
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.24
y[1] (closed_form) = -1.2434846801243888226532958573839
y[1] (numeric) = -1.2434846801243888226532958573841
absolute error = 2e-31
relative error = 1.6083833053736818810420336586120e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.193
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.23
y[1] (closed_form) = -1.2549291322556067596455459083606
y[1] (numeric) = -1.2549291322556067596455459083609
absolute error = 3e-31
relative error = 2.3905732386718976261423804531944e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.2
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
memory used=329.7MB, alloc=44.3MB, time=3.50
TOP MAIN SOLVE Loop
x[1] = -4.22
y[1] (closed_form) = -1.2663518522284335189299473014776
y[1] (numeric) = -1.266351852228433518929947301478
absolute error = 4e-31
relative error = 3.1586797878970935961309490333290e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.207
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.21
y[1] (closed_form) = -1.277752757263451429656857677796
y[1] (numeric) = -1.2777527572634514296568576777963
absolute error = 3e-31
relative error = 2.3478720612781661552735540448225e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.214
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.2
y[1] (closed_form) = -1.2891317646875771815054654113134
y[1] (numeric) = -1.2891317646875771815054654113135
absolute error = 1e-31
relative error = 7.7571589452095406718741863486223e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.22
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.19
y[1] (closed_form) = -1.3004887919348058818755393513369
y[1] (numeric) = -1.3004887919348058818755393513372
absolute error = 3e-31
relative error = 2.3068249558204507914453538681972e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.227
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.18
y[1] (closed_form) = -1.3118237565469541493741418587347
y[1] (numeric) = -1.311823756546954149374141858735
absolute error = 3e-31
relative error = 2.2868925684779065858738116507512e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.17
y[1] (closed_form) = -1.3231365761744022369094687715281
y[1] (numeric) = -1.3231365761744022369094687715283
absolute error = 2e-31
relative error = 1.5115597558209898638328390959668e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.16
y[1] (closed_form) = -1.3344271685768351777127134645939
y[1] (numeric) = -1.3344271685768351777127134645942
absolute error = 3e-31
relative error = 2.2481556660746768660168421129289e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.15
y[1] (closed_form) = -1.3456954516239829476176458094355
y[1] (numeric) = -1.3456954516239829476176458094357
absolute error = 2e-31
relative error = 1.4862203759300839228427625715266e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.254
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.14
y[1] (closed_form) = -1.3569413432963596369364505139039
y[1] (numeric) = -1.356941343296359636936450513904
absolute error = 1e-31
relative error = 7.3695153069088654919454937274003e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.26
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
memory used=370.1MB, alloc=44.3MB, time=3.92
TOP MAIN SOLVE Loop
x[1] = -4.13
y[1] (closed_form) = -1.3681647616860016252792829487349
y[1] (numeric) = -1.368164761686001625279282948735
absolute error = 1e-31
relative error = 7.3090612183849194497139728717568e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.267
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.12
y[1] (closed_form) = -1.3793656249972047526739740675768
y[1] (numeric) = -1.379365624997204752673974067577
absolute error = 2e-31
relative error = 1.4499418890506662772520968572757e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.273
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.11
y[1] (closed_form) = -1.3905438515472604803513493190679
y[1] (numeric) = -1.390543851547260480351349319068
absolute error = 1e-31
relative error = 7.1914308843068725919961599928575e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.28
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.1
y[1] (closed_form) = -1.4016993597671910345707194521785
y[1] (numeric) = -1.4016993597671910345707194521786
absolute error = 1e-31
relative error = 7.1341974513428508148960980823624e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.286
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.09
y[1] (closed_form) = -1.4128320682024835268692537476184
y[1] (numeric) = -1.4128320682024835268692537476187
absolute error = 3e-31
relative error = 2.1233946110926239042663052548346e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.293
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.08
y[1] (closed_form) = -1.423941895513823044128158386262
y[1] (numeric) = -1.4239418955138230441281583862623
absolute error = 3e-31
relative error = 2.1068275394182874717953697994052e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.299
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.07
y[1] (closed_form) = -1.4350287604778247018578543073404
y[1] (numeric) = -1.4350287604778247018578543073407
absolute error = 3e-31
relative error = 2.0905504353801824581520281167778e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.06
y[1] (closed_form) = -1.446092581987764654113679931161
y[1] (numeric) = -1.4460925819877646541136799311611
absolute error = 1e-31
relative error = 6.9151865686595505262995564026779e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.311
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.05
y[1] (closed_form) = -1.4571332790543100534630344393418
y[1] (numeric) = -1.4571332790543100534630344393419
absolute error = 1e-31
relative error = 6.8627902085182432353669310039131e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.317
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.04
y[1] (closed_form) = -1.4681507708062479544343268355024
y[1] (numeric) = -1.4681507708062479544343268355026
absolute error = 2e-31
relative error = 1.3622579095890010989687971324926e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.324
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
memory used=410.6MB, alloc=44.3MB, time=4.34
TOP MAIN SOLVE Loop
x[1] = -4.03
y[1] (closed_form) = -1.4791449764912131538876046659653
y[1] (numeric) = -1.4791449764912131538876046659656
absolute error = 3e-31
relative error = 2.0281987551460419473944784442667e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.33
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.02
y[1] (closed_form) = -1.49011581547641496175630397773
y[1] (numeric) = -1.4901158154764149617563039777303
absolute error = 3e-31
relative error = 2.0132663306045441830974605437100e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.336
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.01
y[1] (closed_form) = -1.5010632072493628956191887436721
y[1] (numeric) = -1.5010632072493628956191887436725
absolute error = 4e-31
relative error = 2.6647778592414085310650475559801e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.342
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4
y[1] (closed_form) = -1.5119870714185912925712335059491
y[1] (numeric) = -1.5119870714185912925712335059496
absolute error = 5e-31
relative error = 3.3069065830760385509790379995962e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.347
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.99
y[1] (closed_form) = -1.5228873277143828318719472907974
y[1] (numeric) = -1.522887327714382831871947290798
absolute error = 6e-31
relative error = 3.9398843833082959505146363851808e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.353
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.98
y[1] (closed_form) = -1.5337638959894909618594398435827
y[1] (numeric) = -1.5337638959894909618594398435833
absolute error = 6e-31
relative error = 3.9119449973290483421189518391504e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.359
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.97
y[1] (closed_form) = -1.5446166962198612246283928338858
y[1] (numeric) = -1.5446166962198612246283928338864
absolute error = 6e-31
relative error = 3.8844588529204646895635424052184e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.365
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.96
y[1] (closed_form) = -1.5554456485053514719800187978263
y[1] (numeric) = -1.555445648505351471980018797827
absolute error = 7e-31
relative error = 4.5003179678611037462385598532051e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.371
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.95
y[1] (closed_form) = -1.5662506730704509661620691294468
y[1] (numeric) = -1.5662506730704509661620691294474
absolute error = 6e-31
relative error = 3.8308044192170738990566633536665e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.376
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
memory used=451.2MB, alloc=44.3MB, time=4.75
TOP MAIN SOLVE Loop
x[1] = -3.94
y[1] (closed_form) = -1.577031690264998358926989315016
y[1] (numeric) = -1.5770316902649983589269893150166
absolute error = 6e-31
relative error = 3.8046159991824787007731438947457e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.382
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.93
y[1] (closed_form) = -1.5877886205648985424464147332099
y[1] (numeric) = -1.5877886205648985424464147332105
absolute error = 6e-31
relative error = 3.7788405347465826337665935919991e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.387
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.92
y[1] (closed_form) = -1.5985213845728383656303536294524
y[1] (numeric) = -1.598521384572838365630353629453
absolute error = 6e-31
relative error = 3.7534687104629118420687668214352e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.393
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.91
y[1] (closed_form) = -1.6092299030190012094096152228503
y[1] (numeric) = -1.6092299030190012094096152228509
absolute error = 6e-31
relative error = 3.7284914907084933484504603360885e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.398
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.9
y[1] (closed_form) = -1.6199140967617804145503102272531
y[1] (numeric) = -1.6199140967617804145503102272536
absolute error = 5e-31
relative error = 3.0865834243896234355777570418956e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.404
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.89
y[1] (closed_form) = -1.6305738867884915555795782715684
y[1] (numeric) = -1.6305738867884915555795782715689
absolute error = 5e-31
relative error = 3.0664050494809442278150752896548e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.409
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.88
y[1] (closed_form) = -1.6412091942160835544120816956342
y[1] (numeric) = -1.6412091942160835544120816956346
absolute error = 4e-31
relative error = 2.4372273894740046421967449025886e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.415
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.87
y[1] (closed_form) = -1.6518199402918486272772478832187
y[1] (numeric) = -1.6518199402918486272772478832191
absolute error = 4e-31
relative error = 2.4215714451862517762490572081269e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.42
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.86
y[1] (closed_form) = -1.6624060463941310585577425791076
y[1] (numeric) = -1.662406046394131058557742579108
absolute error = 4e-31
relative error = 2.4061510174823204128493067843280e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.425
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.85
y[1] (closed_form) = -1.6729674340330347951602144282409
y[1] (numeric) = -1.6729674340330347951602144282414
absolute error = 5e-31
relative error = 2.9887013329042894350042960660882e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.43
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
memory used=491.6MB, alloc=44.3MB, time=5.17
TOP MAIN SOLVE Loop
x[1] = -3.84
y[1] (closed_form) = -1.6835040248511298550499661764588
y[1] (numeric) = -1.6835040248511298550499661764594
absolute error = 6e-31
relative error = 3.5639950433326540212472223118947e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.435
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.83
y[1] (closed_form) = -1.6940157406241575435918804890718
y[1] (numeric) = -1.6940157406241575435918804890724
absolute error = 6e-31
relative error = 3.5418797217252001762333718545560e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.44
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.82
y[1] (closed_form) = -1.704502503261734471350658079132
y[1] (numeric) = -1.7045025032617344713506580791328
absolute error = 8e-31
relative error = 4.6934515993324780273665653796151e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.445
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.81
y[1] (closed_form) = -1.7149642348080553670142126953816
y[1] (numeric) = -1.7149642348080553670142126953822
absolute error = 6e-31
relative error = 3.4986152353617685894831495080955e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.45
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.8
y[1] (closed_form) = -1.7254008574425946791149114033072
y[1] (numeric) = -1.7254008574425946791149114033078
absolute error = 6e-31
relative error = 3.4774527751732175619494036367238e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.455
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.79
y[1] (closed_form) = -1.7358122934808069602342494039516
y[1] (numeric) = -1.735812293480806960234249403952
absolute error = 4e-31
relative error = 2.3043966303400468318910302701581e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.46
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.78
y[1] (closed_form) = -1.746198465374826027387506275997
y[1] (numeric) = -1.7461984653748260273875062759974
absolute error = 4e-31
relative error = 2.2906903649931851420535795960214e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.465
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.77
y[1] (closed_form) = -1.7565592957141628922959448985487
y[1] (numeric) = -1.7565592957141628922959448985491
absolute error = 4e-31
relative error = 2.2771790338986098586983841216518e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.47
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.76
y[1] (closed_form) = -1.7668947072264024552651853158543
y[1] (numeric) = -1.7668947072264024552651853158547
absolute error = 4e-31
relative error = 2.2638587255032491453224729094456e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.474
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.75
y[1] (closed_form) = -1.777204622777898956399513341277
y[1] (numeric) = -1.7772046227778989563995133412775
absolute error = 5e-31
relative error = 2.8134070415508145119209458834532e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.479
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
memory used=532.2MB, alloc=44.3MB, time=5.59
TOP MAIN SOLVE Loop
x[1] = -3.74
y[1] (closed_form) = -1.7874889653744701778930676660396
y[1] (numeric) = -1.78748896537447017789306766604
absolute error = 4e-31
relative error = 2.2377760520395825793016243121862e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.484
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.73
y[1] (closed_form) = -1.7977476581620903911500895379193
y[1] (numeric) = -1.7977476581620903911500895379196
absolute error = 3e-31
relative error = 1.6687547812283179093298086531504e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.488
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.72
y[1] (closed_form) = -1.8079806244275820424977156050378
y[1] (numeric) = -1.8079806244275820424977156050381
absolute error = 3e-31
relative error = 1.6593098175207595140068060153268e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.493
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.71
y[1] (closed_form) = -1.8181877875993061712661471784885
y[1] (numeric) = -1.8181877875993061712661471784888
absolute error = 3e-31
relative error = 1.6499945827714153840531649524311e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.497
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.7
y[1] (closed_form) = -1.8283690712478515540224378525973
y[1] (numeric) = -1.8283690712478515540224378525975
absolute error = 2e-31
relative error = 1.0938710523226097384479775798820e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.501
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.69
y[1] (closed_form) = -1.838524399086722568755606030452
y[1] (numeric) = -1.8385243990867225687556060304523
absolute error = 3e-31
relative error = 1.6317433706565082269254870136917e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.506
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.68
y[1] (closed_form) = -1.8486536949730257728222993317681
y[1] (numeric) = -1.8486536949730257728222993317685
absolute error = 4e-31
relative error = 2.1637367836264028496447442775312e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.51
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.67
y[1] (closed_form) = -1.8587568829081551884738140065118
y[1] (numeric) = -1.8587568829081551884738140065122
absolute error = 4e-31
relative error = 2.1519758914042164276708781149319e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.514
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.66
y[1] (closed_form) = -1.868833887038476289796904236781
y[1] (numeric) = -1.8688338870384762897969042367814
absolute error = 4e-31
relative error = 2.1403721474350847004852419179970e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.518
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
memory used=572.7MB, alloc=44.3MB, time=6.01
TOP MAIN SOLVE Loop
x[1] = -3.65
y[1] (closed_form) = -1.8788846316560086849125034765712
y[1] (numeric) = -1.8788846316560086849125034765717
absolute error = 5e-31
relative error = 2.6611532798547120249087369504298e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.522
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.64
y[1] (closed_form) = -1.8889090411991074872882226490383
y[1] (numeric) = -1.8889090411991074872882226490385
absolute error = 2e-31
relative error = 1.0588122330815730140608163167294e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.526
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.63
y[1] (closed_form) = -1.8989070402531433700322879880279
y[1] (numeric) = -1.8989070402531433700322879880281
absolute error = 2e-31
relative error = 1.0532374453324370863590822158523e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.53
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.62
y[1] (closed_form) = -1.9088785535511812970484344687977
y[1] (numeric) = -1.9088785535511812970484344687979
absolute error = 2e-31
relative error = 1.0477355912869894022171607295838e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.534
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.61
y[1] (closed_form) = -1.9188235059746579249431790153248
y[1] (numeric) = -1.9188235059746579249431790153249
absolute error = 1e-31
relative error = 5.2115267344093453593871237428487e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.538
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.6
y[1] (closed_form) = -1.9287418225540576695888608911998
y[1] (numeric) = -1.9287418225540576695888608912
absolute error = 2e-31
relative error = 1.0369454203837305690420957497233e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.542
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.59
y[1] (closed_form) = -1.9386334284695874312578547701945
y[1] (numeric) = -1.9386334284695874312578547701947
absolute error = 2e-31
relative error = 1.0316545514119485147230158186422e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.58
y[1] (closed_form) = -1.9484982490518499722554348329763
y[1] (numeric) = -1.9484982490518499722554348329765
absolute error = 2e-31
relative error = 1.0264315099965889446814549238043e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.549
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.57
y[1] (closed_form) = -1.9583362097825159409908957394921
y[1] (numeric) = -1.9583362097825159409908957394922
absolute error = 1e-31
relative error = 5.1063754783508574688798206315495e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.553
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.56
y[1] (closed_form) = -1.9681472362949945364387183730921
y[1] (numeric) = -1.9681472362949945364387183730922
absolute error = 1e-31
relative error = 5.0809206829590853630874332871780e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.557
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
memory used=613.3MB, alloc=44.3MB, time=6.44
TOP MAIN SOLVE Loop
x[1] = -3.55
y[1] (closed_form) = -1.9779312543751028069538047328878
y[1] (numeric) = -1.9779312543751028069538047328878
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.56
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.54
y[1] (closed_form) = -1.9876881899617335774170971549938
y[1] (numeric) = -1.9876881899617335774170971549939
absolute error = 1e-31
relative error = 5.0309701745486132966867694292693e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.564
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.53
y[1] (closed_form) = -1.9974179691475219987002420605887
y[1] (numeric) = -1.9974179691475219987002420605887
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.567
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.52
y[1] (closed_form) = -2.0071205181795107134503575480275
y[1] (numeric) = -2.0071205181795107134503575480276
absolute error = 1e-31
relative error = 4.9822618569363011312033537563758e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.571
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.51
y[1] (closed_form) = -2.0167957634598136322084172559671
y[1] (numeric) = -2.0167957634598136322084172559672
absolute error = 1e-31
relative error = 4.9583602768209893107143579655646e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.574
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.5
y[1] (closed_form) = -2.0264436315462783138872699125349
y[1] (numeric) = -2.0264436315462783138872699125348
absolute error = 1e-31
relative error = 4.9347535970539173243611659492379e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.577
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.49
y[1] (closed_form) = -2.0360640491531469446478747394331
y[1] (numeric) = -2.0360640491531469446478747394332
absolute error = 1e-31
relative error = 4.9114368500142543662138669380978e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.58
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.48
y[1] (closed_form) = -2.0456569431517159092249472864666
y[1] (numeric) = -2.0456569431517159092249472864666
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.584
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.47
y[1] (closed_form) = -2.0552222405709939487658782177848
y[1] (numeric) = -2.0552222405709939487658782177849
absolute error = 1e-31
relative error = 4.8656538463800105125991600757036e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.587
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.46
y[1] (closed_form) = -2.0647598685983588992595089421353
y[1] (numeric) = -2.0647598685983588992595089421354
absolute error = 1e-31
relative error = 4.8431782078312078170653776284330e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.59
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
memory used=653.7MB, alloc=44.3MB, time=6.84
TOP MAIN SOLVE Loop
x[1] = -3.45
y[1] (closed_form) = -2.074269754580213004644122661129
y[1] (numeric) = -2.0742697545802130046441226611292
absolute error = 2e-31
relative error = 9.6419474640836018723740568949444e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.593
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.44
y[1] (closed_form) = -2.0837518260226367986968372869621
y[1] (numeric) = -2.0837518260226367986968372869623
absolute error = 2e-31
relative error = 9.5980719729829911025449669548390e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.596
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.43
y[1] (closed_form) = -2.0932060105920415498194676387575
y[1] (numeric) = -2.0932060105920415498194676387577
absolute error = 2e-31
relative error = 9.5547212738717523598759061580513e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.598
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.42
y[1] (closed_form) = -2.1026322361158202628488582487688
y[1] (numeric) = -2.1026322361158202628488582487691
absolute error = 3e-31
relative error = 1.4267830334142891995695940254028e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.601
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.41
y[1] (closed_form) = -2.112030430582997232032674879712
y[1] (numeric) = -2.1120304305829972320326748797123
absolute error = 3e-31
relative error = 1.4204340792437781606754577709498e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.604
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.4
y[1] (closed_form) = -2.1214005221448761393246823555813
y[1] (numeric) = -2.1214005221448761393246823555817
absolute error = 4e-31
relative error = 1.8855468160042383815258431212311e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.39
y[1] (closed_form) = -2.130742439115686692166628423113
y[1] (numeric) = -2.1307424391156866921666284231136
absolute error = 6e-31
relative error = 2.8159198830667471129868310289802e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.609
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.38
y[1] (closed_form) = -2.1400561099732297949369979717448
y[1] (numeric) = -2.1400561099732297949369979717454
absolute error = 6e-31
relative error = 2.8036648067489476627809498330583e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.612
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.37
y[1] (closed_form) = -2.1493414633595212482600989281881
y[1] (numeric) = -2.1493414633595212482600989281889
absolute error = 8e-31
relative error = 3.7220702882154545044799862082484e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.614
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.36
y[1] (closed_form) = -2.1585984280814339703821903888114
y[1] (numeric) = -2.1585984280814339703821903888123
absolute error = 9e-31
relative error = 4.1693720716730140591963073504665e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.617
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
memory used=694.3MB, alloc=44.3MB, time=7.26
TOP MAIN SOLVE Loop
x[1] = -3.35
y[1] (closed_form) = -2.1678269331113387348346649396725
y[1] (numeric) = -2.1678269331113387348346649396733
absolute error = 8e-31
relative error = 3.6903314917847840764805925715931e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.619
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.34
y[1] (closed_form) = -2.1770269075877434186176505205374
y[1] (numeric) = -2.1770269075877434186176505205381
absolute error = 7e-31
relative error = 3.2153943415225658198581363937787e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.622
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.33
y[1] (closed_form) = -2.1861982808159307551508024953928
y[1] (numeric) = -2.1861982808159307551508024953935
absolute error = 7e-31
relative error = 3.2019053630338904754871334611934e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.624
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.32
y[1] (closed_form) = -2.195340982268594586251513677156
y[1] (numeric) = -2.1953409822685945862515136771567
absolute error = 7e-31
relative error = 3.1885707307146544963692618489371e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.626
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.31
y[1] (closed_form) = -2.2044549415864746074142787973889
y[1] (numeric) = -2.2044549415864746074142787973895
absolute error = 6e-31
relative error = 2.7217612330429375509634151398463e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.3
y[1] (closed_form) = -2.2135400885789896006785101912675
y[1] (numeric) = -2.213540088578989600678510191268
absolute error = 5e-31
relative error = 2.2588251397831308372104734667818e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.63
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.29
y[1] (closed_form) = -2.2225963532248691493857131617861
y[1] (numeric) = -2.2225963532248691493857131617866
absolute error = 5e-31
relative error = 2.2496212561247415948113947940995e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.632
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.28
y[1] (closed_form) = -2.2316236656727838291405924726898
y[1] (numeric) = -2.2316236656727838291405924726904
absolute error = 6e-31
relative error = 2.6886253682881321880938983332442e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.634
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.27
y[1] (closed_form) = -2.2406219562419738693043755739656
y[1] (numeric) = -2.2406219562419738693043755739664
absolute error = 8e-31
relative error = 3.5704372072733752564583690860851e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
memory used=734.7MB, alloc=44.3MB, time=7.69
TOP MAIN SOLVE Loop
x[1] = -3.26
y[1] (closed_form) = -2.2495911554228762793624033634478
y[1] (numeric) = -2.2495911554228762793624033634486
absolute error = 8e-31
relative error = 3.5562017483555435814261698084251e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.638
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.25
y[1] (closed_form) = -2.2585311938777504345218554093201
y[1] (numeric) = -2.258531193877750434521855409321
absolute error = 9e-31
relative error = 3.9848907220748137071121346736471e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.64
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.24
y[1] (closed_form) = -2.2674420024413021149093434766913
y[1] (numeric) = -2.2674420024413021149093434766924
absolute error = 1.1e-30
relative error = 4.8512817475183733959952666325392e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.642
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.23
y[1] (closed_form) = -2.2763235121213059927520247921652
y[1] (numeric) = -2.2763235121213059927520247921663
absolute error = 1.1e-30
relative error = 4.8323535479142415305076784391951e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.643
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.22
y[1] (closed_form) = -2.2851756540992265619398546181717
y[1] (numeric) = -2.2851756540992265619398546181728
absolute error = 1.1e-30
relative error = 4.8136343393418454536324607667215e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.645
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.21
y[1] (closed_form) = -2.2939983597308375043806162680614
y[1] (numeric) = -2.2939983597308375043806162680625
absolute error = 1.1e-30
relative error = 4.7951211269787772513206328167298e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.647
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.2
y[1] (closed_form) = -2.3027915605468394875734355474129
y[1] (numeric) = -2.3027915605468394875734355474139
absolute error = 1.0e-30
relative error = 4.3425554319928631373000966196966e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.648
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.19
y[1] (closed_form) = -2.3115551882534763878406056300562
y[1] (numeric) = -2.3115551882534763878406056300573
absolute error = 1.1e-30
relative error = 4.7587010061010845561347857693661e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.65
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.18
y[1] (closed_form) = -2.3202891747331499336717174418948
y[1] (numeric) = -2.3202891747331499336717174418959
absolute error = 1.1e-30
relative error = 4.7407883981810498678480304421430e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.651
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.17
y[1] (closed_form) = -2.3289934520450327636483096041922
y[1] (numeric) = -2.3289934520450327636483096041932
absolute error = 1.0e-30
relative error = 4.2937003499169317574215002851396e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.652
Order of pole (three term test) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
memory used=775.2MB, alloc=44.3MB, time=8.11
TOP MAIN SOLVE Loop
x[1] = -3.16
y[1] (closed_form) = -2.3376679524256798934315207526149
y[1] (numeric) = -2.337667952425679893431520752616
absolute error = 1.1e-30
relative error = 4.7055442534453432176992438060476e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.654
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.15
y[1] (closed_form) = -2.3463126082896385863095454705619
y[1] (numeric) = -2.346312608289638586309545470563
absolute error = 1.1e-30
relative error = 4.6882073433593015295016400759398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.655
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.14
y[1] (closed_form) = -2.3549273522300566218160630263006
y[1] (numeric) = -2.3549273522300566218160630263017
absolute error = 1.1e-30
relative error = 4.6710570453832804247920603824634e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.656
Order of pole (three term test) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.13
y[1] (closed_form) = -2.3635121170192889569452254538643
y[1] (numeric) = -2.3635121170192889569452254538653
absolute error = 1.0e-30
relative error = 4.2309916365528785586026773662836e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.657
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.12
y[1] (closed_form) = -2.3720668356095027745032581377796
y[1] (numeric) = -2.3720668356095027745032581377805
absolute error = 9e-31
relative error = 3.7941595341631464768654264297661e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.658
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.11
y[1] (closed_form) = -2.3805914411332809131512418212936
y[1] (numeric) = -2.3805914411332809131512418212945
absolute error = 9e-31
relative error = 3.7805731149380040819049672934320e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.659
Order of pole (three term test) = 32.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.1
y[1] (closed_form) = -2.3890858669042236737082097262148
y[1] (numeric) = -2.3890858669042236737082097262157
absolute error = 9e-31
relative error = 3.7671312382179865746347248374645e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.09
y[1] (closed_form) = -2.3975500464175489962983071186846
y[1] (numeric) = -2.3975500464175489962983071186855
absolute error = 9e-31
relative error = 3.7538319641952496832584452126681e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.661
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.08
y[1] (closed_form) = -2.4059839133506910029404230476377
y[1] (numeric) = -2.4059839133506910029404230476387
absolute error = 1.0e-30
relative error = 4.1563037660021219201625054569350e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.662
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.07
y[1] (closed_form) = -2.4143874015638969001934149894277
y[1] (numeric) = -2.4143874015638969001934149894286
absolute error = 9e-31
relative error = 3.7276536458773492680659829524238e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.662
Order of pole (three term test) = 32.54
NO COMPLEX POLE (six term test) for Equation 1
memory used=815.8MB, alloc=44.3MB, time=8.53
TOP MAIN SOLVE Loop
x[1] = -3.06
y[1] (closed_form) = -2.4227604451008222364848066206867
y[1] (numeric) = -2.4227604451008222364848066206875
absolute error = 8e-31
relative error = 3.3020185780963924817758615083226e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.663
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.05
y[1] (closed_form) = -2.4311029781891245087656467791261
y[1] (numeric) = -2.4311029781891245087656467791271
absolute error = 1.0e-30
relative error = 4.1133592816577360740989010277962e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.664
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.04
y[1] (closed_form) = -2.4394149352410551131490737253904
y[1] (numeric) = -2.4394149352410551131490737253916
absolute error = 1.2e-30
relative error = 4.9192123187579806786324679288384e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.664
Order of pole (three term test) = 32.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.03
y[1] (closed_form) = -2.4476962508540496342050329545515
y[1] (numeric) = -2.4476962508540496342050329545527
absolute error = 1.2e-30
relative error = 4.9025690977027736409050133178107e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.02
y[1] (closed_form) = -2.4559468598113164675985488892354
y[1] (numeric) = -2.4559468598113164675985488892366
absolute error = 1.2e-30
relative error = 4.8860992053068796682845267885753e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.01
y[1] (closed_form) = -2.4641666970824237707739506831371
y[1] (numeric) = -2.4641666970824237707739506831384
absolute error = 1.3e-30
relative error = 5.2756171144557773171897411880061e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3
y[1] (closed_form) = -2.4723556978238847364024999388077
y[1] (numeric) = -2.472355697823884736402499938809
absolute error = 1.3e-30
relative error = 5.2581430784584618674460985498121e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.99
y[1] (closed_form) = -2.4805137973797411833259632616586
y[1] (numeric) = -2.48051379737974118332596326166
absolute error = 1.4e-30
relative error = 5.6439919885907184912022902245340e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.98
y[1] (closed_form) = -2.4886409312821454597438150972671
y[1] (numeric) = -2.4886409312821454597438150972684
absolute error = 1.3e-30
relative error = 5.2237347045893086173764002020531e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.97
y[1] (closed_form) = -2.4967370352519406534069460950045
y[1] (numeric) = -2.4967370352519406534069460950057
absolute error = 1.2e-30
relative error = 4.8062730798516410118496769760866e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.667
Order of pole (three term test) = 32.51
NO COMPLEX POLE (six term test) for Equation 1
memory used=856.3MB, alloc=44.3MB, time=8.95
TOP MAIN SOLVE Loop
x[1] = -2.96
y[1] (closed_form) = -2.5048020451992391035959891710278
y[1] (numeric) = -2.504802045199239103595989171029
absolute error = 1.2e-30
relative error = 4.7907977490674261051100840015765e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.667
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.95
y[1] (closed_form) = -2.5128358972239992096776593706555
y[1] (numeric) = -2.5128358972239992096776593706566
absolute error = 1.1e-30
relative error = 4.3775242196086145909045240507253e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.667
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.94
y[1] (closed_form) = -2.5208385276166005310478344165254
y[1] (numeric) = -2.5208385276166005310478344165264
absolute error = 1.0e-30
relative error = 3.9669339747257783816600596165057e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.667
Order of pole (three term test) = 32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.93
y[1] (closed_form) = -2.5288098728584171732854803367333
y[1] (numeric) = -2.5288098728584171732854803367344
absolute error = 1.1e-30
relative error = 4.3498722929162920169753140200558e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.667
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.92
y[1] (closed_form) = -2.5367498696223894553569506579762
y[1] (numeric) = -2.5367498696223894553569506579772
absolute error = 1.0e-30
relative error = 3.9420520405855230882722952195555e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.91
y[1] (closed_form) = -2.5446584547735938527256581837613
y[1] (numeric) = -2.5446584547735938527256581837622
absolute error = 9e-31
relative error = 3.5368204259855210652419671156001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.9
y[1] (closed_form) = -2.5525355653698112112376352177478
y[1] (numeric) = -2.5525355653698112112376352177487
absolute error = 9e-31
relative error = 3.5259058177691171557960165265906e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.89
y[1] (closed_form) = -2.5603811386620932266690610976242
y[1] (numeric) = -2.5603811386620932266690610976249
absolute error = 7e-31
relative error = 2.7339679605895684157955315249072e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.88
y[1] (closed_form) = -2.5681951120953271848374449355068
y[1] (numeric) = -2.5681951120953271848374449355073
absolute error = 5e-31
relative error = 1.9468925769898467945743210260833e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.87
y[1] (closed_form) = -2.5759774233087989571938063762114
y[1] (numeric) = -2.5759774233087989571938063762119
absolute error = 5e-31
relative error = 1.9410108003111244228331147269284e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 32.48
NO COMPLEX POLE (six term test) for Equation 1
memory used=896.8MB, alloc=44.3MB, time=9.37
TOP MAIN SOLVE Loop
x[1] = -2.86
y[1] (closed_form) = -2.5837280101367542468288978439892
y[1] (numeric) = -2.5837280101367542468288978439897
absolute error = 5e-31
relative error = 1.9351882165550989219538048004739e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.664
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.85
y[1] (closed_form) = -2.5914468106089580798422580101363
y[1] (numeric) = -2.5914468106089580798422580101368
absolute error = 5e-31
relative error = 1.9294241269127424569728642151592e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.664
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.84
y[1] (closed_form) = -2.5991337629512525370386779365615
y[1] (numeric) = -2.599133762951252537038677936562
absolute error = 5e-31
relative error = 1.9237178444877815102939749878405e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.663
Order of pole (three term test) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.83
y[1] (closed_form) = -2.6067888055861127209324983918053
y[1] (numeric) = -2.6067888055861127209324983918057
absolute error = 4e-31
relative error = 1.5344549552416220504042627514526e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.662
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.82
y[1] (closed_form) = -2.6144118771332009530560390536087
y[1] (numeric) = -2.6144118771332009530560390536092
absolute error = 5e-31
relative error = 1.9124760118067870805233965678068e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.661
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.81
y[1] (closed_form) = -2.6220029164099191965843875630021
y[1] (numeric) = -2.6220029164099191965843875630027
absolute error = 6e-31
relative error = 2.2883269741802113408563673711234e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.661
Order of pole (three term test) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.8
y[1] (closed_form) = -2.6295618624319596993047485356628
y[1] (numeric) = -2.6295618624319596993047485356634
absolute error = 6e-31
relative error = 2.2817489429402046951039257793256e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.79
y[1] (closed_form) = -2.6370886544138538519745695232386
y[1] (numeric) = -2.6370886544138538519745695232392
absolute error = 6e-31
relative error = 2.2752363633878744324002224998859e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.659
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.78
y[1] (closed_form) = -2.6445832317695192571287224062988
y[1] (numeric) = -2.6445832317695192571287224062995
absolute error = 7e-31
relative error = 2.6469199062856585737897815797367e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.658
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
memory used=937.3MB, alloc=44.3MB, time=9.80
TOP MAIN SOLVE Loop
x[1] = -2.77
y[1] (closed_form) = -2.6520455341128050034121246469905
y[1] (numeric) = -2.6520455341128050034121246469912
absolute error = 7e-31
relative error = 2.6394720263887649936017304477449e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.657
Order of pole (three term test) = 32.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.76
y[1] (closed_form) = -2.6594755012580351405303350884123
y[1] (numeric) = -2.6594755012580351405303350884129
absolute error = 6e-31
relative error = 2.2560839523288584940841646016407e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.656
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.75
y[1] (closed_form) = -2.6668730732205503499268534137957
y[1] (numeric) = -2.6668730732205503499268534137964
absolute error = 7e-31
relative error = 2.6247968342740472597339700271728e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.655
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.74
y[1] (closed_form) = -2.6742381902172478063120908260768
y[1] (numeric) = -2.6742381902172478063120908260774
absolute error = 6e-31
relative error = 2.2436296145754228377303397746921e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.653
Order of pole (three term test) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.73
y[1] (closed_form) = -2.6815707926671192251852618311858
y[1] (numeric) = -2.6815707926671192251852618311864
absolute error = 6e-31
relative error = 2.2374945373089834795285072676720e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.652
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.72
y[1] (closed_form) = -2.6888708211917870915067730598473
y[1] (numeric) = -2.6888708211917870915067730598477
absolute error = 4e-31
relative error = 1.4876133016412747080018360069363e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.651
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.71
y[1] (closed_form) = -2.696138216616039064695054695935
y[1] (numeric) = -2.6961382166160390646950546959355
absolute error = 5e-31
relative error = 1.8545043311153276892636818402188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.649
Order of pole (three term test) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.7
y[1] (closed_form) = -2.7033729199683605551381931471318
y[1] (numeric) = -2.7033729199683605551381931471324
absolute error = 6e-31
relative error = 2.2194496200214294348543767271051e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.648
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.69
y[1] (closed_form) = -2.7105748724814654674271799480887
y[1] (numeric) = -2.7105748724814654674271799480892
absolute error = 5e-31
relative error = 1.8446271493038011633022985236886e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.646
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.68
y[1] (closed_form) = -2.717744015592825105534091379361
y[1] (numeric) = -2.7177440155928251055340913793613
absolute error = 3e-31
relative error = 1.1038567218942458134154064423734e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.645
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
memory used=977.8MB, alloc=44.3MB, time=10.22
TOP MAIN SOLVE Loop
x[1] = -2.67
y[1] (closed_form) = -2.7248802909451952351750557686128
y[1] (numeric) = -2.724880290945195235175055768613
absolute error = 2e-31
relative error = 7.3397719769415934599179792091021e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.643
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.66
y[1] (closed_form) = -2.7319836403871412986144507650539
y[1] (numeric) = -2.7319836403871412986144507650541
absolute error = 2e-31
relative error = 7.3206880540345619785665199529650e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.641
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.65
y[1] (closed_form) = -2.739054005973561777183400894533
y[1] (numeric) = -2.7390540059735617771834008945333
absolute error = 3e-31
relative error = 1.0952686560605760311441506346642e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.64
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.64
y[1] (closed_form) = -2.7460913299662096968023162615046
y[1] (numeric) = -2.7460913299662096968023162615049
absolute error = 3e-31
relative error = 1.0924618446819518624545178669218e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.638
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.63
y[1] (closed_form) = -2.7530955548342122718139262151831
y[1] (numeric) = -2.7530955548342122718139262151834
absolute error = 3e-31
relative error = 1.0896824829535043084594357832921e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.62
y[1] (closed_form) = -2.7600666232545886824500169901754
y[1] (numeric) = -2.7600666232545886824500169901756
absolute error = 2e-31
relative error = 7.2462018965384948993651340037321e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.634
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.61
y[1] (closed_form) = -2.7670044781127659812718796159502
y[1] (numeric) = -2.7670044781127659812718796159505
absolute error = 3e-31
relative error = 1.0842049674043709888606836767121e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.632
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.6
y[1] (closed_form) = -2.7739090625030931239413136134811
y[1] (numeric) = -2.7739090625030931239413136134814
absolute error = 3e-31
relative error = 1.0815062543156656805911768439492e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.63
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.59
y[1] (closed_form) = -2.7807803197293531196959130097347
y[1] (numeric) = -2.780780319729353119695913009735
absolute error = 3e-31
relative error = 1.0788338721744057156842871600839e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.58
y[1] (closed_form) = -2.7876181933052732969192838494473
y[1] (numeric) = -2.7876181933052732969192838494477
absolute error = 4e-31
relative error = 1.4349167363042669872199882636371e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
memory used=1018.3MB, alloc=44.3MB, time=10.64
TOP MAIN SOLVE Loop
x[1] = -2.57
y[1] (closed_form) = -2.7944226269550336792138065165213
y[1] (numeric) = -2.7944226269550336792138065165217
absolute error = 4e-31
relative error = 1.4314227065784368960467364919397e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.623
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.56
y[1] (closed_form) = -2.8011935646137734674005616417197
y[1] (numeric) = -2.8011935646137734674005616417203
absolute error = 6e-31
relative error = 2.1419440897606358876560215708258e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.621
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.55
y[1] (closed_form) = -2.8079309504280956228880850160776
y[1] (numeric) = -2.8079309504280956228880850160782
absolute error = 6e-31
relative error = 2.1368046814275270084238028565292e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.619
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.54
y[1] (closed_form) = -2.8146347287565695478687045971719
y[1] (numeric) = -2.8146347287565695478687045971725
absolute error = 6e-31
relative error = 2.1317153301276289434387144429971e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.616
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.53
y[1] (closed_form) = -2.8213048441702318578183412343095
y[1] (numeric) = -2.82130484417023185781834123431
absolute error = 5e-31
relative error = 1.7722296157863577751061356875531e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.614
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.52
y[1] (closed_form) = -2.8279412414530852417928239946366
y[1] (numeric) = -2.8279412414530852417928239946371
absolute error = 5e-31
relative error = 1.7680706822008941689493203278277e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.611
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.51
y[1] (closed_form) = -2.8345438656025954060309807906413
y[1] (numeric) = -2.8345438656025954060309807906419
absolute error = 6e-31
relative error = 2.1167426875309479752024154705661e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.609
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.5
y[1] (closed_form) = -2.8411126618301860963920152355997
y[1] (numeric) = -2.8411126618301860963920152356003
absolute error = 6e-31
relative error = 2.1118486713353084435723037742045e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.606
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.49
y[1] (closed_form) = -2.8476475755617321951719711319741
y[1] (numeric) = -2.8476475755617321951719711319748
absolute error = 7e-31
relative error = 2.4581693535651676043224461017668e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.603
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.48
y[1] (closed_form) = -2.8541485524380508878614165729876
y[1] (numeric) = -2.8541485524380508878614165729882
absolute error = 6e-31
relative error = 2.1022031228454180529186842578290e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.6
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
memory used=1058.8MB, alloc=44.3MB, time=11.06
TOP MAIN SOLVE Loop
x[1] = -2.47
y[1] (closed_form) = -2.8606155383153908954238501535902
y[1] (numeric) = -2.8606155383153908954238501535909
absolute error = 7e-31
relative error = 2.4470257908625784527548756894439e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.598
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.46
y[1] (closed_form) = -2.8670484792659197676917420874791
y[1] (numeric) = -2.8670484792659197676917420874798
absolute error = 7e-31
relative error = 2.4415352759546928842171610371398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.595
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.45
y[1] (closed_form) = -2.8734473215782092334945729550322
y[1] (numeric) = -2.873447321578209233494572955033
absolute error = 8e-31
relative error = 2.7841122890695933406931769217944e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.44
y[1] (closed_form) = -2.8798120117577186031507222059179
y[1] (numeric) = -2.8798120117577186031507222059187
absolute error = 8e-31
relative error = 2.7779591054338055912153312406370e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.589
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.43
y[1] (closed_form) = -2.886142496527276218972587252351
y[1] (numeric) = -2.8861424965272762189725872523518
absolute error = 8e-31
relative error = 2.7718659108571127955229882650435e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.586
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.42
y[1] (closed_form) = -2.8924387228275589494518818567134
y[1] (numeric) = -2.8924387228275589494518818567141
absolute error = 7e-31
relative error = 2.4201031277706777976183118163810e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.583
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.41
y[1] (closed_form) = -2.898700637817569722809669382437
y[1] (numeric) = -2.8987006378175697228096693824376
absolute error = 6e-31
relative error = 2.0698929450394701792306502825729e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.58
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.4
y[1] (closed_form) = -2.9049281888751130956133321812023
y[1] (numeric) = -2.9049281888751130956133321812029
absolute error = 6e-31
relative error = 2.0654555327659937371468912066776e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.576
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.39
y[1] (closed_form) = -2.911121323597268852180362773814
y[1] (numeric) = -2.9111213235972688521803627738146
absolute error = 6e-31
relative error = 2.0610614718681005588663920207622e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.573
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.38
y[1] (closed_form) = -2.9172799898008636305065853874281
y[1] (numeric) = -2.9172799898008636305065853874288
absolute error = 7e-31
relative error = 2.3994954287805013903733639403732e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.57
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
memory used=1099.3MB, alloc=44.3MB, time=11.47
TOP MAIN SOLVE Loop
x[1] = -2.37
y[1] (closed_form) = -2.9234041355229405704741776786116
y[1] (numeric) = -2.9234041355229405704741776786123
absolute error = 7e-31
relative error = 2.3944688026336923541254126880368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.566
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.36
y[1] (closed_form) = -2.9294937090212269801126619401625
y[1] (numeric) = -2.9294937090212269801126619401631
absolute error = 6e-31
relative error = 2.0481354786744566000794029923265e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.563
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.35
y[1] (closed_form) = -2.9355486587746000157038725995165
y[1] (numeric) = -2.9355486587746000157038725995172
absolute error = 7e-31
relative error = 2.3845627559524232733029299381726e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.559
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.34
y[1] (closed_form) = -2.9415689334835503715397822073724
y[1] (numeric) = -2.941568933483550371539782207373
absolute error = 6e-31
relative error = 2.0397278240542557609471914814237e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.33
y[1] (closed_form) = -2.9475544820706439751599812260069
y[1] (numeric) = -2.9475544820706439751599812260076
absolute error = 7e-31
relative error = 2.3748500808312560818955804931642e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.32
y[1] (closed_form) = -2.9535052536809816839135575964033
y[1] (numeric) = -2.9535052536809816839135575964041
absolute error = 8e-31
relative error = 2.7086459352085200878821964853089e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.549
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.31
y[1] (closed_form) = -2.9594211976826569787081101302285
y[1] (numeric) = -2.9594211976826569787081101302292
absolute error = 7e-31
relative error = 2.3653273841118915099487336158179e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.3
y[1] (closed_form) = -2.9653022636672116508266550749689
y[1] (numeric) = -2.9653022636672116508266550749695
absolute error = 6e-31
relative error = 2.0234024954271456949072853166203e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.29
y[1] (closed_form) = -2.9711484014500894777112475759528
y[1] (numeric) = -2.9711484014500894777112475759533
absolute error = 5e-31
relative error = 1.6828509803009891733814028362097e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.537
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
memory used=1139.8MB, alloc=44.3MB, time=11.89
TOP MAIN SOLVE Loop
x[1] = -2.28
y[1] (closed_form) = -2.9769595610710878836302390449753
y[1] (numeric) = -2.9769595610710878836302390449759
absolute error = 6e-31
relative error = 2.0154791749476249774802208118024e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.533
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.27
y[1] (closed_form) = -2.9827356927948075811642274789192
y[1] (numeric) = -2.9827356927948075811642274789198
absolute error = 6e-31
relative error = 2.0115761562426712064600621571338e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.529
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.26
y[1] (closed_form) = -2.9884767471111001894639303898968
y[1] (numeric) = -2.9884767471111001894639303898975
absolute error = 7e-31
relative error = 2.3423304219337687375808884892948e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.525
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.25
y[1] (closed_form) = -2.9941826747355138252514190474794
y[1] (numeric) = -2.9941826747355138252514190474802
absolute error = 8e-31
relative error = 2.6718476689825435482088966695698e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.521
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.24
y[1] (closed_form) = -2.9998534266097366625543980296454
y[1] (numeric) = -2.9998534266097366625543980296461
absolute error = 7e-31
relative error = 2.3334473404292292267483089742913e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.517
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.23
y[1] (closed_form) = -3.0054889539020384571814954679561
y[1] (numeric) = -3.0054889539020384571814954679567
absolute error = 6e-31
relative error = 1.9963473804188086426710275904231e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.513
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.22
y[1] (closed_form) = -3.011089208007710031964846689639
y[1] (numeric) = -3.0110892080077100319648466896396
absolute error = 6e-31
relative error = 1.9926344208081120142360510518429e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.509
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.21
y[1] (closed_form) = -3.0166541405495007188146070398483
y[1] (numeric) = -3.0166541405495007188146070398488
absolute error = 5e-31
relative error = 1.6574654458363667590022578242706e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.504
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.2
y[1] (closed_form) = -3.0221837033780537536484183462211
y[1] (numeric) = -3.0221837033780537536484183462214
absolute error = 3e-31
relative error = 9.9265971047581989768907972438349e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.5
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.19
y[1] (closed_form) = -3.0276778485723396202772775994457
y[1] (numeric) = -3.027677848572339620277277599446
absolute error = 3e-31
relative error = 9.9085839050366909611533267228044e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.496
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
memory used=1180.3MB, alloc=44.3MB, time=12.31
TOP MAIN SOLVE Loop
x[1] = -2.18
y[1] (closed_form) = -3.0331365284400873393477158020948
y[1] (numeric) = -3.0331365284400873393477158020951
absolute error = 3e-31
relative error = 9.8907516093344827635463593251379e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.491
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.17
y[1] (closed_form) = -3.0385596955182136984586894173123
y[1] (numeric) = -3.0385596955182136984586894173129
absolute error = 6e-31
relative error = 1.9746197545007339386730677138534e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.487
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.16
y[1] (closed_form) = -3.0439473025732504195901162626347
y[1] (numeric) = -3.0439473025732504195901162626352
absolute error = 5e-31
relative error = 1.6426039950734917718374217686899e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.482
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.15
y[1] (closed_form) = -3.049299302601769259998551875501
y[1] (numeric) = -3.0492993026017692599985518755016
absolute error = 6e-31
relative error = 1.9676651599534979307747374875141e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.478
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.14
y[1] (closed_form) = -3.0546156488308050427541011587972
y[1] (numeric) = -3.0546156488308050427541011587978
absolute error = 6e-31
relative error = 1.9642405755030359304601650389120e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.473
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.13
y[1] (closed_form) = -3.0598962947182766131112933296825
y[1] (numeric) = -3.059896294718276613111293329683
absolute error = 5e-31
relative error = 1.6340423068031944308073457333626e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.468
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.12
y[1] (closed_form) = -3.0651411939534057169253156752797
y[1] (numeric) = -3.0651411939534057169253156752801
absolute error = 4e-31
relative error = 1.3049969795488662238365740692017e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.464
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.11
y[1] (closed_form) = -3.0703503004571337973437031965537
y[1] (numeric) = -3.070350300457133797343703196554
absolute error = 3e-31
relative error = 9.7708720713507524358585063261832e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.459
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.1
y[1] (closed_form) = -3.0755235683825367060223167285473
y[1] (numeric) = -3.0755235683825367060223167285477
absolute error = 4e-31
relative error = 1.3005915614243395673475494319002e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.454
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.09
y[1] (closed_form) = -3.0806609521152373251332113924729
y[1] (numeric) = -3.0806609521152373251332113924732
absolute error = 3e-31
relative error = 9.7381699792057478384605398184057e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.449
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
memory used=1220.8MB, alloc=44.3MB, time=12.73
TOP MAIN SOLVE Loop
x[1] = -2.08
y[1] (closed_form) = -3.0857624062738160964508000940398
y[1] (numeric) = -3.0857624062738160964508000940402
absolute error = 4e-31
relative error = 1.2962760813559081072946954154282e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.444
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.07
y[1] (closed_form) = -3.0908278857102194538215530636175
y[1] (numeric) = -3.090827885710219453821553063618
absolute error = 5e-31
relative error = 1.6176895592007658507363321354808e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.439
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.06
y[1] (closed_form) = -3.095857345510166155341343967857
y[1] (numeric) = -3.0958573455101661553413439678575
absolute error = 5e-31
relative error = 1.6150614973430083178657197560585e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.434
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.05
y[1] (closed_form) = -3.1008507409935515115834557393962
y[1] (numeric) = -3.1008507409935515115834557393967
absolute error = 5e-31
relative error = 1.6124607140548587708487563877923e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.429
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.04
y[1] (closed_form) = -3.1058080277148495062391948011371
y[1] (numeric) = -3.1058080277148495062391948011375
absolute error = 4e-31
relative error = 1.2879096081617984859837647337036e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.424
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.03
y[1] (closed_form) = -3.1107291614635128055520306338801
y[1] (numeric) = -3.1107291614635128055520306338805
absolute error = 4e-31
relative error = 1.2858721516334484226784005034203e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.418
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.02
y[1] (closed_form) = -3.1156140982643706529451784801222
y[1] (numeric) = -3.1156140982643706529451784801226
absolute error = 4e-31
relative error = 1.2838560469437785098191122515808e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.413
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.01
y[1] (closed_form) = -3.1204627943780246452615762215626
y[1] (numeric) = -3.1204627943780246452615762215629
absolute error = 3e-31
relative error = 9.6139585621880953357617094160155e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.408
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2
y[1] (closed_form) = -3.1252752063012423870542719420128
y[1] (numeric) = -3.1252752063012423870542719420131
absolute error = 3e-31
relative error = 9.5991546406900102423605408475203e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.402
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (closed_form) = -3.1300512907673490193843362193883
y[1] (numeric) = -3.1300512907673490193843362193886
absolute error = 3e-31
relative error = 9.5845074770788620483537497729374e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.397
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
memory used=1261.3MB, alloc=44.3MB, time=13.16
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (closed_form) = -3.1347910047466166196025426083911
y[1] (numeric) = -3.1347910047466166196025426083916
absolute error = 5e-31
relative error = 1.5950026628343432950650283884438e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.392
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (closed_form) = -3.1394943054466514686102209072045
y[1] (numeric) = -3.139494305446651468610220907205
absolute error = 5e-31
relative error = 1.5926131770093008611336869626908e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.386
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (closed_form) = -3.1441611503127791821138804745759
y[1] (numeric) = -3.1441611503127791821138804745763
absolute error = 4e-31
relative error = 1.2721994226034128387828828518780e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.38
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (closed_form) = -3.1487914970284277024074249053116
y[1] (numeric) = -3.1487914970284277024074249053119
absolute error = 3e-31
relative error = 9.5274647522109832689652095760768e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.375
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (closed_form) = -3.153385303515508147235034609446
y[1] (numeric) = -3.1533853035155081472350346094462
absolute error = 2e-31
relative error = 6.3423901854629929397023973420813e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.369
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (closed_form) = -3.1579425279347935123070800998711
y[1] (numeric) = -3.1579425279347935123070800998712
absolute error = 1e-31
relative error = 3.1666187435462042981578970166716e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.363
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (closed_form) = -3.1624631286862952240607459014469
y[1] (numeric) = -3.162463128686295224060745901447
absolute error = 1e-31
relative error = 3.1620922025276087972670830181437e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.358
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (closed_form) = -3.1669470644096375392763927777093
y[1] (numeric) = -3.1669470644096375392763927777094
absolute error = 1e-31
relative error = 3.1576151405814979873722051313318e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.352
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (closed_form) = -3.1713942939844297881800642551113
y[1] (numeric) = -3.1713942939844297881800642551114
absolute error = 1e-31
relative error = 3.1531872334412088694804837159797e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.346
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (closed_form) = -3.1758047765306364576819520348791
y[1] (numeric) = -3.1758047765306364576819520348794
absolute error = 3e-31
relative error = 9.4464244848113997463235819901202e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.34
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
memory used=1301.8MB, alloc=44.3MB, time=13.58
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (closed_form) = -3.1801784714089451114200736443552
y[1] (numeric) = -3.1801784714089451114200736443556
absolute error = 4e-31
relative error = 1.2577910441069810328027026876663e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.334
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (closed_form) = -3.1845153382211321432978844181901
y[1] (numeric) = -3.1845153382211321432978844181906
absolute error = 5e-31
relative error = 1.5700976346350387541660555308678e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.328
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (closed_form) = -3.1888153368104263612240444397096
y[1] (numeric) = -3.1888153368104263612240444397099
absolute error = 3e-31
relative error = 9.4078824990873049474826365005768e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.322
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (closed_form) = -3.1930784272618703977820892387443
y[1] (numeric) = -3.1930784272618703977820892387447
absolute error = 4e-31
relative error = 1.2527096001929652693406976598286e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.316
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (closed_form) = -3.1973045699026799445773106584083
y[1] (numeric) = -3.1973045699026799445773106584087
absolute error = 4e-31
relative error = 1.2510537900121766079297070472550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (closed_form) = -3.2014937253026008070277411937279
y[1] (numeric) = -3.2014937253026008070277411937284
absolute error = 5e-31
relative error = 1.5617709822396752754471715239282e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.303
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (closed_form) = -3.2056458542742637763857510933821
y[1] (numeric) = -3.2056458542742637763857510933825
absolute error = 4e-31
relative error = 1.2477984723941293107023339671657e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (closed_form) = -3.2097609178735373157964124255654
y[1] (numeric) = -3.2097609178735373157964124255658
absolute error = 4e-31
relative error = 1.2461987363999668579852335545133e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (closed_form) = -3.2138388773998780572184579633279
y[1] (numeric) = -3.2138388773998780572184579633282
absolute error = 3e-31
relative error = 9.3346309956494081867466670530779e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.285
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
memory used=1342.2MB, alloc=44.3MB, time=13.98
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (closed_form) = -3.2178796943966791060533649666141
y[1] (numeric) = -3.2178796943966791060533649666145
absolute error = 4e-31
relative error = 1.2430545514070129906392639302032e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.278
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (closed_form) = -3.2218833306516161503478245503039
y[1] (numeric) = -3.2218833306516161503478245503044
absolute error = 5e-31
relative error = 1.5518873549616599977834750438569e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.272
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (closed_form) = -3.2258497481969913714546161522666
y[1] (numeric) = -3.225849748196991371454616152267
absolute error = 4e-31
relative error = 1.2399833570164576611025806131670e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.265
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (closed_form) = -3.2297789093100751530566934749551
y[1] (numeric) = -3.2297789093100751530566934749556
absolute error = 5e-31
relative error = 1.5480935817579130292383522106258e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.259
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (closed_form) = -3.2336707765134455854791029903005
y[1] (numeric) = -3.233670776513445585479102990301
absolute error = 5e-31
relative error = 1.5462303819905303916545940479166e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (closed_form) = -3.2375253125753257622331984922954
y[1] (numeric) = -3.2375253125753257622331984922961
absolute error = 7e-31
relative error = 2.1621452573082035973840326479449e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (closed_form) = -3.2413424805099188657574850760856
y[1] (numeric) = -3.2413424805099188657574850760864
absolute error = 8e-31
relative error = 2.4681131500616567188418258254050e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.239
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (closed_form) = -3.2451222435777410393393231378017
y[1] (numeric) = -3.2451222435777410393393231378024
absolute error = 7e-31
relative error = 2.1570836087464346020141642494256e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.232
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (closed_form) = -3.2488645652859520422216473466799
y[1] (numeric) = -3.2488645652859520422216473466806
absolute error = 7e-31
relative error = 2.1545988942705858980658440386040e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.225
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (closed_form) = -3.2525694093886836849188068609234
y[1] (numeric) = -3.2525694093886836849188068609241
absolute error = 7e-31
relative error = 2.1521446951429212280995744798088e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.219
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
memory used=1382.6MB, alloc=44.3MB, time=14.39
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (closed_form) = -3.2562367398873660417856111616785
y[1] (numeric) = -3.2562367398873660417856111616792
absolute error = 7e-31
relative error = 2.1497208462312637526370434524182e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (closed_form) = -3.2598665210310514379036705856483
y[1] (numeric) = -3.259866521031051437903670585649
absolute error = 7e-31
relative error = 2.1473271849750446893395619612954e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.205
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (closed_form) = -3.2634587173167362073691517661896
y[1] (numeric) = -3.2634587173167362073691517661904
absolute error = 8e-31
relative error = 2.4513869158356376430558223874469e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.198
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (closed_form) = -3.267013293489680220086125564962
y[1] (numeric) = -3.2670132934896802200861255649626
absolute error = 6e-31
relative error = 1.8365398181747412858290012654983e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.191
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (closed_form) = -3.2705302145437241741897685108028
y[1] (numeric) = -3.2705302145437241741897685108033
absolute error = 5e-31
relative error = 1.5288040996427719451803239790336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.184
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (closed_form) = -3.2740094457216046512437880787382
y[1] (numeric) = -3.2740094457216046512437880787386
absolute error = 4e-31
relative error = 1.2217435735340049254838527262133e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.177
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (closed_form) = -3.2774509525152669313765771589246
y[1] (numeric) = -3.277450952515266931376577158925
absolute error = 4e-31
relative error = 1.2204606744550107224328582153911e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.17
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (closed_form) = -3.280854700666175565540763601633
y[1] (numeric) = -3.2808547006661755655407636016333
absolute error = 3e-31
relative error = 9.1439587354808849407776625611903e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.163
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (closed_form) = -3.2842206561656227021010065986901
y[1] (numeric) = -3.2842206561656227021010065986904
absolute error = 3e-31
relative error = 9.1345872098086898408857064021132e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.155
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (closed_form) = -3.2875487852550341649751026924152
y[1] (numeric) = -3.2875487852550341649751026924154
absolute error = 2e-31
relative error = 6.0835599123887934571495385938882e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.148
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
memory used=1423.1MB, alloc=44.3MB, time=14.81
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (closed_form) = -3.2908390544262732805737002081234
y[1] (numeric) = -3.2908390544262732805737002081236
absolute error = 2e-31
relative error = 6.0774774059823509583703152388160e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.141
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (closed_form) = -3.2940914304219424508041817035981
y[1] (numeric) = -3.2940914304219424508041817035981
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.134
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (closed_form) = -3.2973058802356824694245594362074
y[1] (numeric) = -3.2973058802356824694245594362073
absolute error = 1e-31
relative error = 3.0327789908545661399834923697482e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.126
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (closed_form) = -3.3004823711124695790535386829889
y[1] (numeric) = -3.3004823711124695790535386829886
absolute error = 3e-31
relative error = 9.0895804390823388264791098440987e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.119
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (closed_form) = -3.3036208705489102661632378282693
y[1] (numeric) = -3.3036208705489102661632378282689
absolute error = 4e-31
relative error = 1.2107926898207854772275881591084e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.111
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (closed_form) = -3.3067213462935337914014122742016
y[1] (numeric) = -3.3067213462935337914014122742013
absolute error = 3e-31
relative error = 9.0724306218383528233181568780811e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.104
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (closed_form) = -3.3097837663470824526104112487855
y[1] (numeric) = -3.3097837663470824526104112487853
absolute error = 2e-31
relative error = 6.0426908257132010018581470964161e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.096
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (closed_form) = -3.3128080989627995779305023000329
y[1] (numeric) = -3.3128080989627995779305023000327
absolute error = 2e-31
relative error = 6.0371743253893154144367532161189e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.089
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (closed_form) = -3.3157943126467152463956274903123
y[1] (numeric) = -3.3157943126467152463956274903121
absolute error = 2e-31
relative error = 6.0317372292118171567744097810411e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.081
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (closed_form) = -3.3187423761579297334501078576789
y[1] (numeric) = -3.3187423761579297334501078576786
absolute error = 3e-31
relative error = 9.0395687883223579601999018039363e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
memory used=1463.6MB, alloc=44.3MB, time=15.23
TOP MAIN SOLVE Loop
x[1] = -1.49
y[1] (closed_form) = -3.3216522585088946788352884071073
y[1] (numeric) = -3.3216522585088946788352884071069
absolute error = 4e-31
relative error = 1.2042199750902338021108459040658e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.066
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (closed_form) = -3.3245239289656919743156145497045
y[1] (numeric) = -3.3245239289656919743156145497041
absolute error = 4e-31
relative error = 1.2031797891869764680254043856962e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.058
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (closed_form) = -3.327357357048310368734152337707
y[1] (numeric) = -3.3273573570483103687341523377066
absolute error = 4e-31
relative error = 1.2021552153172958507300895060051e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (closed_form) = -3.3301525125309197879081088626627
y[1] (numeric) = -3.3301525125309197879081088626622
absolute error = 5e-31
relative error = 1.5014327365445476780480488864804e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.043
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.45
y[1] (closed_form) = -3.3329093654421433668954756087737
y[1] (numeric) = -3.3329093654421433668954756087733
absolute error = 4e-31
relative error = 1.2001526478561652898378036067412e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.035
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.44
y[1] (closed_form) = -3.3356278860653271921845061978269
y[1] (numeric) = -3.3356278860653271921845061978265
absolute error = 4e-31
relative error = 1.1991745292423368639104311386133e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.027
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.43
y[1] (closed_form) = -3.338308044938807751378350641171
y[1] (numeric) = -3.3383080449388077513783506411706
absolute error = 4e-31
relative error = 1.1982117725967141156052677320626e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.019
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.42
y[1] (closed_form) = -3.340949812856177087967800742318
y[1] (numeric) = -3.3409498128561770879678007423176
absolute error = 4e-31
relative error = 1.1972643182509829700106010361989e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.011
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (closed_form) = -3.3435531608665456588057554852532
y[1] (numeric) = -3.3435531608665456588057554852528
absolute error = 4e-31
relative error = 1.1963321076561927927057652706026e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.003
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1504.0MB, alloc=44.3MB, time=15.66
TOP MAIN SOLVE Loop
x[1] = -1.4
y[1] (closed_form) = -3.3461180602748028919176909125536
y[1] (numeric) = -3.3461180602748028919176909125533
absolute error = 3e-31
relative error = 8.9656131252990588100626107940906e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9953
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.39
y[1] (closed_form) = -3.3486444826418754423031159578506
y[1] (numeric) = -3.3486444826418754423031159578503
absolute error = 3e-31
relative error = 8.9588489179752629494718144517053e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9873
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (closed_form) = -3.3511323997849831434037137627597
y[1] (numeric) = -3.3511323997849831434037137627593
absolute error = 4e-31
relative error = 1.1936263694793586161847526594521e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9792
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (closed_form) = -3.353581783777892651934606992678
y[1] (numeric) = -3.3535817837778926519346069926776
absolute error = 4e-31
relative error = 1.1927545704562783236232299789857e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9711
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.36
y[1] (closed_form) = -3.3559926069511687837959453821641
y[1] (numeric) = -3.3559926069511687837959453821637
absolute error = 4e-31
relative error = 1.1918977389029158299875516154661e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.963
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.35
y[1] (closed_form) = -3.3583648418924235388027940021278
y[1] (numeric) = -3.3583648418924235388027940021274
absolute error = 4e-31
relative error = 1.1910558227932191920273863465877e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9548
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.34
y[1] (closed_form) = -3.3606984614465628119921013607537
y[1] (numeric) = -3.3606984614465628119921013607533
absolute error = 4e-31
relative error = 1.1902287711579631937224839428112e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9466
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (closed_form) = -3.3629934387160307892863472407452
y[1] (numeric) = -3.3629934387160307892863472407447
absolute error = 5e-31
relative error = 1.4867706675957618759390565342603e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9383
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (closed_form) = -3.3652497470610520253143109497287
y[1] (numeric) = -3.3652497470610520253143109497283
absolute error = 4e-31
relative error = 1.1886190626693574784174370027939e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.93
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (closed_form) = -3.3674673600998712012102612309293
y[1] (numeric) = -3.367467360099871201210261230929
absolute error = 3e-31
relative error = 8.9087723181703742504205300351608e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9217
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
memory used=1544.5MB, alloc=44.3MB, time=16.08
TOP MAIN SOLVE Loop
x[1] = -1.3
y[1] (closed_form) = -3.3696462517089905602337492597729
y[1] (numeric) = -3.3696462517089905602337492597726
absolute error = 3e-31
relative error = 8.9030116988644837863885451166958e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9134
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.29
y[1] (closed_form) = -3.3717863960234050190730857509674
y[1] (numeric) = -3.3717863960234050190730857509671
absolute error = 3e-31
relative error = 8.8973607685769182104237104623885e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.905
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (closed_form) = -3.3738877674368349527165020317708
y[1] (numeric) = -3.3738877674368349527165020317707
absolute error = 1e-31
relative error = 2.9639397304543614737236774327231e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8966
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.27
y[1] (closed_form) = -3.3759503406019566507959328122931
y[1] (numeric) = -3.3759503406019566507959328122929
absolute error = 2e-31
relative error = 5.9242577592044359399011420107100e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8881
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.26
y[1] (closed_form) = -3.377974090430630443329315114367
y[1] (numeric) = -3.3779740904306304433293151143669
absolute error = 1e-31
relative error = 2.9603542633227187752566537770732e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8797
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.25
y[1] (closed_form) = -3.3799589920941264938082732181464
y[1] (numeric) = -3.3799589920941264938082732181464
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8711
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.24
y[1] (closed_form) = -3.3819050210233482575990533613687
y[1] (numeric) = -3.3819050210233482575990533613688
absolute error = 1e-31
relative error = 2.9569133189240329130259420887187e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8626
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.23
y[1] (closed_form) = -3.3838121529090536036455840912158
y[1] (numeric) = -3.3838121529090536036455840912158
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.854
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (closed_form) = -3.3856803637020735974845684337978
y[1] (numeric) = -3.3856803637020735974845684337978
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8454
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (closed_form) = -3.3875096296135289436035622222185
y[1] (numeric) = -3.3875096296135289436035622222186
absolute error = 1e-31
relative error = 2.9520211286132552556255815781786e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8368
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
memory used=1584.9MB, alloc=44.3MB, time=16.48
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (closed_form) = -3.3892999271150440851940588215002
y[1] (numeric) = -3.3892999271150440851940588215003
absolute error = 1e-31
relative error = 2.9504618107114386457444656240063e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8281
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (closed_form) = -3.3910512329389589593726839177801
y[1] (numeric) = -3.3910512329389589593726839177802
absolute error = 1e-31
relative error = 2.9489380469587279299981740654083e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8194
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (closed_form) = -3.3927635240785384059647048103715
y[1] (numeric) = -3.3927635240785384059647048103716
absolute error = 1e-31
relative error = 2.9474497497481678286852835179067e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8107
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (closed_form) = -3.3944367777881792279651765686157
y[1] (numeric) = -3.3944367777881792279651765686158
absolute error = 1e-31
relative error = 2.9459968338299754669208957170760e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.802
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.16
y[1] (closed_form) = -3.3960709715836149018141823008664
y[1] (numeric) = -3.3960709715836149018141823008664
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7932
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.15
y[1] (closed_form) = -3.3976660832421179356437764402384
y[1] (numeric) = -3.3976660832421179356437764402384
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7844
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (closed_form) = -3.3992220908026998736754081905483
y[1] (numeric) = -3.3992220908026998736754081905485
absolute error = 2e-31
relative error = 5.8836991128394189346362147170679e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7755
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (closed_form) = -3.4007389725663089449677869056667
y[1] (numeric) = -3.4007389725663089449677869056669
absolute error = 2e-31
relative error = 5.8810747197416758336800594940884e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7667
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (closed_form) = -3.4022167070960253547363520056202
y[1] (numeric) = -3.4022167070960253547363520056204
absolute error = 2e-31
relative error = 5.8785203065653845201216955312220e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7578
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (closed_form) = -3.4036552732172542164867268724318
y[1] (numeric) = -3.4036552732172542164867268724321
absolute error = 3e-31
relative error = 8.8140535958692869928479976461253e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7489
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
memory used=1625.4MB, alloc=44.3MB, time=16.91
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (closed_form) = -3.4050546500179161232257688269053
y[1] (numeric) = -3.4050546500179161232257688269056
absolute error = 3e-31
relative error = 8.8104312804031357404228825507345e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7399
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.09
y[1] (closed_form) = -3.4064148168486353560350755732589
y[1] (numeric) = -3.4064148168486353560350755732593
absolute error = 4e-31
relative error = 1.1742551083959017156912335621676e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7309
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (closed_form) = -3.4077357533229257283130722204584
y[1] (numeric) = -3.4077357533229257283130722204586
absolute error = 2e-31
relative error = 5.8689996665667958580721383268073e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7219
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (closed_form) = -3.409017439317374064013081955914
y[1] (numeric) = -3.4090174393173740640130819559141
absolute error = 1e-31
relative error = 2.9333965513542261510075982860106e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7129
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (closed_form) = -3.4102598549718213082260774673834
y[1] (numeric) = -3.4102598549718213082260774673835
absolute error = 1e-31
relative error = 2.9323278651100413470078573070916e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7039
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (closed_form) = -3.411462980689541268478119090814
y[1] (numeric) = -3.4114629806895412684781190908141
absolute error = 1e-31
relative error = 2.9312937166853711577766641712423e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6948
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.04
y[1] (closed_form) = -3.4126267971374169851338092136835
y[1] (numeric) = -3.4126267971374169851338092136836
absolute error = 1e-31
relative error = 2.9302940504330007539450141489176e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6857
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (closed_form) = -3.4137512852461147293184304932508
y[1] (numeric) = -3.4137512852461147293184304932509
absolute error = 1e-31
relative error = 2.9293288129158621560576090026635e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6766
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (closed_form) = -3.4148364262102556267927877649577
y[1] (numeric) = -3.4148364262102556267927877649578
absolute error = 1e-31
relative error = 2.9283979528992783014533902180514e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6674
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
memory used=1665.9MB, alloc=44.3MB, time=17.33
TOP MAIN SOLVE Loop
x[1] = -1.01
y[1] (closed_form) = -3.4158822014885849062361399258645
y[1] (numeric) = -3.4158822014885849062361399258647
absolute error = 2e-31
relative error = 5.8550028426871193457450791845500e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6582
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (closed_form) = -3.4168885928041387704139883891606
y[1] (numeric) = -3.4168885928041387704139883891609
absolute error = 3e-31
relative error = 8.7799175141908542289992008689935e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.649
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (closed_form) = -3.4178555821444088887288827260301
y[1] (numeric) = -3.4178555821444088887288827260305
absolute error = 4e-31
relative error = 1.1703244633555715710151371385928e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6398
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (closed_form) = -3.4187831517615045096738116479505
y[1] (numeric) = -3.4187831517615045096738116479509
absolute error = 4e-31
relative error = 1.1700069359295360707538539855845e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6306
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (closed_form) = -3.4196712841723121917291683431605
y[1] (numeric) = -3.4196712841723121917291683431607
absolute error = 2e-31
relative error = 5.8485153507497855462152714651086e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6213
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (closed_form) = -3.4205199621586531512657131727943
y[1] (numeric) = -3.4205199621586531512657131727944
absolute error = 1e-31
relative error = 2.9235321268784843347288074294806e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.612
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (closed_form) = -3.421329168767438226037403662116
y[1] (numeric) = -3.4213291687674382260374036621161
absolute error = 1e-31
relative error = 2.9228406583288744668902584558768e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6027
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (closed_form) = -3.4220988873108204528694213973867
y[1] (numeric) = -3.4220988873108204528694213973868
absolute error = 1e-31
relative error = 2.9221832358731969288234252254515e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5934
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (closed_form) = -3.4228291013663452581681976660214
y[1] (numeric) = -3.4228291013663452581681976660214
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.584
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (closed_form) = -3.4235197947770982599017242635911
y[1] (numeric) = -3.4235197947770982599017242635911
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5746
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
memory used=1706.3MB, alloc=44.3MB, time=17.75
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (closed_form) = -3.4241709516518506797199326425361
y[1] (numeric) = -3.424170951651850679719932642536
absolute error = 1e-31
relative error = 2.9204149387389407641519285860557e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5652
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (closed_form) = -3.4247825563652023639064333007083
y[1] (numeric) = -3.4247825563652023639064333007082
absolute error = 1e-31
relative error = 2.9198934050321786403444422509691e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5558
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (closed_form) = -3.4253545935577224118744278094811
y[1] (numeric) = -3.425354593557722411874427809481
absolute error = 1e-31
relative error = 2.9194057802972055591128975468255e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5464
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (closed_form) = -3.4258870481360874109411379674585
y[1] (numeric) = -3.4258870481360874109411379674585
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5369
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (closed_form) = -3.4263799052732172761366400430078
y[1] (numeric) = -3.4263799052732172761366400430076
absolute error = 2e-31
relative error = 5.8370643515682226070113048853855e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5274
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (closed_form) = -3.4268331504084086938245467430242
y[1] (numeric) = -3.4268331504084086938245467430241
absolute error = 1e-31
relative error = 2.9181461603428820975031268092310e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5179
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (closed_form) = -3.4272467692474661679335452225349
y[1] (numeric) = -3.4272467692474661679335452225347
absolute error = 2e-31
relative error = 5.8355879650858865274317457733582e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5084
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (closed_form) = -3.4276207477628306676203759358621
y[1] (numeric) = -3.4276207477628306676203759358618
absolute error = 3e-31
relative error = 8.7524268895795023475867465485308e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (closed_form) = -3.427955072193705875206424230906
y[1] (numeric) = -3.4279550721937058752064242309057
absolute error = 3e-31
relative error = 8.7515732756677065454852127979454e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (closed_form) = -3.4282497290461820332516941093989
y[1] (numeric) = -3.4282497290461820332516941093984
absolute error = 5e-31
relative error = 1.4584701801729931330923315395193e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
memory used=1746.8MB, alloc=44.3MB, time=18.17
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (closed_form) = -3.4285047050933573896515413233304
y[1] (numeric) = -3.42850470509335738965154132333
absolute error = 4e-31
relative error = 1.1666893716253718618510276361774e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (closed_form) = -3.4287199873754572396631607567047
y[1] (numeric) = -3.4287199873754572396631607567042
absolute error = 5e-31
relative error = 1.4582701469965450158894779212639e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4606
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (closed_form) = -3.4288955631999505637904506577719
y[1] (numeric) = -3.4288955631999505637904506577714
absolute error = 5e-31
relative error = 1.4581954766023397232109507884672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.451
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (closed_form) = -3.4290314201416642604775135452657
y[1] (numeric) = -3.4290314201416642604775135452652
absolute error = 5e-31
relative error = 1.4581377034432172104644455773472e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4413
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (closed_form) = -3.4291275460428949725827003182052
y[1] (numeric) = -3.4291275460428949725827003182048
absolute error = 4e-31
relative error = 1.1664774629383132257539315300874e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (closed_form) = -3.4291839290135185066267600576963
y[1] (numeric) = -3.4291839290135185066267600576959
absolute error = 4e-31
relative error = 1.1664582836041371247086753477908e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.422
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (closed_form) = -3.4292005574310968438303230259608
y[1] (numeric) = -3.4292005574310968438303230259604
absolute error = 4e-31
relative error = 1.1664526273716996698430410320231e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4123
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (closed_form) = -3.4291774199409827419776182475732
y[1] (numeric) = -3.4291774199409827419776182475727
absolute error = 5e-31
relative error = 1.4580756221374079924997955359623e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (closed_form) = -3.4291145054564219271650096055072
y[1] (numeric) = -3.4291145054564219271650096055069
absolute error = 3e-31
relative error = 8.7486142420335831356637016709050e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (closed_form) = -3.4290118031586528745146254049633
y[1] (numeric) = -3.4290118031586528745146254049627
absolute error = 6e-31
relative error = 1.7497752543380187152259602661114e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3832
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=1787.2MB, alloc=44.3MB, time=18.59
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (closed_form) = -3.4288693024970041769550556558282
y[1] (numeric) = -3.4288693024970041769550556558275
absolute error = 7e-31
relative error = 2.0414893022905226177537600379755e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3735
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (closed_form) = -3.4286869931889895011927987047328
y[1] (numeric) = -3.4286869931889895011927987047322
absolute error = 6e-31
relative error = 1.7499410158812591034003964577049e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3637
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (closed_form) = -3.4284648652204001300198541146393
y[1] (numeric) = -3.4284648652204001300198541146385
absolute error = 8e-31
relative error = 2.3334058578680277785307849282469e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.354
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (closed_form) = -3.4282029088453950901245816482822
y[1] (numeric) = -3.4282029088453950901245816482813
absolute error = 9e-31
relative error = 2.6252821782451505161374138115558e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3442
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (closed_form) = -3.4279011145865888645946766660965
y[1] (numeric) = -3.4279011145865888645946766660957
absolute error = 8e-31
relative error = 2.3337896084452292060427440819365e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3344
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (closed_form) = -3.427559473235136689322850003912
y[1] (numeric) = -3.4275594732351366893228500039112
absolute error = 8e-31
relative error = 2.3340222284893335650625711398403e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3246
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (closed_form) = -3.4271779758508174325475452550454
y[1] (numeric) = -3.4271779758508174325475452550446
absolute error = 8e-31
relative error = 2.3342820409009987720637029954899e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3148
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (closed_form) = -3.426756613762114056782778149773
y[1] (numeric) = -3.4267566137621140567827781497721
absolute error = 9e-31
relative error = 2.6263902034522435770528020809723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3049
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (closed_form) = -3.4262953785662916624129412067458
y[1] (numeric) = -3.426295378566291662412941206745
absolute error = 8e-31
relative error = 2.3348833407782669668623045615025e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2951
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
memory used=1827.6MB, alloc=44.3MB, time=19.00
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (closed_form) = -3.4257942621294731122501818299001
y[1] (numeric) = -3.4257942621294731122501818298993
absolute error = 8e-31
relative error = 2.3352248815511768075877251607600e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2853
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (closed_form) = -3.4252532565867122363737333449255
y[1] (numeric) = -3.4252532565867122363737333449246
absolute error = 9e-31
relative error = 2.6275429364801364070492931715788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2754
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (closed_form) = -3.424672354342064616592355915445
y[1] (numeric) = -3.4246723543420646165923559154441
absolute error = 9e-31
relative error = 2.6279886274636181087172071727101e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2655
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (closed_form) = -3.4240515480686559498928276547324
y[1] (numeric) = -3.4240515480686559498928276547315
absolute error = 9e-31
relative error = 2.6284651015480390284396126384638e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2557
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (closed_form) = -3.4233908307087479902592153580006
y[1] (numeric) = -3.4233908307087479902592153579998
absolute error = 8e-31
relative error = 2.3368643533884070391190379194187e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
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) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (closed_form) = -3.422690195473802068269448926932
y[1] (numeric) = -3.4226901954738020682694489269312
absolute error = 8e-31
relative error = 2.3373427167259472593197157630509e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2359
Order of pole (three term test) = 32.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (closed_form) = -3.4219496358445401878975235460376
y[1] (numeric) = -3.4219496358445401878975235460369
absolute error = 7e-31
relative error = 2.0456174826992723482310099544619e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.226
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (closed_form) = -3.4211691455710036999714588034286
y[1] (numeric) = -3.4211691455710036999714588034279
absolute error = 7e-31
relative error = 2.0460841607501631942137312040834e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2161
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (closed_form) = -3.4203487186726095517589540304144
y[1] (numeric) = -3.4203487186726095517589540304137
absolute error = 7e-31
relative error = 2.0465749476903056940853475557675e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2061
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.53
y[1] (closed_form) = -3.4194883494382041121744939687131
y[1] (numeric) = -3.4194883494382041121744939687126
absolute error = 5e-31
relative error = 1.4622070582054949572936189162176e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1962
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=1868.1MB, alloc=44.3MB, time=19.42
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (closed_form) = -3.4185880324261145721234782646448
y[1] (numeric) = -3.4185880324261145721234782646443
absolute error = 5e-31
relative error = 1.4625921440588393700733598599262e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1863
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (closed_form) = -3.4176477624641979195207720400917
y[1] (numeric) = -3.4176477624641979195207720400913
absolute error = 4e-31
relative error = 1.1703956282246926254075128704987e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1763
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (closed_form) = -3.4166675346498874885429027038551
y[1] (numeric) = -3.4166675346498874885429027038548
absolute error = 3e-31
relative error = 8.7804855742495173315753450001171e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1664
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (closed_form) = -3.4156473443502370826949600478413
y[1] (numeric) = -3.415647344350237082694960047841
absolute error = 3e-31
relative error = 8.7831081418936526567213479532747e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1564
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (closed_form) = -3.4145871872019626712950923238095
y[1] (numeric) = -3.4145871872019626712950923238091
absolute error = 4e-31
relative error = 1.1714446815100205267793642686874e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1465
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (closed_form) = -3.4134870591114816590013302216654
y[1] (numeric) = -3.4134870591114816590013302216651
absolute error = 3e-31
relative error = 8.7886666861449568651840132900735e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1365
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (closed_form) = -3.4123469562549497280273132729564
y[1] (numeric) = -3.4123469562549497280273132729562
absolute error = 2e-31
relative error = 5.8610687179213443746945173052820e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1265
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (closed_form) = -3.4111668750782952527153389867141
y[1] (numeric) = -3.4111668750782952527153389867137
absolute error = 4e-31
relative error = 1.1726192668038820229710147335774e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1166
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (closed_form) = -3.4099468122972512861570037925001
y[1] (numeric) = -3.4099468122972512861570037924998
absolute error = 3e-31
relative error = 8.7977911830798507057443118721765e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1066
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (closed_form) = -3.4086867648973851185735564207976
y[1] (numeric) = -3.4086867648973851185735564207973
absolute error = 3e-31
relative error = 8.8010433545668189374560684694220e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09661
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
memory used=1908.7MB, alloc=44.3MB, time=19.84
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (closed_form) = -3.4073867301341254071899384970856
y[1] (numeric) = -3.4073867301341254071899384970853
absolute error = 3e-31
relative error = 8.8044012541010001810772146165115e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08663
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (closed_form) = -3.4060467055327868773583436663588
y[1] (numeric) = -3.4060467055327868773583436663584
absolute error = 4e-31
relative error = 1.1743820169883151007299538173293e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07664
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (closed_form) = -3.4046666888885925947089853027916
y[1] (numeric) = -3.4046666888885925947089853027913
absolute error = 3e-31
relative error = 8.8114352273916993510355196176180e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06665
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (closed_form) = -3.4032466782666938081276235979759
y[1] (numeric) = -3.4032466782666938081276235979754
absolute error = 5e-31
relative error = 1.4691853023556164848975565664462e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05666
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (closed_form) = -3.4017866720021873633812653639273
y[1] (numeric) = -3.4017866720021873633812653639268
absolute error = 5e-31
relative error = 1.4698158591635475073119054676523e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04666
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (closed_form) = -3.4002866687001306872353140371037
y[1] (numeric) = -3.4002866687001306872353140371033
absolute error = 4e-31
relative error = 1.1763714032761623264936701259302e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03666
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (closed_form) = -3.3987466672355543419273129302306
y[1] (numeric) = -3.3987466672355543419273129302302
absolute error = 4e-31
relative error = 1.1769044273174641562986176044332e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02667
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (closed_form) = -3.3971666667534721498842915529838
y[1] (numeric) = -3.3971666667534721498842915529832
absolute error = 6e-31
relative error = 1.7661776970553950129693120357963e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01667
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
TOP MAIN SOLVE Loop
x[1] = -0.33967564517668046387662788466246
y[1] (closed_form) = -3.395493451436252280062302436758
y[1] (numeric) = -3.3954934514362522800623024367576
absolute error = 4e-31
relative error = 1.1780320172044651799589521793519e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.00070469898288217293521933271003028
SETTING H FOR POLE
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.006342
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=1949.3MB, alloc=44.3MB, time=20.27
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memory used=1990.5MB, alloc=44.3MB, time=20.69
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memory used=2031.0MB, alloc=44.3MB, time=21.09
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memory used=2071.5MB, alloc=44.3MB, time=21.52
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memory used=2112.0MB, alloc=44.3MB, time=21.92
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memory used=2152.6MB, alloc=44.3MB, time=22.34
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memory used=2193.1MB, alloc=44.3MB, time=22.75
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memory used=2233.5MB, alloc=44.3MB, time=23.17
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memory used=2274.1MB, alloc=44.3MB, time=23.58
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memory used=2314.5MB, alloc=44.3MB, time=24.00
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memory used=2355.0MB, alloc=44.3MB, time=24.41
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memory used=2395.4MB, alloc=44.3MB, time=24.83
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memory used=2435.9MB, alloc=44.3MB, time=25.25
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memory used=2476.5MB, alloc=44.3MB, time=25.66
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memory used=2516.9MB, alloc=44.3MB, time=26.08
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memory used=2557.4MB, alloc=44.3MB, time=26.50
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memory used=2598.0MB, alloc=44.3MB, time=26.91
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memory used=2638.5MB, alloc=44.3MB, time=27.33
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memory used=2679.0MB, alloc=44.3MB, time=27.73
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memory used=2719.6MB, alloc=44.3MB, time=28.16
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memory used=2760.0MB, alloc=44.3MB, time=28.56
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memory used=2800.5MB, alloc=44.3MB, time=28.98
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memory used=2841.0MB, alloc=44.3MB, time=29.41
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memory used=2881.6MB, alloc=44.3MB, time=29.81
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memory used=2922.2MB, alloc=44.3MB, time=30.23
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memory used=2962.8MB, alloc=44.3MB, time=30.66
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memory used=3003.3MB, alloc=44.3MB, time=31.06
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memory used=3043.7MB, alloc=44.3MB, time=31.48
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memory used=3084.3MB, alloc=44.3MB, time=31.91
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memory used=3124.7MB, alloc=44.3MB, time=32.31
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memory used=3165.3MB, alloc=44.3MB, time=32.73
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memory used=3205.8MB, alloc=44.3MB, time=33.16
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memory used=3246.4MB, alloc=44.3MB, time=33.58
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memory used=3287.0MB, alloc=44.3MB, time=33.98
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memory used=3327.4MB, alloc=44.3MB, time=34.42
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memory used=3367.8MB, alloc=44.3MB, time=34.83
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memory used=3408.3MB, alloc=44.3MB, time=35.25
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memory used=3448.8MB, alloc=44.3MB, time=35.67
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TOP MAIN SOLVE Loop
x[1] = -0.32999956507812628663912984295438
y[1] (closed_form) = -3.393886593599893012800216209982
y[1] (numeric) = -3.3938865935998930128002162099853
absolute error = 3.3e-30
relative error = 9.7233655544739119522397076605198e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 1e-06
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NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.003334
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
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memory used=3489.2MB, alloc=44.3MB, time=36.08
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memory used=3651.4MB, alloc=44.3MB, time=37.75
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memory used=3691.8MB, alloc=44.3MB, time=38.14
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memory used=3732.1MB, alloc=44.3MB, time=38.56
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memory used=3772.6MB, alloc=44.3MB, time=38.97
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memory used=3813.1MB, alloc=44.3MB, time=39.39
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memory used=3853.6MB, alloc=44.3MB, time=39.81
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memory used=3894.2MB, alloc=44.3MB, time=40.22
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memory used=3934.7MB, alloc=44.3MB, time=40.64
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memory used=3975.2MB, alloc=44.3MB, time=41.05
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memory used=4015.7MB, alloc=44.3MB, time=41.47
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memory used=4056.2MB, alloc=44.3MB, time=41.89
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memory used=4096.6MB, alloc=44.3MB, time=42.30
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memory used=4137.2MB, alloc=44.3MB, time=42.72
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memory used=4177.7MB, alloc=44.3MB, time=43.14
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memory used=4218.3MB, alloc=44.3MB, time=43.55
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memory used=4258.8MB, alloc=44.3MB, time=43.97
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memory used=4299.3MB, alloc=44.3MB, time=44.38
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memory used=4339.8MB, alloc=44.3MB, time=44.80
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memory used=4380.4MB, alloc=44.3MB, time=45.22
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memory used=4420.9MB, alloc=44.3MB, time=45.63
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memory used=4461.4MB, alloc=44.3MB, time=46.05
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memory used=4501.8MB, alloc=44.3MB, time=46.47
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memory used=4542.4MB, alloc=44.3MB, time=46.87
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memory used=4582.9MB, alloc=44.3MB, time=47.30
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memory used=4623.5MB, alloc=44.3MB, time=47.70
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memory used=4664.0MB, alloc=44.3MB, time=48.13
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memory used=4704.6MB, alloc=44.3MB, time=48.55
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memory used=4745.1MB, alloc=44.3MB, time=48.95
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memory used=4785.7MB, alloc=44.3MB, time=49.38
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memory used=4826.3MB, alloc=44.3MB, time=49.80
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memory used=4866.7MB, alloc=44.3MB, time=50.20
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memory used=4907.1MB, alloc=44.3MB, time=50.63
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memory used=4947.7MB, alloc=44.3MB, time=51.05
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memory used=4988.3MB, alloc=44.3MB, time=51.45
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memory used=5028.9MB, alloc=44.3MB, time=51.87
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memory used=5069.5MB, alloc=44.3MB, time=52.30
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memory used=5110.0MB, alloc=44.3MB, time=52.70
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memory used=5150.5MB, alloc=44.3MB, time=53.13
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memory used=5191.0MB, alloc=44.3MB, time=53.55
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memory used=5231.6MB, alloc=44.3MB, time=53.95
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memory used=5272.1MB, alloc=44.3MB, time=54.38
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memory used=5312.7MB, alloc=44.3MB, time=54.80
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memory used=5353.2MB, alloc=44.3MB, time=55.20
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memory used=5393.7MB, alloc=44.3MB, time=55.63
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memory used=5434.3MB, alloc=44.3MB, time=56.05
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memory used=5474.9MB, alloc=44.3MB, time=56.45
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memory used=5515.4MB, alloc=44.3MB, time=56.87
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memory used=5556.0MB, alloc=44.3MB, time=57.30
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memory used=5596.6MB, alloc=44.3MB, time=57.70
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memory used=5637.1MB, alloc=44.3MB, time=58.12
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memory used=5677.6MB, alloc=44.3MB, time=58.55
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memory used=5718.1MB, alloc=44.3MB, time=58.95
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memory used=5758.7MB, alloc=44.3MB, time=59.38
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memory used=5799.3MB, alloc=44.3MB, time=59.80
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memory used=5839.9MB, alloc=44.3MB, time=60.22
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memory used=5880.4MB, alloc=44.3MB, time=60.64
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memory used=5921.0MB, alloc=44.3MB, time=61.05
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memory used=5961.5MB, alloc=44.3MB, time=61.47
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memory used=6002.0MB, alloc=44.3MB, time=61.89
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memory used=6042.4MB, alloc=44.3MB, time=62.30
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memory used=6083.0MB, alloc=44.3MB, time=62.72
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memory used=6123.5MB, alloc=44.3MB, time=63.14
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memory used=6164.1MB, alloc=44.3MB, time=63.55
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memory used=6204.6MB, alloc=44.3MB, time=63.97
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memory used=6245.2MB, alloc=44.3MB, time=64.39
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memory used=6285.8MB, alloc=44.3MB, time=64.80
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memory used=6326.4MB, alloc=44.3MB, time=65.22
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memory used=6367.0MB, alloc=44.3MB, time=65.64
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memory used=6407.5MB, alloc=44.3MB, time=66.05
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memory used=6448.0MB, alloc=44.3MB, time=66.47
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memory used=6488.5MB, alloc=44.3MB, time=66.87
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memory used=6529.1MB, alloc=44.3MB, time=67.30
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memory used=6569.5MB, alloc=44.3MB, time=67.70
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memory used=6610.1MB, alloc=44.3MB, time=68.13
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memory used=6650.6MB, alloc=44.3MB, time=68.55
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memory used=6691.2MB, alloc=44.3MB, time=68.95
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memory used=6731.8MB, alloc=44.3MB, time=69.38
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memory used=6772.3MB, alloc=44.3MB, time=69.78
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memory used=6812.9MB, alloc=44.3MB, time=70.20
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memory used=6853.4MB, alloc=44.3MB, time=70.63
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memory used=6894.0MB, alloc=44.3MB, time=71.03
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memory used=6934.6MB, alloc=44.3MB, time=71.45
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memory used=6975.1MB, alloc=44.3MB, time=71.86
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memory used=7015.7MB, alloc=44.3MB, time=72.28
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memory used=7056.2MB, alloc=44.3MB, time=72.70
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memory used=7096.7MB, alloc=44.3MB, time=73.11
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memory used=7137.3MB, alloc=44.3MB, time=73.53
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memory used=7177.9MB, alloc=44.3MB, time=73.95
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memory used=7218.4MB, alloc=44.3MB, time=74.36
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memory used=7259.0MB, alloc=44.3MB, time=74.78
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memory used=7299.5MB, alloc=44.3MB, time=75.20
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memory used=7340.0MB, alloc=44.3MB, time=75.62
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memory used=7380.5MB, alloc=44.3MB, time=76.03
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memory used=7421.0MB, alloc=44.3MB, time=76.45
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memory used=7461.6MB, alloc=44.3MB, time=76.88
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memory used=7502.1MB, alloc=44.3MB, time=77.28
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memory used=7542.6MB, alloc=44.3MB, time=77.70
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memory used=7583.1MB, alloc=44.3MB, time=78.11
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memory used=7623.6MB, alloc=44.3MB, time=78.53
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memory used=7664.2MB, alloc=44.3MB, time=78.95
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memory used=7704.8MB, alloc=44.3MB, time=79.36
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memory used=7745.3MB, alloc=44.3MB, time=79.78
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memory used=7785.8MB, alloc=44.3MB, time=80.20
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memory used=7826.4MB, alloc=44.3MB, time=80.61
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memory used=7867.0MB, alloc=44.3MB, time=81.03
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memory used=7907.4MB, alloc=44.3MB, time=81.45
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memory used=7948.0MB, alloc=44.3MB, time=81.86
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TOP MAIN SOLVE Loop
x[1] = -0.31999956507812628663912984295438
y[1] (closed_form) = -3.3921865918956267325438828296883
y[1] (numeric) = -3.3921865918956267325438828296892
absolute error = 9e-31
relative error = 2.6531559382677138281512320746251e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 1e-06
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NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01333
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
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memory used=7988.7MB, alloc=44.3MB, time=82.27
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memory used=8029.2MB, alloc=44.3MB, time=82.67
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memory used=8069.9MB, alloc=44.3MB, time=83.09
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memory used=8110.4MB, alloc=44.3MB, time=83.50
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memory used=8150.9MB, alloc=44.3MB, time=83.92
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memory used=8191.4MB, alloc=44.3MB, time=84.33
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memory used=8232.0MB, alloc=44.3MB, time=84.75
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memory used=8272.6MB, alloc=44.3MB, time=85.17
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memory used=8313.2MB, alloc=44.3MB, time=85.59
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memory used=8353.7MB, alloc=44.3MB, time=86.00
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memory used=8394.2MB, alloc=44.3MB, time=86.42
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memory used=8434.7MB, alloc=44.3MB, time=86.83
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memory used=8475.2MB, alloc=44.3MB, time=87.25
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memory used=8515.6MB, alloc=44.3MB, time=87.67
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memory used=8556.1MB, alloc=44.3MB, time=88.08
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memory used=8596.7MB, alloc=44.3MB, time=88.50
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memory used=8637.2MB, alloc=44.3MB, time=88.91
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memory used=8677.9MB, alloc=44.3MB, time=89.33
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memory used=8718.5MB, alloc=44.3MB, time=89.75
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memory used=8759.0MB, alloc=44.3MB, time=90.16
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memory used=8799.6MB, alloc=44.3MB, time=90.58
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memory used=8840.1MB, alloc=44.3MB, time=91.00
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memory used=8880.6MB, alloc=44.3MB, time=91.41
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memory used=8921.1MB, alloc=44.3MB, time=91.83
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memory used=8961.6MB, alloc=44.3MB, time=92.25
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memory used=9002.2MB, alloc=44.3MB, time=92.66
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memory used=9042.7MB, alloc=44.3MB, time=93.08
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memory used=9083.3MB, alloc=44.3MB, time=93.50
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memory used=9123.8MB, alloc=44.3MB, time=93.91
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memory used=9164.4MB, alloc=44.3MB, time=94.33
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memory used=9204.9MB, alloc=44.3MB, time=94.75
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memory used=9245.5MB, alloc=44.3MB, time=95.16
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memory used=9286.0MB, alloc=44.3MB, time=95.58
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memory used=9326.5MB, alloc=44.3MB, time=96.00
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memory used=9367.1MB, alloc=44.3MB, time=96.41
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memory used=9407.6MB, alloc=44.3MB, time=96.83
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memory used=9448.2MB, alloc=44.3MB, time=97.23
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memory used=9488.8MB, alloc=44.3MB, time=97.66
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memory used=9529.3MB, alloc=44.3MB, time=98.08
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memory used=9569.9MB, alloc=44.3MB, time=98.48
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memory used=9610.5MB, alloc=44.3MB, time=98.91
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memory used=9651.0MB, alloc=44.3MB, time=99.33
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memory used=9691.5MB, alloc=44.3MB, time=99.73
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memory used=9732.0MB, alloc=44.3MB, time=100.16
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memory used=9772.5MB, alloc=44.3MB, time=100.56
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memory used=9813.2MB, alloc=44.3MB, time=100.98
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memory used=9853.7MB, alloc=44.3MB, time=101.41
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memory used=9894.3MB, alloc=44.3MB, time=101.81
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memory used=9934.8MB, alloc=44.3MB, time=102.23
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memory used=9975.4MB, alloc=44.3MB, time=102.66
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memory used=10015.9MB, alloc=44.3MB, time=103.08
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memory used=10056.4MB, alloc=44.3MB, time=103.48
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memory used=10097.0MB, alloc=44.3MB, time=103.91
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memory used=10137.4MB, alloc=44.3MB, time=104.31
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memory used=10177.9MB, alloc=44.3MB, time=104.73
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memory used=10218.4MB, alloc=44.3MB, time=105.14
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memory used=10259.0MB, alloc=44.3MB, time=105.56
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memory used=10299.5MB, alloc=44.3MB, time=105.98
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memory used=10340.1MB, alloc=44.3MB, time=106.39
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memory used=10380.6MB, alloc=44.3MB, time=106.81
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memory used=10421.2MB, alloc=44.3MB, time=107.23
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memory used=10461.8MB, alloc=44.3MB, time=107.64
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memory used=10502.3MB, alloc=44.3MB, time=108.06
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memory used=10542.7MB, alloc=44.3MB, time=108.48
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memory used=10583.3MB, alloc=44.3MB, time=108.89
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memory used=10623.9MB, alloc=44.3MB, time=109.31
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memory used=10664.4MB, alloc=44.3MB, time=109.72
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memory used=10704.8MB, alloc=44.3MB, time=110.14
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memory used=10745.5MB, alloc=44.3MB, time=110.55
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memory used=10785.9MB, alloc=44.3MB, time=110.97
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memory used=10826.5MB, alloc=44.3MB, time=111.39
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memory used=10867.0MB, alloc=44.3MB, time=111.80
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memory used=10907.6MB, alloc=44.3MB, time=112.22
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memory used=10948.0MB, alloc=44.3MB, time=112.63
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memory used=10988.6MB, alloc=44.3MB, time=113.05
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memory used=11029.2MB, alloc=44.3MB, time=113.47
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memory used=11069.8MB, alloc=44.3MB, time=113.88
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memory used=11110.3MB, alloc=44.3MB, time=114.31
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memory used=11150.9MB, alloc=44.3MB, time=114.73
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memory used=11191.4MB, alloc=44.3MB, time=115.16
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memory used=11231.9MB, alloc=44.3MB, time=115.56
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memory used=11272.4MB, alloc=44.3MB, time=115.98
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memory used=11312.9MB, alloc=44.3MB, time=116.41
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memory used=11353.4MB, alloc=44.3MB, time=116.81
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memory used=11393.9MB, alloc=44.3MB, time=117.23
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memory used=11434.5MB, alloc=44.3MB, time=117.64
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memory used=11475.0MB, alloc=44.3MB, time=118.06
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memory used=11515.6MB, alloc=44.3MB, time=118.48
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memory used=11556.2MB, alloc=44.3MB, time=118.89
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memory used=11596.8MB, alloc=44.3MB, time=119.31
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memory used=11637.3MB, alloc=44.3MB, time=119.73
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memory used=11677.8MB, alloc=44.3MB, time=120.16
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memory used=11718.3MB, alloc=44.3MB, time=120.58
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memory used=11758.8MB, alloc=44.3MB, time=120.98
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memory used=11799.4MB, alloc=44.3MB, time=121.41
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memory used=11840.0MB, alloc=44.3MB, time=121.81
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memory used=11880.6MB, alloc=44.3MB, time=122.23
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memory used=11921.2MB, alloc=44.3MB, time=122.66
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memory used=11961.7MB, alloc=44.3MB, time=123.06
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memory used=12002.3MB, alloc=44.3MB, time=123.48
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memory used=12042.8MB, alloc=44.3MB, time=123.91
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memory used=12083.3MB, alloc=44.3MB, time=124.31
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memory used=12123.8MB, alloc=44.3MB, time=124.73
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memory used=12164.4MB, alloc=44.3MB, time=125.16
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memory used=12204.9MB, alloc=44.3MB, time=125.56
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memory used=12245.6MB, alloc=44.3MB, time=125.98
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memory used=12286.1MB, alloc=44.3MB, time=126.41
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memory used=12326.7MB, alloc=44.3MB, time=126.81
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memory used=12367.3MB, alloc=44.3MB, time=127.23
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memory used=12407.8MB, alloc=44.3MB, time=127.66
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TOP MAIN SOLVE Loop
x[1] = -0.30999956507812628663912984295438
y[1] (closed_form) = -3.3904465904538756029273333238475
y[1] (numeric) = -3.3904465904538756029273333238476
absolute error = 1e-31
relative error = 2.9494639520811063035907468795667e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 1e-06
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NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02333
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
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memory used=12448.5MB, alloc=44.3MB, time=128.06
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memory used=12489.0MB, alloc=44.3MB, time=128.48
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memory used=12529.4MB, alloc=44.3MB, time=128.91
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memory used=12570.0MB, alloc=44.3MB, time=129.31
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memory used=12610.5MB, alloc=44.3MB, time=129.73
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memory used=12651.2MB, alloc=44.3MB, time=130.16
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memory used=12691.7MB, alloc=44.3MB, time=130.58
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memory used=12732.2MB, alloc=44.3MB, time=130.98
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memory used=12772.7MB, alloc=44.3MB, time=131.41
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memory used=12813.3MB, alloc=44.3MB, time=131.83
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memory used=12853.9MB, alloc=44.3MB, time=132.23
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memory used=12894.3MB, alloc=44.3MB, time=132.66
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memory used=12934.9MB, alloc=44.3MB, time=133.08
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memory used=12975.3MB, alloc=44.3MB, time=133.50
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memory used=13016.0MB, alloc=44.3MB, time=133.91
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memory used=13056.6MB, alloc=44.3MB, time=134.33
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memory used=13097.2MB, alloc=44.3MB, time=134.75
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memory used=13137.7MB, alloc=44.3MB, time=135.17
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memory used=13178.3MB, alloc=44.3MB, time=135.56
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memory used=13218.8MB, alloc=44.3MB, time=135.98
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memory used=13259.3MB, alloc=44.3MB, time=136.41
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memory used=13299.8MB, alloc=44.3MB, time=136.81
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memory used=13340.3MB, alloc=44.3MB, time=137.23
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memory used=13380.9MB, alloc=44.3MB, time=137.66
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memory used=13421.6MB, alloc=44.3MB, time=138.06
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memory used=13462.1MB, alloc=44.3MB, time=138.48
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memory used=13502.6MB, alloc=44.3MB, time=138.91
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memory used=13543.2MB, alloc=44.3MB, time=139.31
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memory used=13583.8MB, alloc=44.3MB, time=139.73
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memory used=13624.3MB, alloc=44.3MB, time=140.16
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memory used=13664.9MB, alloc=44.3MB, time=140.56
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memory used=13705.4MB, alloc=44.3MB, time=140.98
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memory used=13746.0MB, alloc=44.3MB, time=141.41
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memory used=13786.6MB, alloc=44.3MB, time=141.83
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memory used=13827.1MB, alloc=44.3MB, time=142.25
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memory used=13867.7MB, alloc=44.3MB, time=142.67
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memory used=13908.2MB, alloc=44.3MB, time=143.09
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memory used=13948.8MB, alloc=44.3MB, time=143.50
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memory used=13989.3MB, alloc=44.3MB, time=143.92
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memory used=14029.8MB, alloc=44.3MB, time=144.34
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memory used=14070.3MB, alloc=44.3MB, time=144.75
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memory used=14110.9MB, alloc=44.3MB, time=145.17
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memory used=14151.5MB, alloc=44.3MB, time=145.59
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memory used=14192.1MB, alloc=44.3MB, time=146.02
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memory used=14232.7MB, alloc=44.3MB, time=146.42
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memory used=14273.2MB, alloc=44.3MB, time=146.84
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memory used=14313.8MB, alloc=44.3MB, time=147.27
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memory used=14354.3MB, alloc=44.3MB, time=147.69
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memory used=14394.9MB, alloc=44.3MB, time=148.09
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memory used=14435.3MB, alloc=44.3MB, time=148.51
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memory used=14475.9MB, alloc=44.3MB, time=148.94
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memory used=14516.4MB, alloc=44.3MB, time=149.36
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memory used=14557.0MB, alloc=44.3MB, time=149.76
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memory used=14597.6MB, alloc=44.3MB, time=150.19
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memory used=14638.2MB, alloc=44.3MB, time=150.61
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memory used=14678.7MB, alloc=44.3MB, time=151.02
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memory used=14719.2MB, alloc=44.3MB, time=151.44
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memory used=14759.8MB, alloc=44.3MB, time=151.86
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memory used=14800.3MB, alloc=44.3MB, time=152.26
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memory used=14840.8MB, alloc=44.3MB, time=152.69
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memory used=14881.3MB, alloc=44.3MB, time=153.11
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memory used=14921.9MB, alloc=44.3MB, time=153.52
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memory used=14962.6MB, alloc=44.3MB, time=153.94
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memory used=15003.1MB, alloc=44.3MB, time=154.36
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memory used=15043.6MB, alloc=44.3MB, time=154.77
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memory used=15084.1MB, alloc=44.3MB, time=155.19
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memory used=15124.6MB, alloc=44.3MB, time=155.59
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memory used=15165.2MB, alloc=44.3MB, time=156.01
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memory used=15205.7MB, alloc=44.3MB, time=156.44
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memory used=15246.2MB, alloc=44.3MB, time=156.84
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memory used=15286.8MB, alloc=44.3MB, time=157.26
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memory used=15327.4MB, alloc=44.3MB, time=157.69
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memory used=15367.9MB, alloc=44.3MB, time=158.11
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memory used=15408.5MB, alloc=44.3MB, time=158.51
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memory used=15449.1MB, alloc=44.3MB, time=158.94
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memory used=15489.5MB, alloc=44.3MB, time=159.36
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memory used=15530.1MB, alloc=44.3MB, time=159.78
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memory used=15570.6MB, alloc=44.3MB, time=160.19
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memory used=15611.1MB, alloc=44.3MB, time=160.61
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memory used=15651.6MB, alloc=44.3MB, time=161.03
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memory used=15692.3MB, alloc=44.3MB, time=161.44
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memory used=15732.8MB, alloc=44.3MB, time=161.86
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memory used=15773.4MB, alloc=44.3MB, time=162.28
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memory used=15814.0MB, alloc=44.3MB, time=162.69
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memory used=15854.5MB, alloc=44.3MB, time=163.11
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memory used=15895.1MB, alloc=44.3MB, time=163.53
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memory used=15935.6MB, alloc=44.3MB, time=163.94
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memory used=15976.1MB, alloc=44.3MB, time=164.36
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memory used=16016.6MB, alloc=44.3MB, time=164.78
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memory used=16057.1MB, alloc=44.3MB, time=165.19
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memory used=16097.7MB, alloc=44.3MB, time=165.61
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memory used=16138.3MB, alloc=44.3MB, time=166.03
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memory used=16178.9MB, alloc=44.3MB, time=166.44
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memory used=16219.4MB, alloc=44.3MB, time=166.86
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memory used=16260.0MB, alloc=44.3MB, time=167.27
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memory used=16300.5MB, alloc=44.3MB, time=167.69
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memory used=16340.9MB, alloc=44.3MB, time=168.11
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memory used=16381.4MB, alloc=44.3MB, time=168.52
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memory used=16422.0MB, alloc=44.3MB, time=168.94
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memory used=16462.5MB, alloc=44.3MB, time=169.36
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memory used=16503.2MB, alloc=44.3MB, time=169.76
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memory used=16543.7MB, alloc=44.3MB, time=170.19
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memory used=16584.3MB, alloc=44.3MB, time=170.61
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memory used=16624.8MB, alloc=44.3MB, time=171.02
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memory used=16665.4MB, alloc=44.3MB, time=171.44
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memory used=16706.0MB, alloc=44.3MB, time=171.86
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memory used=16746.6MB, alloc=44.3MB, time=172.28
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memory used=16787.1MB, alloc=44.3MB, time=172.69
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memory used=16827.7MB, alloc=44.3MB, time=173.11
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memory used=16868.2MB, alloc=44.3MB, time=173.52
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TOP MAIN SOLVE Loop
x[1] = -0.29999956507812628663912984295438
y[1] (closed_form) = -3.3886665897696483141571861007012
y[1] (numeric) = -3.3886665897696483141571861007022
absolute error = 1.0e-30
relative error = 2.9510132481578162213526091084314e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 1e-06
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NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03333
Order of pole (three term test) = 32
NO COMPLEX POLE (six term test) for Equation 1
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memory used=16949.4MB, alloc=44.3MB, time=174.36
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memory used=17152.0MB, alloc=44.3MB, time=176.44
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memory used=17192.6MB, alloc=44.3MB, time=176.86
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memory used=17233.2MB, alloc=44.3MB, time=177.27
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memory used=17273.7MB, alloc=44.3MB, time=177.69
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memory used=17314.2MB, alloc=44.3MB, time=178.11
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Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ;
Iterations = 39348
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 3 Minutes 0 Seconds
Expected Time Remaining = 3 Minutes 22 Seconds
Optimized Time Remaining = 3 Minutes 22 Seconds
Expected Total Time = 6 Minutes 22 Seconds
Time to Timeout = 0 Seconds
Percent Done = 47.01 %
> quit
memory used=17507.3MB, alloc=44.3MB, time=180.08