|\^/| 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.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3,
> array_const_0D1,
> array_const_0D2,
#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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_0D3[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D1[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp3[1] := sin(array_tmp2[1]);
> array_tmp3_g[1] := cos(array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_tmp5[1] + array_const_0D2[1];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp4[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_0D3[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := array_tmp3_g[1] * array_tmp2[2] / c(1);
> array_tmp3_g[2] := neg(array_tmp3[1]) * array_tmp2[2] / c(1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[2];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp4[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_tmp3[3] := array_tmp3_g[2] * array_tmp2[2] / c(2);
> array_tmp3_g[3] := neg(array_tmp3[2]) * array_tmp2[2] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp4[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_tmp3[4] := array_tmp3_g[3] * array_tmp2[2] / c(3);
> array_tmp3_g[4] := neg(array_tmp3[3]) * array_tmp2[2] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp4[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_tmp3[5] := array_tmp3_g[4] * array_tmp2[2] / c(4);
> array_tmp3_g[5] := neg(array_tmp3[4]) * array_tmp2[2] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre sub FULL - LINEAR $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp4[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_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_tmp2[2] / c(kkk - 1);
> array_tmp3_g[kkk] := neg(array_tmp3[kkk - 1]) * array_tmp2[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit FULL - NOT FULL sub $eq_no = 1
> array_tmp7[kkk] := array_tmp4[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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_0D3[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D1[1];
array_tmp3[1] := sin(array_tmp2[1]);
array_tmp3_g[1] := cos(array_tmp2[1]);
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
array_tmp5[1] := array_const_0D1[1]*array_x[1];
array_tmp6[1] := array_tmp5[1] + array_const_0D2[1];
array_tmp7[1] := array_tmp4[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_0D3[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp3_g[1]*array_tmp2[2]/c(1);
array_tmp3_g[2] := neg(array_tmp3[1])*array_tmp2[2]/c(1);
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] := array_const_0D1[1]*array_x[2];
array_tmp6[2] := array_tmp5[2];
array_tmp7[2] := array_tmp4[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_tmp3[3] := array_tmp3_g[2]*array_tmp2[2]/c(2);
array_tmp3_g[3] := neg(array_tmp3[2])*array_tmp2[2]/c(2);
array_tmp4[3] := array_tmp3[3];
array_tmp7[3] := array_tmp4[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_tmp3[4] := array_tmp3_g[3]*array_tmp2[2]/c(3);
array_tmp3_g[4] := neg(array_tmp3[3])*array_tmp2[2]/c(3);
array_tmp4[4] := array_tmp3[4];
array_tmp7[4] := array_tmp4[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_tmp3[5] := array_tmp3_g[4]*array_tmp2[2]/c(4);
array_tmp3_g[5] := neg(array_tmp3[4])*array_tmp2[2]/c(4);
array_tmp4[5] := array_tmp3[5];
array_tmp7[5] := array_tmp4[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_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_tmp2[2]/c(kkk - 1);
array_tmp3_g[kkk] :=
neg(array_tmp3[kkk - 1])*array_tmp2[2]/c(kkk - 1);
array_tmp4[kkk] := array_tmp3[kkk];
array_tmp7[kkk] := array_tmp4[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_0D3,
> array_const_0D1,
> array_const_0D2,
> #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_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> 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_g:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= 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_g[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[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_g);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> 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_0D3);
> array_const_0D3[1] := c(0.3);
> 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_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/sub_full_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
> 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(0.1);");
> 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,"");
> 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(1.0000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.005);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> 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(0.1);
> 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(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.005);
> 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 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
> 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,"2015-05-02T21:56:12-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub_full_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ")
> ;
> 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,"sub_full_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub_full_lin 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_0D3,
array_const_0D1, array_const_0D2, 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_g, array_tmp3, array_tmp4, array_tmp5,
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_g := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := 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_g[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[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_g);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
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_0D3);
array_const_0D3[1] := c(0.3);
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_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/sub_full_linpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( 0.3 * x \
+ 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
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(0.1);");
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, "");
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(1.0000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.005);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
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(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.1);
x_end := c(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(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.005);
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 ) = sin ( 0.3 * \
x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ");
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, "2015-05-02T21:56:12-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sub_full_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = s\
in ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;\
");
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, "sub_full_lin diffeq.mxt");
logitem_str(html_log_file, "sub_full_lin 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/sub_full_linpostode.ode#################
diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(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(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.005);
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] = 0.1
y[1] (closed_form) = -3.3257063123826267986483739038394
y[1] (numeric) = -3.3257063123826267986483739038394
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4285
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
memory used=3.9MB, alloc=40.3MB, time=0.11
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = -3.3265000994836904604552861567236
y[1] (numeric) = -3.3265000994836904604552861567236
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4381
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = -3.3272741515511600542791827214267
y[1] (numeric) = -3.3272741515511600542791827214267
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4478
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = -3.328028480653557921497890021765
y[1] (numeric) = -3.3280284806535579214978900217649
absolute error = 1e-31
relative error = 3.0047819777179914446189806112699e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4574
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = -3.328763099126912888504819883098
y[1] (numeric) = -3.3287630991269128885048198830979
absolute error = 1e-31
relative error = 3.0041188580295357925426433875960e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = -3.3294780195746492425328001612199
y[1] (numeric) = -3.3294780195746492425328001612198
absolute error = 1e-31
relative error = 3.0034738001596808426838058665210e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4766
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = -3.330173254867473300920562735326
y[1] (numeric) = -3.3301732548674733009205627353258
absolute error = 2e-31
relative error = 6.0056935388473999201540491752425e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4862
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = -3.330848818143257574842764701004
y[1] (numeric) = -3.3308488181432575748427647010039
absolute error = 1e-31
relative error = 3.0022377315744946258540139828798e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4957
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = -3.3315047228069225285460684111671
y[1] (numeric) = -3.331504722806922528546068411167
absolute error = 1e-31
relative error = 3.0016466527997626212342414471578e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5053
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = -3.3321409825303159351554464420811
y[1] (numeric) = -3.332140982530315935155446442081
absolute error = 1e-31
relative error = 3.0010734997191913233778619928584e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5148
Order of pole (three term test) = 32.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = -3.3327576112520898301365084133945
y[1] (numeric) = -3.3327576112520898301365084133943
absolute error = 2e-31
relative error = 6.0010364787633515461876642699693e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5243
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = -3.3333546231775750635212676706652
y[1] (numeric) = -3.333354623177575063521267670665
absolute error = 2e-31
relative error = 5.9999616785251223550392494805603e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5338
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = -3.333932032778653452026376951713
y[1] (numeric) = -3.3339320327786534520263769517128
absolute error = 2e-31
relative error = 5.9989225345218190279098536687192e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5432
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = -3.3344898547936275322144631097015
y[1] (numeric) = -3.3344898547936275322144631097014
absolute error = 1e-31
relative error = 2.9989594916967899040407564418025e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5527
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = -3.3350281042270879158707815617738
y[1] (numeric) = -3.3350281042270879158707815617736
absolute error = 2e-31
relative error = 5.9969509626171848608565687282346e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5621
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = -3.3355467963497782487889911779985
y[1] (numeric) = -3.3355467963497782487889911779983
absolute error = 2e-31
relative error = 5.9960184105007301419579616592564e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5715
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = -3.3360459466984577741814196271259
y[1] (numeric) = -3.3360459466984577741814196271258
absolute error = 1e-31
relative error = 2.9975606330891734283802003880948e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5809
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = -3.336525571075761501950747559069
y[1] (numeric) = -3.3365255710757615019507475590689
absolute error = 1e-31
relative error = 2.9971297348024829358486334749798e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5902
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = -3.3369856855500579850815872350936
y[1] (numeric) = -3.3369856855500579850815872350935
absolute error = 1e-31
relative error = 2.9967164807755632223288391615200e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5996
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = -3.3374263064553047044319671215027
y[1] (numeric) = -3.3374263064553047044319671215026
absolute error = 1e-31
relative error = 2.9963208417989143232759676094520e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6089
Order of pole (three term test) = 32.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = -3.3378474503909010632262583472997
y[1] (numeric) = -3.3378474503909010632262583472995
absolute error = 2e-31
relative error = 5.9918855781314288514828144048733e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6182
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = -3.3382491342215389925725915972059
y[1] (numeric) = -3.3382491342215389925725915972057
absolute error = 2e-31
relative error = 5.9911645883385776781161253034616e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6275
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = -3.3386313750770511693493137748686
y[1] (numeric) = -3.3386313750770511693493137748684
absolute error = 2e-31
relative error = 5.9904786582011997698977741761505e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6367
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = -3.3389941903522568478265224336202
y[1] (numeric) = -3.33899419035225684782652243362
absolute error = 2e-31
relative error = 5.9898277324915148067174841491734e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.646
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = -3.3393375977068053064101923403414
y[1] (numeric) = -3.3393375977068053064101923403412
absolute error = 2e-31
relative error = 5.9892117567670991454724438663706e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6552
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = -3.3396616150650169109178724185576
y[1] (numeric) = -3.3396616150650169109178724185573
absolute error = 3e-31
relative error = 8.9829460160489812376079564114041e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6643
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = -3.3399662606157217958163825166702
y[1] (numeric) = -3.3399662606157217958163825166699
absolute error = 3e-31
relative error = 8.9821266621027210141218321688503e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6735
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = -3.3402515528120961648733777731541
y[1] (numeric) = -3.3402515528120961648733777731537
absolute error = 4e-31
relative error = 1.1975145993517984559524949674564e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6826
Order of pole (three term test) = 32.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = -3.3405175103714962126960736096685
y[1] (numeric) = -3.3405175103714962126960736096681
absolute error = 4e-31
relative error = 1.1974192584175867051475283179590e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6918
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = -3.3407641522752896686518363825296
y[1] (numeric) = -3.3407641522752896686518363825292
absolute error = 4e-31
relative error = 1.1973308553600605043732848070390e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7008
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = -3.340991497768684964686743270149
y[1] (numeric) = -3.3409914977686849646867432701486
absolute error = 4e-31
relative error = 1.1972493802128621228424068665670e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7099
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = -3.3411995663605580285795998762834
y[1] (numeric) = -3.341199566360558028579599876283
absolute error = 4e-31
relative error = 1.1971748231600090558303083494937e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7189
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = -3.341388377823276704190275093791
y[1] (numeric) = -3.3413883778232767041902750937907
absolute error = 3e-31
relative error = 8.9783038090122534806726535936219e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7279
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = -3.3415579521925228002825698087188
y[1] (numeric) = -3.3415579521925228002825698087185
absolute error = 3e-31
relative error = 8.9778481861479802121627249846791e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7369
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = -3.3417083097671117695231788377313
y[1] (numeric) = -3.341708309767111769523178837731
absolute error = 3e-31
relative error = 8.9774442348293232996310623082487e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7459
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = -3.3418394711088100192796338910574
y[1] (numeric) = -3.3418394711088100192796338910571
absolute error = 3e-31
relative error = 8.9770918858786806336163763008391e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7548
Order of pole (three term test) = 32.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = -3.3419514570421498558614291463175
y[1] (numeric) = -3.3419514570421498558614291463172
absolute error = 3e-31
relative error = 8.9767910712120285445098399146042e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7637
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = -3.3420442886542420638698300139739
y[1] (numeric) = -3.3420442886542420638698300139735
absolute error = 4e-31
relative error = 1.1968722298442969772392739723071e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7726
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = -3.3421179872945861223431496810361
y[1] (numeric) = -3.3421179872945861223431496810358
absolute error = 3e-31
relative error = 8.9763437778223757525506675710306e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7814
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = -3.3421725745748780594055468444938
y[1] (numeric) = -3.3421725745748780594055468444935
absolute error = 3e-31
relative error = 8.9761971683392137102204549810623e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7903
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = -3.342208072368815947148651498314
y[1] (numeric) = -3.3422080723688159471486514983137
absolute error = 3e-31
relative error = 8.9761018316065722497223615520031e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.799
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = -3.3422245028119030384965635264639
y[1] (numeric) = -3.3422245028119030384965635264637
absolute error = 2e-31
relative error = 5.9840384699392467633151229385321e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8078
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = -3.3422218883012485478259909881449
y[1] (numeric) = -3.3422218883012485478259909881446
absolute error = 3e-31
relative error = 8.9760647265846562297195605778817e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8165
Order of pole (three term test) = 32.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = -3.3422002514953660771345011692623
y[1] (numeric) = -3.342200251495366077134501169262
absolute error = 3e-31
relative error = 8.9761228360201966973173032211572e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8252
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = -3.3421596153139696895710475252506
y[1] (numeric) = -3.3421596153139696895710475252503
absolute error = 3e-31
relative error = 8.9762319736431065796711096263913e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8339
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = -3.3421000029377676321641093640055
y[1] (numeric) = -3.3421000029377676321641093640052
absolute error = 3e-31
relative error = 8.9763920809160246225638574424026e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8426
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = -3.3420214378082537096039383232972
y[1] (numeric) = -3.3420214378082537096039383232969
absolute error = 3e-31
relative error = 8.9766031003303307789392244994770e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8512
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = -3.341923943627496310956546194218
y[1] (numeric) = -3.3419239436274963109565461942177
absolute error = 3e-31
relative error = 8.9768649753999055459597969873170e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8598
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
memory used=46.6MB, alloc=44.3MB, time=0.58
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = -3.3418075443579250912081922407056
y[1] (numeric) = -3.3418075443579250912081922407053
absolute error = 3e-31
relative error = 8.9771776506549303757862332198224e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8683
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = -3.3416722642221153095602346748574
y[1] (numeric) = -3.341672264222115309560234674857
absolute error = 4e-31
relative error = 1.1970054762180971192046621461273e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8768
Order of pole (three term test) = 32.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = -3.3415181277025698264153001786549
y[1] (numeric) = -3.3415181277025698264153001786545
absolute error = 4e-31
relative error = 1.1970606913182192885024500257280e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8853
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = -3.3413451595414987610167971250549
y[1] (numeric) = -3.3413451595414987610167971250544
absolute error = 5e-31
relative error = 1.4964033229916608727756393844348e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8938
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = -3.3411533847405968117248522555154
y[1] (numeric) = -3.3411533847405968117248522555149
absolute error = 5e-31
relative error = 1.4964892132266457060995897063174e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9022
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = -3.340942828560818240932786827441
y[1] (numeric) = -3.3409428285608182409327868274405
absolute error = 5e-31
relative error = 1.4965835264394080374527331834264e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9106
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = -3.3407135165221495266492664644088
y[1] (numeric) = -3.3407135165221495266492664644083
absolute error = 5e-31
relative error = 1.4966862543799478496596254120956e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9189
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = -3.3404654744033796827922589352268
y[1] (numeric) = -3.3404654744033796827922589352264
absolute error = 4e-31
relative error = 1.1974379111684774369350163319672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9273
Order of pole (three term test) = 32.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = -3.3401987282418682502619156658658
y[1] (numeric) = -3.3401987282418682502619156658654
absolute error = 4e-31
relative error = 1.1975335378040281256527016078628e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9356
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = -3.3399133043333109608804557622718
y[1] (numeric) = -3.3399133043333109608804557622714
absolute error = 4e-31
relative error = 1.1976358771978516107573421494113e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9438
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = -3.3396092292315030763080755033352
y[1] (numeric) = -3.3396092292315030763080755033348
absolute error = 4e-31
relative error = 1.1977449232647088141197133088846e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.952
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = -3.3392865297481004040648314633692
y[1] (numeric) = -3.3392865297481004040648314633687
absolute error = 5e-31
relative error = 1.4973258375576341373329397524688e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9602
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = -3.3389452329523779928093514540074
y[1] (numeric) = -3.3389452329523779928093514540069
absolute error = 5e-31
relative error = 1.4974788896369157518463956196183e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9684
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = -3.3385853661709865090461141483171
y[1] (numeric) = -3.3385853661709865090461141483166
absolute error = 5e-31
relative error = 1.4976403031846044797980164903134e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9765
Order of pole (three term test) = 32.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = -3.3382069569877062974539053771537
y[1] (numeric) = -3.3382069569877062974539053771531
absolute error = 6e-31
relative error = 1.7973720854665681405754076351625e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9846
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = -3.3378100332431991270489064815571
y[1] (numeric) = -3.3378100332431991270489064815565
absolute error = 6e-31
relative error = 1.7975858243106996786752569700311e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9927
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = -3.3373946230347576254166975776839
y[1] (numeric) = -3.3373946230347576254166975776832
absolute error = 7e-31
relative error = 2.0974445010745430836931443367782e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.001
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = -3.3369607547160524032682659549249
y[1] (numeric) = -3.3369607547160524032682659549242
absolute error = 7e-31
relative error = 2.0977172087226545042300322395542e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = -3.3365084568968768715958968962261
y[1] (numeric) = -3.3365084568968768715958968962254
absolute error = 7e-31
relative error = 2.0980015757281662079377209040117e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.017
Order of pole (three term test) = 32.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = -3.3360377584428897537255907951102
y[1] (numeric) = -3.3360377584428897537255907951096
absolute error = 6e-31
relative error = 1.7985407943345720101204361003152e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.024
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = -3.3355486884753552945833963596028
y[1] (numeric) = -3.3355486884753552945833963596022
absolute error = 6e-31
relative error = 1.7988045027585964458550417588468e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.032
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = -3.3350412763708811695137747524766
y[1] (numeric) = -3.3350412763708811695137747524761
absolute error = 5e-31
relative error = 1.4992318192357998118850156091097e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.04
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = -3.3345155517611540950088135334219
y[1] (numeric) = -3.3345155517611540950088135334214
absolute error = 5e-31
relative error = 1.4994681903220410701875066641901e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.048
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = -3.3339715445326731437277920555908
y[1] (numeric) = -3.3339715445326731437277920555902
absolute error = 6e-31
relative error = 1.7996554319245179146765895664387e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.056
Order of pole (three term test) = 32.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = -3.333409284826480766207261340303
y[1] (numeric) = -3.3334092848264807662072613403024
absolute error = 6e-31
relative error = 1.7999589871281970417577566381334e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.063
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = -3.3328288030378915216824412235928
y[1] (numeric) = -3.3328288030378915216824412235922
absolute error = 6e-31
relative error = 1.8002724876030138341317281283711e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = -3.3322301298162185204613555509543
y[1] (numeric) = -3.3322301298162185204613555509536
absolute error = 7e-31
relative error = 2.1006952483158985423360588627672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.079
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = -3.3316132960644975803137222065566
y[1] (numeric) = -3.3316132960644975803137222065559
absolute error = 7e-31
relative error = 2.1010841829298802132543742407148e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.086
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = -3.3309783329392090993571886149744
y[1] (numeric) = -3.3309783329392090993571886149737
absolute error = 7e-31
relative error = 2.1014846991884504544301259682873e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.094
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = -3.3303252718499976479440548619566
y[1] (numeric) = -3.3303252718499976479440548619559
absolute error = 7e-31
relative error = 2.1018967904331746795043442852168e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.101
Order of pole (three term test) = 32.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = -3.3296541444593892820721555609705
y[1] (numeric) = -3.3296541444593892820721555609699
absolute error = 6e-31
relative error = 1.8019889573168190247317993930443e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.109
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = -3.3289649826825065808640778594523
y[1] (numeric) = -3.3289649826825065808640778594516
absolute error = 7e-31
relative error = 2.1027556722327983370033080218710e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.116
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = -3.3282578186867814106793763483029
y[1] (numeric) = -3.3282578186867814106793763483022
absolute error = 7e-31
relative error = 2.1032024504525807904626261817007e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.124
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = -3.3275326848916654184449059258564
y[1] (numeric) = -3.3275326848916654184449059258557
absolute error = 7e-31
relative error = 2.1036607789858266141194320871420e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.131
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = -3.3267896139683382568088306891525
y[1] (numeric) = -3.3267896139683382568088306891519
absolute error = 6e-31
relative error = 1.8035405589844141066906139698554e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.139
Order of pole (three term test) = 32.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = -3.3260286388394135437442804969567
y[1] (numeric) = -3.3260286388394135437442804969561
absolute error = 6e-31
relative error = 1.8039531980980307040987372287871e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.146
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = -3.325249792678642559249016786844
y[1] (numeric) = -3.3252497926786425592490167868433
absolute error = 7e-31
relative error = 2.1051050105806265239912644295660e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.153
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = -3.3244531089106156818078353493093
y[1] (numeric) = -3.3244531089106156818078353493086
absolute error = 7e-31
relative error = 2.1056094854331748880246874263252e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = -3.3236386212104615673047758819753
y[1] (numeric) = -3.3236386212104615673047758819747
absolute error = 6e-31
relative error = 1.8052504149247169818277746777868e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.167
Order of pole (three term test) = 32.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = -3.3228063635035440730925260834705
y[1] (numeric) = -3.3228063635035440730925260834699
absolute error = 6e-31
relative error = 1.8057025729521119168574432347823e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.174
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = -3.3219563699651569299467016165777
y[1] (numeric) = -3.3219563699651569299467016165772
absolute error = 5e-31
relative error = 1.5051371671243363138312187786870e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.182
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = -3.3210886750202161646529522911714
y[1] (numeric) = -3.3210886750202161646529522911709
absolute error = 5e-31
relative error = 1.5055304116411658141914067232908e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = -3.3202033133429502759950891068393
y[1] (numeric) = -3.3202033133429502759950891068388
absolute error = 5e-31
relative error = 1.5059318746856332192168859945893e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.196
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = -3.3193003198565881669326461707355
y[1] (numeric) = -3.319300319856588166932646170735
absolute error = 5e-31
relative error = 1.5063415533958154179306135021300e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.203
Order of pole (three term test) = 32.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = -3.318379729733044835776485786148
y[1] (numeric) = -3.3183797297330448357764857861476
absolute error = 4e-31
relative error = 1.2054075560309036036923040097190e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.209
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = -3.3174415783926048291912240097545
y[1] (numeric) = -3.3174415783926048291912240097541
absolute error = 4e-31
relative error = 1.2057484376071859013173692004193e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = -3.316485901503603459873397519041
y[1] (numeric) = -3.3164859015036034598733975190407
absolute error = 3e-31
relative error = 9.0457191409735302666563975465556e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.223
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
memory used=89.4MB, alloc=44.3MB, time=1.05
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = -3.3155127349821057917744105346046
y[1] (numeric) = -3.3155127349821057917744105346043
absolute error = 3e-31
relative error = 9.0483742328807292283334348627970e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.23
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = -3.3145221149915833957573926239669
y[1] (numeric) = -3.3145221149915833957573926239665
absolute error = 4e-31
relative error = 1.2068104725890951691971487693277e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.237
Order of pole (three term test) = 32.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = -3.3135140779425888785971642932799
y[1] (numeric) = -3.3135140779425888785971642932796
absolute error = 3e-31
relative error = 9.0538320629763114746387443825486e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = -3.3124886604924281882525471703067
y[1] (numeric) = -3.3124886604924281882525471703064
absolute error = 3e-31
relative error = 9.0566347766878869089473567352603e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.25
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = -3.3114458995448306983602691159434
y[1] (numeric) = -3.3114458995448306983602691159432
absolute error = 2e-31
relative error = 6.0396577829488522869142432395082e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.257
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = -3.3103858322496170749197015922115
y[1] (numeric) = -3.3103858322496170749197015922113
absolute error = 2e-31
relative error = 6.0415918305234927429468167888235e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 32.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = -3.3093084960023649281576268821809
y[1] (numeric) = -3.3093084960023649281576268821807
absolute error = 2e-31
relative error = 6.0435586540692540554148210180121e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = -3.3082139284440722525821661220729
y[1] (numeric) = -3.3082139284440722525821661220727
absolute error = 2e-31
relative error = 6.0455582476210816953135726620708e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.276
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = -3.3071021674608186582549053884098
y[1] (numeric) = -3.3071021674608186582549053884096
absolute error = 2e-31
relative error = 6.0475906056920912209030039107596e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.282
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = -3.3059732511834243963301361043887
y[1] (numeric) = -3.3059732511834243963301361043885
absolute error = 2e-31
relative error = 6.0496557232702018468188780599653e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.289
Order of pole (three term test) = 32.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = -3.3048272179871071819299776107393
y[1] (numeric) = -3.3048272179871071819299776107391
absolute error = 2e-31
relative error = 6.0517535958147704162715606279798e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.295
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = -3.3036641064911368174439737085169
y[1] (numeric) = -3.3036641064911368174439737085166
absolute error = 3e-31
relative error = 9.0808263288798379604613814413591e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.301
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = -3.3024839555584876193615511461702
y[1] (numeric) = -3.30248395555848761936155114617
absolute error = 2e-31
relative error = 6.0560475899776998004319131439784e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.308
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = -3.3012868042954886517654962126398
y[1] (numeric) = -3.3012868042954886517654962126397
absolute error = 1e-31
relative error = 3.0291218524208322215783969482998e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.314
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = -3.3000726920514717696343456342736
y[1] (numeric) = -3.3000726920514717696343456342734
absolute error = 2e-31
relative error = 6.0604725611565579272569784249857e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.32
Order of pole (three term test) = 32.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = -3.2988416584184174751212996783347
y[1] (numeric) = -3.2988416584184174751212996783345
absolute error = 2e-31
relative error = 6.0627341566884160166704099822909e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.326
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = -3.2975937432305985899969485624153
y[1] (numeric) = -3.2975937432305985899969485624152
absolute error = 1e-31
relative error = 3.0325142448272490220446100324495e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.332
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = -3.2963289865642217474627577800071
y[1] (numeric) = -3.296328986564221747462757780007
absolute error = 1e-31
relative error = 3.0336777793599552511687883789128e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = -3.2950474287370667065618836009314
y[1] (numeric) = -3.2950474287370667065618836009313
absolute error = 1e-31
relative error = 3.0348576814971136263155750086369e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.344
Order of pole (three term test) = 32.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = -3.2937491103081234924334866146632
y[1] (numeric) = -3.2937491103081234924334866146631
absolute error = 1e-31
relative error = 3.0360539510140529353788772088103e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.35
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = -3.2924340720772273656762785784231
y[1] (numeric) = -3.292434072077227365676278578423
absolute error = 1e-31
relative error = 3.0372665879049498253884919473545e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.356
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = -3.2911023550846916241065758341615
y[1] (numeric) = -3.2911023550846916241065758341613
absolute error = 2e-31
relative error = 6.0769911847622647843418833252264e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.361
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = -3.2897540006109382402156409933645
y[1] (numeric) = -3.2897540006109382402156409933644
absolute error = 1e-31
relative error = 3.0397409648693811160990474393544e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 32.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = -3.2883890501761263376505732804125
y[1] (numeric) = -3.2883890501761263376505732804124
absolute error = 1e-31
relative error = 3.0410027060102269014078293884125e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = -3.287007545539778510062456698693
y[1] (numeric) = -3.2870075455397785100624566986929
absolute error = 1e-31
relative error = 3.0422808166562459757279618744297e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.379
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = -3.2856095287004049856848938637889
y[1] (numeric) = -3.2856095287004049856848938637888
absolute error = 1e-31
relative error = 3.0435752978703514056355085984826e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = -3.2841950418951256410254417600485
y[1] (numeric) = -3.2841950418951256410254417600485
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 32.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = -3.2827641275992898670718236462092
y[1] (numeric) = -3.2827641275992898670718236462092
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.395
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = -3.2813168285260942914341186882642
y[1] (numeric) = -3.2813168285260942914341186882643
absolute error = 1e-31
relative error = 3.0475569786693873227842493224263e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.401
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = -3.2798531876261983598634274594928
y[1] (numeric) = -3.2798531876261983598634274594929
absolute error = 1e-31
relative error = 3.0489169569316985413620521533388e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.406
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = -3.2783732480873377806067770448384
y[1] (numeric) = -3.2783732480873377806067770448386
absolute error = 2e-31
relative error = 6.1005866283432984820040586503034e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.411
Order of pole (three term test) = 32.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = -3.2768770533339358350772639462408
y[1] (numeric) = -3.276877053333935835077263946241
absolute error = 2e-31
relative error = 6.1033721053561496984277046551233e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.417
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = -3.2753646470267125583376361339824
y[1] (numeric) = -3.2753646470267125583376361339826
absolute error = 2e-31
relative error = 6.1061903498761455716653287384364e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.422
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = -3.2738360730622917929146872537802
y[1] (numeric) = -3.2738360730622917929146872537804
absolute error = 2e-31
relative error = 6.1090413672705160091999289109073e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.427
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = -3.2722913755728061194809760076898
y[1] (numeric) = -3.2722913755728061194809760076899
absolute error = 1e-31
relative error = 3.0559625816480129103194963555492e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.432
Order of pole (three term test) = 32.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = -3.2707305989254996679594919066284
y[1] (numeric) = -3.2707305989254996679594919066285
absolute error = 1e-31
relative error = 3.0574208720477313974446159511157e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.437
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = -3.2691537877223288126259647715032
y[1] (numeric) = -3.2691537877223288126259647715033
absolute error = 1e-31
relative error = 3.0588955580970567548197496756423e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.442
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = -3.26756098679956075480255936685
y[1] (numeric) = -3.2675609867995607548025593668501
absolute error = 1e-31
relative error = 3.0603866432481131801396981332084e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.447
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = -3.2659522412273699967557082141659
y[1] (numeric) = -3.2659522412273699967557082141661
absolute error = 2e-31
relative error = 6.1237882622814612930135680154040e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.452
Order of pole (three term test) = 32.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = -3.2643275963094327104298147806401
y[1] (numeric) = -3.2643275963094327104298147806403
absolute error = 2e-31
relative error = 6.1268360512013257245145901502546e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = -3.2626870975825190046675057019428
y[1] (numeric) = -3.2626870975825190046675057019431
absolute error = 3e-31
relative error = 9.1948749919133941919863086629515e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.462
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = -3.2610307908160830945860243046089
y[1] (numeric) = -3.2610307908160830945860243046092
absolute error = 3e-31
relative error = 9.1995451513330871445455560904040e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.467
Order of pole (three term test) = 32.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = -3.2593587220118513767982382741164
y[1] (numeric) = -3.2593587220118513767982382741167
absolute error = 3e-31
relative error = 9.2042645681793465360244666758571e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.471
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = -3.2576709374034084141855816991013
y[1] (numeric) = -3.2576709374034084141855816991016
absolute error = 3e-31
relative error = 9.2090332561066153189467295973629e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = -3.255967483455780833949065740627
y[1] (numeric) = -3.2559674834557808339490657406273
absolute error = 3e-31
relative error = 9.2138512293000388059548086602089e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.481
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = -3.2542484068650191426832726587259
y[1] (numeric) = -3.2542484068650191426832726587262
absolute error = 3e-31
relative error = 9.2187185024699777096103451850766e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.485
Order of pole (three term test) = 32.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = -3.2525137545577774622369947075191
y[1] (numeric) = -3.2525137545577774622369947075194
absolute error = 3e-31
relative error = 9.2236350908464949189043613593646e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = -3.2507635736908911901428923163821
y[1] (numeric) = -3.2507635736908911901428923163824
absolute error = 3e-31
relative error = 9.2286010101738152043477185018026e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.494
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
memory used=132.3MB, alloc=44.3MB, time=1.52
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = -3.2489979116509525884172248394417
y[1] (numeric) = -3.248997911650952588417224839442
absolute error = 3e-31
relative error = 9.2336162767047570392320945462394e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.499
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = -3.2472168160538843045493518110525
y[1] (numeric) = -3.2472168160538843045493518110528
absolute error = 3e-31
relative error = 9.2386809071951357203006106357335e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.503
Order of pole (three term test) = 32.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = -3.2454203347445108285193129230097
y[1] (numeric) = -3.24542033474451082851931292301
absolute error = 3e-31
relative error = 9.2437949188981369666455454704346e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.507
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = -3.2436085157961278897003706726133
y[1] (numeric) = -3.2436085157961278897003706726135
absolute error = 2e-31
relative error = 6.1659722197057734474391501199237e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.512
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = -3.2417814075100697975219406521301
y[1] (numeric) = -3.2417814075100697975219406521304
absolute error = 3e-31
relative error = 9.2541711574076304742985734413840e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.516
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = -3.2399390584152747297868405928328
y[1] (numeric) = -3.2399390584152747297868405928331
absolute error = 3e-31
relative error = 9.2594334211562788253068695101900e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.52
Order of pole (three term test) = 32.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = -3.2380815172678479725552603740685
y[1] (numeric) = -3.2380815172678479725552603740687
absolute error = 2e-31
relative error = 6.1764967599935927942056134270233e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.524
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = -3.2362088330506231155262910935001
y[1] (numeric) = -3.2362088330506231155262910935003
absolute error = 2e-31
relative error = 6.1800708890430080466390307567665e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.528
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = -3.2343210549727212068662518028266
y[1] (numeric) = -3.2343210549727212068662518028269
absolute error = 3e-31
relative error = 9.2755170219961434564669687449103e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.532
Order of pole (three term test) = 32.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = -3.2324182324691078714514174783385
y[1] (numeric) = -3.2324182324691078714514174783387
absolute error = 2e-31
relative error = 6.1873181505732456072818808944269e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.536
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = -3.2305004152001483965110810523045
y[1] (numeric) = -3.2305004152001483965110810523047
absolute error = 2e-31
relative error = 6.1909913107876455779163912867159e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = -3.2285676530511607886751757144625
y[1] (numeric) = -3.2285676530511607886751757144627
absolute error = 2e-31
relative error = 6.1946975096213275447208434211084e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = -3.2266199961319668064489410381473
y[1] (numeric) = -3.2266199961319668064489410381475
absolute error = 2e-31
relative error = 6.1984367616811893381650070261579e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.547
Order of pole (three term test) = 32.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = -3.2246574947764409721553376285322
y[1] (numeric) = -3.2246574947764409721553376285324
absolute error = 2e-31
relative error = 6.2022090818629901755909199474195e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.551
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = -3.2226801995420575674040997670831
y[1] (numeric) = -3.2226801995420575674040997670833
absolute error = 2e-31
relative error = 6.2060144853473197154794774338739e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.555
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = -3.2206881612094356161644637729721
y[1] (numeric) = -3.2206881612094356161644637729723
absolute error = 2e-31
relative error = 6.2098529875955400244824236071633e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.558
Order of pole (three term test) = 32.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = -3.2186814307818818595367213555316
y[1] (numeric) = -3.2186814307818818595367213555318
absolute error = 2e-31
relative error = 6.2137246043456998637187607657571e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.562
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = -3.2166600594849317263358219288494
y[1] (numeric) = -3.2166600594849317263358219288496
absolute error = 2e-31
relative error = 6.2176293516084206972174336913469e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.565
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = -3.2146240987658883036182855376373
y[1] (numeric) = -3.2146240987658883036182855376375
absolute error = 2e-31
relative error = 6.2215672456627538217291943898499e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.569
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = -3.2125736002933593113016885402071
y[1] (numeric) = -3.2125736002933593113016885402073
absolute error = 2e-31
relative error = 6.2255383030520080134302230988148e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 32.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = -3.2105086159567920850439473477642
y[1] (numeric) = -3.2105086159567920850439473477644
absolute error = 2e-31
relative error = 6.2295425405795470832988019144039e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.575
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = -3.2084291978660065715675511675993
y[1] (numeric) = -3.2084291978660065715675511675995
absolute error = 2e-31
relative error = 6.2335799753045567291645490386658e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.578
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = -3.2063353983507263406317826798036
y[1] (numeric) = -3.2063353983507263406317826798038
absolute error = 2e-31
relative error = 6.2376506245377800686078788621985e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.582
Order of pole (three term test) = 32.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = -3.2042272699601076178738157318529
y[1] (numeric) = -3.2042272699601076178738157318531
absolute error = 2e-31
relative error = 6.2417545058372212330259241828122e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = -3.202104865462266342757391302154
y[1] (numeric) = -3.2021048654622663427573913021542
absolute error = 2e-31
relative error = 6.2458916370038163992806244192137e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = -3.1999682378438032558855470021118
y[1] (numeric) = -3.1999682378438032558855470021121
absolute error = 3e-31
relative error = 9.3750930541156074471083175758524e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.591
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = -3.1978174403093270199516110964921
y[1] (numeric) = -3.1978174403093270199516110964924
absolute error = 3e-31
relative error = 9.3813985819960003513061418384674e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.594
Order of pole (three term test) = 32.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = -3.1956525262809753786203692642011
y[1] (numeric) = -3.1956525262809753786203692642013
absolute error = 2e-31
relative error = 6.2585027112680256498903407096265e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.597
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = -3.1934735493979343576489709368039
y[1] (numeric) = -3.1934735493979343576489709368041
absolute error = 2e-31
relative error = 6.2627730246178492582051423491959e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = -3.1912805635159555125747618812348
y[1] (numeric) = -3.1912805635159555125747618812349
absolute error = 1e-31
relative error = 3.1335383401648078848426834454041e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.602
Order of pole (three term test) = 32.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = -3.1890736227068712273148105776266
y[1] (numeric) = -3.1890736227068712273148105776268
absolute error = 2e-31
relative error = 6.2714136975690422309731351922706e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.605
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = -3.186852781258108068039437724791
y[1] (numeric) = -3.1868527812581080680394377247912
absolute error = 2e-31
relative error = 6.2757840957135099902259200748783e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = -3.1846180936721981966995607267213
y[1] (numeric) = -3.1846180936721981966995607267215
absolute error = 2e-31
relative error = 6.2801878943474522998275357595740e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = -3.182369614666288848605128116062
y[1] (numeric) = -3.1823696146662888486051281160621
absolute error = 1e-31
relative error = 3.1423125566288517813526125207557e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.613
Order of pole (three term test) = 32.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = -3.1801073991716498784693423976073
y[1] (numeric) = -3.1801073991716498784693423976074
absolute error = 1e-31
relative error = 3.1445478862144047788149150787743e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = -3.1778315023331793793507535897631
y[1] (numeric) = -3.1778315023331793793507535897631
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.618
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = -3.1755419795089073789426496480555
y[1] (numeric) = -3.1755419795089073789426496480556
absolute error = 1e-31
relative error = 3.1490687462259542934695789954884e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.62
Order of pole (three term test) = 32.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = -3.1732388862694976176764738161271
y[1] (numeric) = -3.1732388862694976176764738161272
absolute error = 1e-31
relative error = 3.1513542971093911914435364757632e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = -3.1709222783977474131232626104643
y[1] (numeric) = -3.1709222783977474131232626104645
absolute error = 2e-31
relative error = 6.3073132180666089740581921404669e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = -3.1685922118880856151943214500028
y[1] (numeric) = -3.168592211888085615194321450003
absolute error = 2e-31
relative error = 6.3119513848967315949977057065063e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.627
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = -3.1662487429460686566595377357267
y[1] (numeric) = -3.1662487429460686566595377357269
absolute error = 2e-31
relative error = 6.3166231157792090025977434842197e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.629
Order of pole (three term test) = 32.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = -3.1638919279878747035188733137868
y[1] (numeric) = -3.163891927987874703518873313787
absolute error = 2e-31
relative error = 6.3213284319478335801714979247062e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.631
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = -3.1615218236397959097796795642219
y[1] (numeric) = -3.1615218236397959097796795642221
absolute error = 2e-31
relative error = 6.3260673547951049463343637605138e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.633
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = -3.1591384867377287812095386921676
y[1] (numeric) = -3.1591384867377287812095386921679
absolute error = 3e-31
relative error = 9.4962598588007375464950940098251e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.635
Order of pole (three term test) = 32.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = -3.1567419743266626526513540059379
y[1] (numeric) = -3.1567419743266626526513540059381
absolute error = 2e-31
relative error = 6.3356461068586472428846445942051e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.637
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = -3.1543323436601662835043898933892
y[1] (numeric) = -3.1543323436601662835043898933894
absolute error = 2e-31
relative error = 6.3404859796075790150913637306886e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.639
Order of pole (three term test) = 32.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = -3.1519096521998725759918987017286
y[1] (numeric) = -3.1519096521998725759918987017288
absolute error = 2e-31
relative error = 6.3453595460901036772256395565770e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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
memory used=175.1MB, alloc=44.3MB, time=1.98
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = -3.1494739576149614208528666339729
y[1] (numeric) = -3.149473957614961420852866633973
absolute error = 1e-31
relative error = 3.1751334142076271323812899515429e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = -3.147025317781640675112263945555
y[1] (numeric) = -3.1470253177816406751122639455551
absolute error = 1e-31
relative error = 3.1776039244098192691104205488981e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.644
Order of pole (three term test) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = -3.1445637907826252766009960054276
y[1] (numeric) = -3.1445637907826252766009960054277
absolute error = 1e-31
relative error = 3.1800913148310405733934663798861e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.03
y[1] (closed_form) = -3.1420894349066144999135210261274
y[1] (numeric) = -3.1420894349066144999135210261275
absolute error = 1e-31
relative error = 3.1825955967091077664922373493110e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = -3.1396023086477673585078273157203
y[1] (numeric) = -3.1396023086477673585078273157204
absolute error = 1e-31
relative error = 3.1851167813375124184722208992183e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.05
y[1] (closed_form) = -3.1371024707051761576691476107969
y[1] (numeric) = -3.1371024707051761576691476107969
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = -3.1345899799823382030754302635724
y[1] (numeric) = -3.1345899799823382030754302635725
absolute error = 1e-31
relative error = 3.1902099042811158477180368339928e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.07
y[1] (closed_form) = -3.1320648955866256697191866278861
y[1] (numeric) = -3.1320648955866256697191866278861
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.08
y[1] (closed_form) = -3.1295272768287536359568907690869
y[1] (numeric) = -3.1295272768287536359568907690869
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = -3.1269771832222462874736214624423
y[1] (numeric) = -3.1269771832222462874736214624423
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.1
y[1] (closed_form) = -3.1244146744829012959671071951678
y[1] (numeric) = -3.1244146744829012959671071951677
absolute error = 1e-31
relative error = 3.2005994856156620267251184160912e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.11
y[1] (closed_form) = -3.1218398105282523773717624002295
y[1] (numeric) = -3.1218398105282523773717624002294
absolute error = 1e-31
relative error = 3.2032393098055473958814485891307e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = -3.1192526514770300344596872778642
y[1] (numeric) = -3.1192526514770300344596872778641
absolute error = 1e-31
relative error = 3.2058961287617388512792866656858e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.13
y[1] (closed_form) = -3.1166532576486204886719441558311
y[1] (numeric) = -3.1166532576486204886719441558309
absolute error = 2e-31
relative error = 6.4171399083031557067434698703851e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.14
y[1] (closed_form) = -3.1140416895625228060497202546981
y[1] (numeric) = -3.1140416895625228060497202546979
absolute error = 2e-31
relative error = 6.4225215953385989272397327246624e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = -3.1114180079378042221512398133014
y[1] (numeric) = -3.1114180079378042221512398133012
absolute error = 2e-31
relative error = 6.4279373420659942914854038470216e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.16
y[1] (closed_form) = -3.1087822736925536708564976456109
y[1] (numeric) = -3.1087822736925536708564976456107
absolute error = 2e-31
relative error = 6.4333871719631148636621946957587e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.17
y[1] (closed_form) = -3.1061345479433335219780511977215
y[1] (numeric) = -3.1061345479433335219780511977212
absolute error = 3e-31
relative error = 9.6583066628146921542297691974680e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.18
y[1] (closed_form) = -3.1034748920046295326122289070712
y[1] (numeric) = -3.1034748920046295326122289070709
absolute error = 3e-31
relative error = 9.6665837630225133573338555771839e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.19
y[1] (closed_form) = -3.100803367388299017181188990184
y[1] (numeric) = -3.1008033673882990171811889901837
absolute error = 3e-31
relative error = 9.6749120939158349226012311880994e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.2
y[1] (closed_form) = -3.0981200358030172411322945555567
y[1] (numeric) = -3.0981200358030172411322945555563
absolute error = 4e-31
relative error = 1.2911055587822697051104064874002e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = -3.0954249591537220432772580104725
y[1] (numeric) = -3.095424959153722043277258010472
absolute error = 5e-31
relative error = 1.6152870982105739255246722473604e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.22
y[1] (closed_form) = -3.0927181995410566917694499606439
y[1] (numeric) = -3.0927181995410566917694499606434
absolute error = 5e-31
relative error = 1.6167008040829500778457020265001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.23
y[1] (closed_form) = -3.0899998192608109787336650461838
y[1] (numeric) = -3.0899998192608109787336650461833
absolute error = 5e-31
relative error = 1.6181230719929617374136133895365e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.24
y[1] (closed_form) = -3.0872698808033605585784892734012
y[1] (numeric) = -3.0872698808033605585784892734007
absolute error = 5e-31
relative error = 1.6195539078361734504249938009642e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.25
y[1] (closed_form) = -3.0845284468531045350372202466516
y[1] (numeric) = -3.0845284468531045350372202466511
absolute error = 5e-31
relative error = 1.6209933175040406969137979638980e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.26
y[1] (closed_form) = -3.0817755802879013019990531356729
y[1] (numeric) = -3.0817755802879013019990531356724
absolute error = 5e-31
relative error = 1.6224413068822152959403893022771e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.27
y[1] (closed_form) = -3.07901134417850264320796108966
y[1] (numeric) = -3.0790113441785026432079610896595
absolute error = 5e-31
relative error = 1.6238978818488334662628556807290e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.28
y[1] (closed_form) = -3.0762358017879860959223689883283
y[1] (numeric) = -3.0762358017879860959223689883278
absolute error = 5e-31
relative error = 1.6253630482727863282984548218296e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.29
y[1] (closed_form) = -3.0734490165711855836443437613588
y[1] (numeric) = -3.0734490165711855836443437613582
absolute error = 6e-31
relative error = 1.9522041744143671583990269225183e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.3
y[1] (closed_form) = -3.0706510521741203230426028702832
y[1] (numeric) = -3.0706510521741203230426028702826
absolute error = 6e-31
relative error = 1.9539830146938401929043904642899e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.31
y[1] (closed_form) = -3.0678419724334220102091747908561
y[1] (numeric) = -3.0678419724334220102091747908555
absolute error = 6e-31
relative error = 1.9557721857624827123056366875742e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.32
y[1] (closed_form) = -3.0650218413757602914050313194782
y[1] (numeric) = -3.0650218413757602914050313194776
absolute error = 6e-31
relative error = 1.9575716945974031281272813697691e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.33
y[1] (closed_form) = -3.0621907232172665234654511149086
y[1] (numeric) = -3.062190723217266523465451114908
absolute error = 6e-31
relative error = 1.9593815481539135937387025381980e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.34
y[1] (closed_form) = -3.0593486823629558290512669373775
y[1] (numeric) = -3.0593486823629558290512669373769
absolute error = 6e-31
relative error = 1.9612017533633227072844052043587e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.35
y[1] (closed_form) = -3.0564957834061474519474954227494
y[1] (numeric) = -3.0564957834061474519474954227489
absolute error = 5e-31
relative error = 1.6358602642755877546461229844481e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.36
y[1] (closed_form) = -3.0536320911278834176261477914676
y[1] (numeric) = -3.0536320911278834176261477914671
absolute error = 5e-31
relative error = 1.6373943719438742339684160599122e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.37
y[1] (closed_form) = -3.0507576704963455043052725029433
y[1] (numeric) = -3.0507576704963455043052725029427
absolute error = 6e-31
relative error = 1.9667245478149777502600578054064e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.38
y[1] (closed_form) = -3.0478725866662705297514863885618
y[1] (numeric) = -3.0478725866662705297514863885612
absolute error = 6e-31
relative error = 1.9685862283904505090583907910892e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.39
y[1] (closed_form) = -3.0449769049783639590884090937133
y[1] (numeric) = -3.0449769049783639590884090937126
absolute error = 7e-31
relative error = 2.2988680106425104075883324159840e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.4
y[1] (closed_form) = -3.0420706909587118388885265947898
y[1] (numeric) = -3.0420706909587118388885265947891
absolute error = 7e-31
relative error = 2.3010642128746661363988056488189e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.41
y[1] (closed_form) = -3.0391540103181910628410729949361
y[1] (numeric) = -3.0391540103181910628410729949355
absolute error = 6e-31
relative error = 1.9742336122583720292012900684397e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.42
y[1] (closed_form) = -3.0362269289518779743035356069107
y[1] (numeric) = -3.0362269289518779743035356069101
absolute error = 6e-31
relative error = 1.9761368765908523794517191318250e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.43
y[1] (closed_form) = -3.0332895129384553110593563675796
y[1] (numeric) = -3.033289512938455311059356367579
absolute error = 6e-31
relative error = 1.9780505535020911490634076394784e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.44
y[1] (closed_form) = -3.0303418285396174976193227616103
y[1] (numeric) = -3.0303418285396174976193227616097
absolute error = 6e-31
relative error = 1.9799746495567862498766497165598e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.45
y[1] (closed_form) = -3.0273839421994742904190135275694
y[1] (numeric) = -3.0273839421994742904190135275688
absolute error = 6e-31
relative error = 1.9819091712697801164415456424591e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.46
y[1] (closed_form) = -3.0244159205439527812794883440211
y[1] (numeric) = -3.0244159205439527812794883440205
absolute error = 6e-31
relative error = 1.9838541251035595100944756259848e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.47
y[1] (closed_form) = -3.0214378303801977645131863129418
y[1] (numeric) = -3.0214378303801977645131863129413
absolute error = 5e-31
relative error = 1.6548412645547742581193869822162e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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
memory used=218.0MB, alloc=44.3MB, time=2.44
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = -3.018449738695970473071725239846
y[1] (numeric) = -3.0184497386959704730717252398455
absolute error = 5e-31
relative error = 1.6564794622553821716214128447716e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.49
y[1] (closed_form) = -3.0154517126590456891469723218978
y[1] (numeric) = -3.0154517126590456891469723218973
absolute error = 5e-31
relative error = 1.6581263692632525114287529482196e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.5
y[1] (closed_form) = -3.0124438196166072346513867648716
y[1] (numeric) = -3.012443819616607234651386764871
absolute error = 6e-31
relative error = 1.9917383889215959183529744268032e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = -3.0094261270946418470182159254384
y[1] (numeric) = -3.0094261270946418470182159254379
absolute error = 5e-31
relative error = 1.6614463319048461395998525371331e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.52
y[1] (closed_form) = -3.0063987027973314457766586856783
y[1] (numeric) = -3.0063987027973314457766586856777
absolute error = 6e-31
relative error = 1.9957432773029221216411415452135e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.53
y[1] (closed_form) = -3.0033616146064437953715927811452
y[1] (numeric) = -3.0033616146064437953715927811446
absolute error = 6e-31
relative error = 1.9977614319966699737319581081878e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = -3.0003149305807215697118965919177
y[1] (numeric) = -3.0003149305807215697118965919171
absolute error = 6e-31
relative error = 1.9997900683174878486614095314990e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.55
y[1] (closed_form) = -2.9972587189552698239457803379228
y[1] (numeric) = -2.9972587189552698239457803379222
absolute error = 6e-31
relative error = 2.0018291921397333908948040309302e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = -2.9941930481409418789758765659908
y[1] (numeric) = -2.9941930481409418789758765659901
absolute error = 7e-31
relative error = 2.3378586108020707069030719476170e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.644
Order of pole (three term test) = 32.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = -2.9911179867237236242411251475458
y[1] (numeric) = -2.9911179867237236242411251475451
absolute error = 7e-31
relative error = 2.3402620796203848061990365513247e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.58
y[1] (closed_form) = -2.9880336034641162443067235940147
y[1] (numeric) = -2.9880336034641162443067235940139
absolute error = 8e-31
relative error = 2.6773460615454130156267003900024e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = -2.9849399672965173748175992138048
y[1] (numeric) = -2.984939967296517374817599213804
absolute error = 8e-31
relative error = 2.6801209028152282386265675179752e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.639
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = -2.981837147328600693384995352407
y[1] (numeric) = -2.9818371473286006933849953524061
absolute error = 9e-31
relative error = 3.0182734855466582728918633809832e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.637
Order of pole (three term test) = 32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = -2.978725212840693950989849548586
y[1] (numeric) = -2.9787252128406939509898495485852
absolute error = 8e-31
relative error = 2.6857126550356460395832725375147e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.635
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = -2.9756042332851554495006767779696
y[1] (numeric) = -2.9756042332851554495006767779688
absolute error = 8e-31
relative error = 2.6885295801477478067148263665523e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.633
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = -2.9724742782857489709176559143099
y[1] (numeric) = -2.9724742782857489709176559143091
absolute error = 8e-31
relative error = 2.6913605471511994336198475941681e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.631
Order of pole (three term test) = 32.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = -2.9693354176370171639685519924143
y[1] (numeric) = -2.9693354176370171639685519924135
absolute error = 8e-31
relative error = 2.6942055627943715101150638861761e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.629
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = -2.9661877213036533936959906798049
y[1] (numeric) = -2.9661877213036533936959906798041
absolute error = 8e-31
relative error = 2.6970646336854103547022239201431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.627
Order of pole (three term test) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = -2.963031259419872059689434431623
y[1] (numeric) = -2.9630312594198720596894344316222
absolute error = 8e-31
relative error = 2.6999377662881320176566220839739e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = -2.9598661022887773886289919906428
y[1] (numeric) = -2.9598661022887773886289919906421
absolute error = 7e-31
relative error = 2.3649718460531393342453597127595e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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) = 32.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = -2.9566923203817307068219240774588
y[1] (numeric) = -2.9566923203817307068219240774581
absolute error = 7e-31
relative error = 2.3675104615201383409808491354693e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.62
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = -2.9535099843377161984263881713874
y[1] (numeric) = -2.9535099843377161984263881713867
absolute error = 7e-31
relative error = 2.3700613971581522423980452252238e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.618
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = -2.9503191649627051550705940872489
y[1] (numeric) = -2.9503191649627051550705940872482
absolute error = 7e-31
relative error = 2.3726246580811831145390069855550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 32.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = -2.9471199332290187225891194843154
y[1] (numeric) = -2.9471199332290187225891194843146
absolute error = 8e-31
relative error = 2.7145145705810423632311598418270e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.613
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = -2.9439123602746891506116603791272
y[1] (numeric) = -2.9439123602746891506116603791265
absolute error = 7e-31
relative error = 2.3777881755103767374836542283766e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = -2.9406965174028195507529660518597
y[1] (numeric) = -2.940696517402819550752966051859
absolute error = 7e-31
relative error = 2.3803884415051092459859430248506e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = -2.937472476080942169166130315194
y[1] (numeric) = -2.9374724760809421691661303151933
absolute error = 7e-31
relative error = 2.3830010517542342840137108083944e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.605
Order of pole (three term test) = 32.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = -2.9342403079403751792347818344126
y[1] (numeric) = -2.9342403079403751792347818344119
absolute error = 7e-31
relative error = 2.3856260106090269561164400997825e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.602
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = -2.9310000847755780001930349273582
y[1] (numeric) = -2.9310000847755780001930349273575
absolute error = 7e-31
relative error = 2.3882633222564300372056844566368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.599
Order of pole (three term test) = 32.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = -2.9277518785435051474753289131013
y[1] (numeric) = -2.9277518785435051474753289131005
absolute error = 8e-31
relative error = 2.7324719893886060410325318875084e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
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] = 2.78
y[1] (closed_form) = -2.9244957613629586206114984992521
y[1] (numeric) = -2.9244957613629586206114984992513
absolute error = 8e-31
relative error = 2.7355143083782782408922776337215e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.594
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = -2.9212318055139388344955797809049
y[1] (numeric) = -2.9212318055139388344955797809041
absolute error = 8e-31
relative error = 2.7385707580273802121073824805420e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.591
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = -2.9179600834369940998699660507467
y[1] (numeric) = -2.9179600834369940998699660507459
absolute error = 8e-31
relative error = 2.7416413423232969254587110821025e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 32.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = -2.9146806677325686588795846719229
y[1] (numeric) = -2.9146806677325686588795846719221
absolute error = 8e-31
relative error = 2.7447260650421364693329001306233e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = -2.9113936311603492815637706253097
y[1] (numeric) = -2.9113936311603492815637706253088
absolute error = 9e-31
relative error = 3.0913030459618779654753311726203e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = -2.9080990466386104291664638938584
y[1] (numeric) = -2.9080990466386104291664638938575
absolute error = 9e-31
relative error = 3.0948051822384955778373711681875e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.578
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = -2.9047969872435579901582564720901
y[1] (numeric) = -2.9047969872435579901582564720892
absolute error = 9e-31
relative error = 3.0983232355044365170638732493203e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.575
Order of pole (three term test) = 32.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = -2.9014875262086715948766603725351
y[1] (numeric) = -2.9014875262086715948766603725341
absolute error = 1.0e-30
relative error = 3.4465080100023189542389337723897e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = -2.8981707369240455147037604273318
y[1] (numeric) = -2.8981707369240455147037604273308
absolute error = 1.0e-30
relative error = 3.4504523396759689701812394694066e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.568
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = -2.8948466929357281517131548371806
y[1] (numeric) = -2.8948466929357281517131548371796
absolute error = 1.0e-30
relative error = 3.4544143648100336883625667996688e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.565
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = -2.8915154679450601247307721867428
y[1] (numeric) = -2.8915154679450601247307721867417
absolute error = 1.1e-30
relative error = 3.8042334969134614754948438424798e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.561
Order of pole (three term test) = 32.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = -2.8881771358080109577667859112155
y[1] (numeric) = -2.8881771358080109577667859112144
absolute error = 1.1e-30
relative error = 3.8086306631336809229678378175326e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.558
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = -2.8848317705345143767884258494995
y[1] (numeric) = -2.8848317705345143767884258494984
absolute error = 1.1e-30
relative error = 3.8130473022216721488713341642218e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.554
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = -2.8814794462878022208160114419108
y[1] (numeric) = -2.8814794462878022208160114419097
absolute error = 1.1e-30
relative error = 3.8174834160872649844061359571911e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.551
Order of pole (three term test) = 32.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = -2.8781202373837369733370022120385
y[1] (numeric) = -2.8781202373837369733370022120374
absolute error = 1.1e-30
relative error = 3.8219390062727878638845936697577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.547
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = -2.8747542182901429200452783008831
y[1] (numeric) = -2.874754218290142920045278300882
absolute error = 1.1e-30
relative error = 3.8264140739456401929116371177078e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = -2.8713814636261359389252268850663
y[1] (numeric) = -2.8713814636261359389252268850653
absolute error = 1.0e-30
relative error = 3.4826441999007191138757684756602e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.539
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = -2.8680020481614519287125191984192
y[1] (numeric) = -2.8680020481614519287125191984182
absolute error = 1.0e-30
relative error = 3.4867478586392759205199991045406e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.536
Order of pole (three term test) = 32.69
NO COMPLEX POLE (six term test) for Equation 1
memory used=261.0MB, alloc=44.3MB, time=2.91
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = -2.8646160468157738817757174768489
y[1] (numeric) = -2.8646160468157738817757174768479
absolute error = 1.0e-30
relative error = 3.4908692252547132668482480033336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.532
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = -2.8612235346580576074750513497645
y[1] (numeric) = -2.8612235346580576074750513497634
absolute error = 1.1e-30
relative error = 3.8445091293136593921388668743327e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.528
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = -2.857824586905856112066848897709
y[1] (numeric) = -2.857824586905856112066848897708
absolute error = 1.0e-30
relative error = 3.4991650802566998158362763187308e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.524
Order of pole (three term test) = 32.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = -2.8544192789246426412341986758835
y[1] (numeric) = -2.8544192789246426412341986758825
absolute error = 1.0e-30
relative error = 3.5033395667672697275848619738125e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.52
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = -2.8510076862271323913364553581433
y[1] (numeric) = -2.8510076862271323913364553581422
absolute error = 1.1e-30
relative error = 3.8582849331272053668821298641977e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.515
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = -2.8475898844726028954821831774678
y[1] (numeric) = -2.8475898844726028954821831774668
absolute error = 1.0e-30
relative error = 3.5117416502032849362125868028596e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.511
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = -2.8441659494662130905420579190215
y[1] (numeric) = -2.8441659494662130905420579190205
absolute error = 1.0e-30
relative error = 3.5159692428906190779450699965164e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.507
Order of pole (three term test) = 32.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = -2.8407359571583210712301197533899
y[1] (numeric) = -2.8407359571583210712301197533889
absolute error = 1.0e-30
relative error = 3.5202145327168384429403111532591e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.503
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = -2.8372999836438005373935855735579
y[1] (numeric) = -2.8372999836438005373935855735569
absolute error = 1.0e-30
relative error = 3.5244775165287622957798371626032e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = -2.8338581051613559406631906133399
y[1] (numeric) = -2.8338581051613559406631906133389
absolute error = 1.0e-30
relative error = 3.5287581907459738188829481934805e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.494
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = -2.8304103980928363366277348714274
y[1] (numeric) = -2.8304103980928363366277348714264
absolute error = 1.0e-30
relative error = 3.5330565513531596249717261031575e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 32.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = -2.8269569389625479487081601386415
y[1] (numeric) = -2.8269569389625479487081601386405
absolute error = 1.0e-30
relative error = 3.5373725938923761794960987513509e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.485
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = -2.8234978044365654499180781215028
y[1] (numeric) = -2.8234978044365654499180781215019
absolute error = 9e-31
relative error = 3.1875356821097184217288814787759e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.48
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = -2.8200330713220419687092091685204
y[1] (numeric) = -2.8200330713220419687092091685195
absolute error = 9e-31
relative error = 3.1914519342075540276765023114258e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = -2.8165628165665178251116743327912
y[1] (numeric) = -2.8165628165665178251116743327902
absolute error = 1.0e-30
relative error = 3.5504267617188552533716149580209e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.471
Order of pole (three term test) = 32.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = -2.8130871172572280033905108422517
y[1] (numeric) = -2.8130871172572280033905108422507
absolute error = 1.0e-30
relative error = 3.5548134782793512848598088359201e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.466
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = -2.8096060506204083674511523943855
y[1] (numeric) = -2.8096060506204083674511523943845
absolute error = 1.0e-30
relative error = 3.5592178475668613632818874960144e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.462
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = -2.8061196940206006252379309430181
y[1] (numeric) = -2.8061196940206006252379309430171
absolute error = 1.0e-30
relative error = 3.5636398623011078125143520865991e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 32.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = -2.8026281249599560483809156991947
y[1] (numeric) = -2.8026281249599560483809156991936
absolute error = 1.1e-30
relative error = 3.9248874661732612148840804351574e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.452
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = -2.7991314210775379533576078246989
y[1] (numeric) = -2.7991314210775379533576078246978
absolute error = 1.1e-30
relative error = 3.9297904761347366867188953402931e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.447
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = -2.7956296601486229504471556547098
y[1] (numeric) = -2.7956296601486229504471556547087
absolute error = 1.1e-30
relative error = 3.9347128687335544166055339639317e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.442
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = -2.7921229200840009667658451450909
y[1] (numeric) = -2.7921229200840009667658451450899
absolute error = 1.0e-30
relative error = 3.5815042124646683476517649175305e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.437
Order of pole (three term test) = 32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = -2.7886112789292740496836535000557
y[1] (numeric) = -2.7886112789292740496836535000547
absolute error = 1.0e-30
relative error = 3.5860143274754445512513954795657e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.432
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = -2.78509481486415395693263049815
y[1] (numeric) = -2.7850948148641539569326304981489
absolute error = 1.1e-30
relative error = 3.9495962368292072025874713339992e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.427
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = -2.7815736062017585397287917998547
y[1] (numeric) = -2.7815736062017585397287917998536
absolute error = 1.1e-30
relative error = 3.9545960514848681935023965850111e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.422
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = -2.7780477313879069252400713903567
y[1] (numeric) = -2.7780477313879069252400713903555
absolute error = 1.2e-30
relative error = 4.3195802089422073082520997310486e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.416
Order of pole (three term test) = 32.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = -2.7745172690004135047436861883984
y[1] (numeric) = -2.7745172690004135047436861883972
absolute error = 1.2e-30
relative error = 4.3250767021981046318968989872789e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.411
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = -2.7709822977483807338270146393469
y[1] (numeric) = -2.7709822977483807338270146393457
absolute error = 1.2e-30
relative error = 4.3305942480220279439620779673879e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.406
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = -2.7674428964714907509967827109768
y[1] (numeric) = -2.7674428964714907509967827109756
absolute error = 1.2e-30
relative error = 4.3361328305274464009438441409725e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.4
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = -2.7638991441392958210719850277215
y[1] (numeric) = -2.7638991441392958210719850277203
absolute error = 1.2e-30
relative error = 4.3416924331140573585587220484491e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.395
Order of pole (three term test) = 32.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = -2.7603511198505076097465458175956
y[1] (numeric) = -2.7603511198505076097465458175944
absolute error = 1.2e-30
relative error = 4.3472730384567468495106867172061e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.389
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = -2.7567989028322852957182438104454
y[1] (numeric) = -2.7567989028322852957182438104442
absolute error = 1.2e-30
relative error = 4.3528746284944531846737703633085e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = -2.7532425724395225267908871219617
y[1] (numeric) = -2.7532425724395225267908871219605
absolute error = 1.2e-30
relative error = 4.3584971844189333218305413046985e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.378
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = -2.7496822081541332263671283908357
y[1] (numeric) = -2.7496822081541332263671283908344
absolute error = 1.3e-30
relative error = 4.7278190772187176300586585219358e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 32.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = -2.7461178895843362567596569129171
y[1] (numeric) = -2.7461178895843362567596569129158
absolute error = 1.3e-30
relative error = 4.7339555411321884948502226961640e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = -2.7425496964639389457587931431252
y[1] (numeric) = -2.7425496964639389457587931431239
absolute error = 1.3e-30
relative error = 4.7401146519829102143581503150159e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.361
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = -2.7389777086516194829047416205657
y[1] (numeric) = -2.7389777086516194829047416205644
absolute error = 1.3e-30
relative error = 4.7462963860336831931675171702897e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.355
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = -2.7354020061302081919229310227556
y[1] (numeric) = -2.7354020061302081919229310227543
absolute error = 1.3e-30
relative error = 4.7525007186754199793143104463287e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.349
Order of pole (three term test) = 32.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = -2.7318226690059676857909845794854
y[1] (numeric) = -2.7318226690059676857909845794841
absolute error = 1.3e-30
relative error = 4.7587276244143361740192868878146e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.344
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = -2.7282397775078719109159203846322
y[1] (numeric) = -2.7282397775078719109159203846308
absolute error = 1.4e-30
relative error = 5.1315137750789593788549474802386e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = -2.7246534119868840869101791446714
y[1] (numeric) = -2.72465341198688408691017914467
absolute error = 1.4e-30
relative error = 5.1382682063003590121303931943435e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.332
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = -2.7210636529152335484650165057321
y[1] (numeric) = -2.7210636529152335484650165057307
absolute error = 1.4e-30
relative error = 5.1450468587903067937532248558521e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.326
Order of pole (three term test) = 32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = -2.7174705808856914958296782173495
y[1] (numeric) = -2.717470580885691495829678217348
absolute error = 1.5e-30
relative error = 5.5198389655100242409610495358431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.32
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = -2.713874276610845660414598931654
y[1] (numeric) = -2.7138742766108456604145989316525
absolute error = 1.5e-30
relative error = 5.5271536081370639750389755360517e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.313
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = -2.7102748209223738920466293132038
y[1] (numeric) = -2.7102748209223738920466293132023
absolute error = 1.5e-30
relative error = 5.5344940978697972548919362125942e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.307
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = -2.7066722947703166744140012591308
y[1] (numeric) = -2.7066722947703166744140012591293
absolute error = 1.5e-30
relative error = 5.5418603977223895610466667434022e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.301
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=303.8MB, alloc=44.3MB, time=3.38
x[1] = 3.42
y[1] (closed_form) = -2.7030667792223485752483873143951
y[1] (numeric) = -2.7030667792223485752483873143935
absolute error = 1.6e-30
relative error = 5.9192026342031684329610209725329e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.295
Order of pole (three term test) = 32.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = -2.6994583554630486378009977259016
y[1] (numeric) = -2.6994583554630486378009977259001
absolute error = 1.5e-30
relative error = 5.5566702741102266046493474909742e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.288
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = -2.6958471047931697201791869257517
y[1] (numeric) = -2.6958471047931697201791869257501
absolute error = 1.6e-30
relative error = 5.9350546889518606516328165581248e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.282
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = -2.6922331086289067891195104822109
y[1] (numeric) = -2.6922331086289067891195104822093
absolute error = 1.6e-30
relative error = 5.9430217794730400644802897440353e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.276
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = -2.6886164485011641747825836218671
y[1] (numeric) = -2.6886164485011641747825836218655
absolute error = 1.6e-30
relative error = 5.9510161848930130046501501055274e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.269
Order of pole (three term test) = 32.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = -2.6849972060548217931644432232215
y[1] (numeric) = -2.6849972060548217931644432232199
absolute error = 1.6e-30
relative error = 5.9590378581843912946997415057691e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = -2.6813754630480003427284066264593
y[1] (numeric) = -2.6813754630480003427284066264577
absolute error = 1.6e-30
relative error = 5.9670867509961911629762864184890e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = -2.6777513013513254818706526127476
y[1] (numeric) = -2.677751301351325481870652612746
absolute error = 1.6e-30
relative error = 5.9751628136360573260136781036000e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.249
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = -2.6741248029471909938419223960331
y[1] (numeric) = -2.6741248029471909938419223960315
absolute error = 1.6e-30
relative error = 5.9832659950523522109443356412473e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 32.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = -2.6704960499290209457568513583932
y[1] (numeric) = -2.6704960499290209457568513583917
absolute error = 1.5e-30
relative error = 5.6169339776401034787072991791315e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.236
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = -2.666865124500530848331495464532
y[1] (numeric) = -2.6668651245005308483314954645305
absolute error = 1.5e-30
relative error = 5.6245814091589295896330911629191e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.229
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = -2.6632321089749878229986097305112
y[1] (numeric) = -2.6632321089749878229986097305096
absolute error = 1.6e-30
relative error = 6.0077377206742991394474188895702e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.223
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = -2.6595970857744697830591697153401
y[1] (numeric) = -2.6595970857744697830591697153385
absolute error = 1.6e-30
relative error = 6.0159488388598641466299911614823e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = -2.6559601374291236355375006712059
y[1] (numeric) = -2.6559601374291236355375006712043
absolute error = 1.6e-30
relative error = 6.0241867995381284065654550028574e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.209
Order of pole (three term test) = 32.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = -2.6523213465764225104161926490453
y[1] (numeric) = -2.6523213465764225104161926490438
absolute error = 1.5e-30
relative error = 5.6554233216732127794950995640630e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.202
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = -2.6486807959604220239357334315207
y[1] (numeric) = -2.6486807959604220239357334315192
absolute error = 1.5e-30
relative error = 5.6631965704878157233084734794893e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.195
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = -2.6450385684310155826524845764828
y[1] (numeric) = -2.6450385684310155826524845764813
absolute error = 1.5e-30
relative error = 5.6709948123356486599033715734996e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.188
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = -2.6413947469431887349572590224398
y[1] (numeric) = -2.6413947469431887349572590224383
absolute error = 1.5e-30
relative error = 5.6788179871104365582336852537593e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.181
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = -2.6377494145562725767653315557092
y[1] (numeric) = -2.6377494145562725767653315557078
absolute error = 1.4e-30
relative error = 5.3075549643729549222618569948684e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.174
Order of pole (three term test) = 32.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = -2.6341026544331962180972258896467
y[1] (numeric) = -2.6341026544331962180972258896454
absolute error = 1.3e-30
relative error = 4.9352670360515346053337865957175e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.167
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = -2.6304545498397383172780740830206
y[1] (numeric) = -2.6304545498397383172780740830193
absolute error = 1.3e-30
relative error = 4.9421116212755058340107788649544e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = -2.6268051841437776894917354511536
y[1] (numeric) = -2.6268051841437776894917354511524
absolute error = 1.2e-30
relative error = 4.5682870098002601813031177441784e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.153
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = -2.623154640814542996434192924372
y[1] (numeric) = -2.6231546408145429964341929243707
absolute error = 1.3e-30
relative error = 4.9558648955454776231032106177458e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.145
Order of pole (three term test) = 32.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = -2.6195030034218615238190149086001
y[1] (numeric) = -2.6195030034218615238190149085987
absolute error = 1.4e-30
relative error = 5.3445252712868718268713838938234e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.138
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = -2.6158503556354070534958800281944
y[1] (numeric) = -2.6158503556354070534958800281931
absolute error = 1.3e-30
relative error = 4.9697032446805297104041068531014e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.131
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = -2.6121967812239468369513106074327
y[1] (numeric) = -2.6121967812239468369513106074315
absolute error = 1.2e-30
relative error = 4.5938346169990266395805778190504e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.123
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = -2.6085423640545876769688483011286
y[1] (numeric) = -2.6085423640545876769688483011274
absolute error = 1.2e-30
relative error = 4.6002703139341776586663779964797e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.116
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = -2.6048871880920211242339318438447
y[1] (numeric) = -2.6048871880920211242339318438435
absolute error = 1.2e-30
relative error = 4.6067254101662401622282775741194e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.108
Order of pole (three term test) = 32.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = -2.6012313373977677956767023788826
y[1] (numeric) = -2.6012313373977677956767023788814
absolute error = 1.2e-30
relative error = 4.6131998440417903004139419513798e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.101
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = -2.5975748961294208213538661809524
y[1] (numeric) = -2.5975748961294208213538661809512
absolute error = 1.2e-30
relative error = 4.6196935525827916170397017587392e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.093
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = -2.593917948539888426678587729025
y[1] (numeric) = -2.5939179485398884266785877290238
absolute error = 1.2e-30
relative error = 4.6262064714709952986636350997155e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.086
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = -2.5902605789766356568151679477611
y[1] (numeric) = -2.5902605789766356568151679477599
absolute error = 1.2e-30
relative error = 4.6327385350322473841802962152331e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.078
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = -2.5866028718809252500629829470542
y[1] (numeric) = -2.586602871880925250062982947053
absolute error = 1.2e-30
relative error = 4.6392896762207036852317254753657e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 32.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = -2.5829449117870576670618176801359
y[1] (numeric) = -2.5829449117870576670618176801346
absolute error = 1.3e-30
relative error = 5.0330148121531993074935272619452e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.063
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = -2.5792867833216102826583265424381
y[1] (numeric) = -2.5792867833216102826583265424369
absolute error = 1.2e-30
relative error = 4.6524489163420508982470166804988e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.055
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = -2.5756285712026757472808889776155
y[1] (numeric) = -2.5756285712026757472808889776142
absolute error = 1.3e-30
relative error = 5.0473116136965823194133745879261e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.047
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = -2.5719703602390995246776025759664
y[1] (numeric) = -2.5719703602390995246776025759651
absolute error = 1.3e-30
relative error = 5.0544905963813182127486939019520e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.04
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = -2.5683122353297166128795688766971
y[1] (numeric) = -2.5683122353297166128795688766958
absolute error = 1.3e-30
relative error = 5.0616898604351650272656430641569e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.032
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = -2.5646542814625874552589780523246
y[1] (numeric) = -2.5646542814625874552589780523232
absolute error = 1.4e-30
relative error = 5.4588254257864301350574307420807e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.024
Order of pole (three term test) = 32.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = -2.5609965837142330485587877948568
y[1] (numeric) = -2.5609965837142330485587877948554
absolute error = 1.4e-30
relative error = 5.4666218959557112294410788368598e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.016
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = -2.5573392272488692547780189736216
y[1] (numeric) = -2.5573392272488692547780189736202
absolute error = 1.4e-30
relative error = 5.4744399377398594184891281921991e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = -2.55368229731764032380385592869
y[1] (numeric) = -2.5536822973176403238038559286886
absolute error = 1.4e-30
relative error = 5.4822794576699871205170819331758e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = -2.5500258792578516336888425372703
y[1] (numeric) = -2.5500258792578516336888425372689
absolute error = 1.4e-30
relative error = 5.4901403604870467821896814938077e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9921
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = -2.5463700584922016554785063793067
y[1] (numeric) = -2.5463700584922016554785063793054
absolute error = 1.3e-30
relative error = 5.1053066527564233610650853435939e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9841
Order of pole (three term test) = 32.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = -2.5427149205280131495017223694303
y[1] (numeric) = -2.5427149205280131495017223694289
absolute error = 1.4e-30
relative error = 5.5059259246777057931400904169122e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.976
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = -2.5390605509564636000430440525642
y[1] (numeric) = -2.5390605509564636000430440525628
absolute error = 1.4e-30
relative error = 5.5138503864061858663903111479951e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9678
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = -2.5354070354518148953230853176387
y[1] (numeric) = -2.5354070354518148953230853176373
absolute error = 1.4e-30
relative error = 5.5217958316918413040171681501430e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9597
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
memory used=346.7MB, alloc=44.3MB, time=3.83
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = -2.5317544597706422597198275063216
y[1] (numeric) = -2.5317544597706422597198275063202
absolute error = 1.4e-30
relative error = 5.5297621560300495145148739192665e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9515
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = -2.5281029097510624451704567202932
y[1] (numeric) = -2.5281029097510624451704567202918
absolute error = 1.4e-30
relative error = 5.5377492530074868504078473600433e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9433
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = -2.5244524713119611887000035008251
y[1] (numeric) = -2.5244524713119611887000035008237
absolute error = 1.4e-30
relative error = 5.5457570142820641163828768263779e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.935
Order of pole (three term test) = 32.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = -2.5208032304522199430296619082445
y[1] (numeric) = -2.5208032304522199430296619082431
absolute error = 1.4e-30
relative error = 5.5537853295627788903881038126137e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9267
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = -2.5171552732499418872242073068458
y[1] (numeric) = -2.5171552732499418872242073068445
absolute error = 1.3e-30
relative error = 5.1645602232616660955245353045093e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9184
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = -2.5135086858616772243444118040629
y[1] (numeric) = -2.5135086858616772243444118040616
absolute error = 1.3e-30
relative error = 5.1720529446045497847686210315723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.91
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = -2.5098635545216477730767732429238
y[1] (numeric) = -2.5098635545216477730767732429224
absolute error = 1.4e-30
relative error = 5.5779924668726643661270750450313e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9016
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = -2.506219965540970860319227846222
y[1] (numeric) = -2.5062199655409708603192278462205
absolute error = 1.5e-30
relative error = 5.9851091309785453585715371070945e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8932
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = -2.5025780053068825217078080022669
y[1] (numeric) = -2.5025780053068825217078080022654
absolute error = 1.5e-30
relative error = 5.9938191609578226358721175800337e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8847
Order of pole (three term test) = 32.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = -2.498937760281960017075435208899
y[1] (numeric) = -2.4989377602819600170754352088975
absolute error = 1.5e-30
relative error = 6.0025504590028367773687163346570e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8762
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = -2.4952993170033436678402037986135
y[1] (numeric) = -2.495299317003343667840203798612
absolute error = 1.5e-30
relative error = 6.0113028917163368100433956825433e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8677
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = -2.4916627620819580233266136976429
y[1] (numeric) = -2.4916627620819580233266136976414
absolute error = 1.5e-30
relative error = 6.0200763234373073013223971523357e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8592
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = -2.488028182201732363029250070779
y[1] (numeric) = -2.4880281822017323630292500707775
absolute error = 1.5e-30
relative error = 6.0288706162186798269122639309134e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8506
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = -2.4843956641188205418343842172076
y[1] (numeric) = -2.4843956641188205418343842172061
absolute error = 1.5e-30
relative error = 6.0376856298049789713531302782695e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.842
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = -2.4807652946608201852208834569065
y[1] (numeric) = -2.480765294660820185220883456905
absolute error = 1.5e-30
relative error = 6.0465212216099056432517713404072e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8333
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = -2.4771371607259912414676679289857
y[1] (numeric) = -2.4771371607259912414676679289841
absolute error = 1.6e-30
relative error = 6.4590690631401179384533955193024e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8246
Order of pole (three term test) = 32.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = -2.4735113492824738979007391600876
y[1] (numeric) = -2.473511349282473897900739160086
absolute error = 1.6e-30
relative error = 6.4685371282575049562327474308322e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8159
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = -2.4698879473675058682185289005279
y[1] (numeric) = -2.4698879473675058682185289005263
absolute error = 1.6e-30
relative error = 6.4780266720412831681989988071332e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8072
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = -2.4662670420866390579399770167267
y[1] (numeric) = -2.4662670420866390579399770167251
absolute error = 1.6e-30
relative error = 6.4875375322142126164206014319688e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7984
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = -2.462648720612955615025344119723
y[1] (numeric) = -2.4626487206129556150253441197214
absolute error = 1.6e-30
relative error = 6.4970695438923927168390489813989e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7897
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = -2.4590330701862833727252980508027
y[1] (numeric) = -2.4590330701862833727252980508011
absolute error = 1.6e-30
relative error = 6.5066225395610171311279395212896e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7808
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = -2.4554201781124106917192832867019
y[1] (numeric) = -2.4554201781124106917192832867003
absolute error = 1.6e-30
relative error = 6.5161963490500850079047495812804e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.772
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = -2.451810131762300708609588719247
y[1] (numeric) = -2.4518101317623007086095887192454
absolute error = 1.6e-30
relative error = 6.5257907995100722786333642869344e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7631
Order of pole (three term test) = 32.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = -2.4482030185713049978428720590002
y[1] (numeric) = -2.4482030185713049978428720589986
absolute error = 1.6e-30
relative error = 6.5354057153875667887393366615773e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7542
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = -2.4445989260383766541361782614116
y[1] (numeric) = -2.44459892603837665413617826141
absolute error = 1.6e-30
relative error = 6.5450409184008711408422647903076e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7453
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = -2.4409979417252828024897048296182
y[1] (numeric) = -2.4409979417252828024897048296166
absolute error = 1.6e-30
relative error = 6.5546962275155772245851338276942e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7363
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = -2.4374001532558165428737185634477
y[1] (numeric) = -2.4374001532558165428737185634461
absolute error = 1.6e-30
relative error = 6.5643714589201165063027496823562e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7273
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = -2.4338056483150083366821162530041
y[1] (numeric) = -2.4338056483150083366821162530025
absolute error = 1.6e-30
relative error = 6.5740664260012902517134716035677e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7183
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = -2.4302145146483368420501459116485
y[1] (numeric) = -2.430214514648336842050145911647
absolute error = 1.5e-30
relative error = 6.1722946306122974586867071924891e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7093
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = -2.4266268400609392051387653620253
y[1] (numeric) = -2.4266268400609392051387653620237
absolute error = 1.6e-30
relative error = 6.5935148065856703573821795422299e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7002
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = -2.4230427124168208144930112853723
y[1] (numeric) = -2.4230427124168208144930112853707
absolute error = 1.6e-30
relative error = 6.6032678326339055156061294296993e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6911
Order of pole (three term test) = 32.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = -2.4194622196380645255865841746395
y[1] (numeric) = -2.4194622196380645255865841746379
absolute error = 1.6e-30
relative error = 6.6130398193998225375675775093233e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.682
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = -2.4158854497040393626696229524164
y[1] (numeric) = -2.4158854497040393626696229524148
absolute error = 1.6e-30
relative error = 6.6228305658946276427192670418308e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6729
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = -2.4123124906506087050413472824371
y[1] (numeric) = -2.4123124906506087050413472824355
absolute error = 1.6e-30
relative error = 6.6326398681809033639572997952319e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6637
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = -2.4087434305693379648738857761415
y[1] (numeric) = -2.4087434305693379648738857761399
absolute error = 1.6e-30
relative error = 6.6424675193481237895035797610142e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6545
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = -2.4051783576067017637181843316641
y[1] (numeric) = -2.4051783576067017637181843316625
absolute error = 1.6e-30
relative error = 6.6523133094881868597853698449440e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6453
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = -2.4016173599632906148274007005201
y[1] (numeric) = -2.4016173599632906148274007005185
absolute error = 1.6e-30
relative error = 6.6621770256709688434811270544115e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6361
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = -2.3980605258930171184376390165437
y[1] (numeric) = -2.3980605258930171184376390165422
absolute error = 1.5e-30
relative error = 6.2550547986749120888088526276998e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6268
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = -2.3945079437023216771502614022885
y[1] (numeric) = -2.3945079437023216771502614022871
absolute error = 1.4e-30
relative error = 5.8467126980391590758224550760712e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6176
Order of pole (three term test) = 32.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = -2.3909597017493777385643328506655
y[1] (numeric) = -2.390959701749377738564332850664
absolute error = 1.5e-30
relative error = 6.2736314581233003580956227617189e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6083
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = -2.3874158884432965723120103252038
y[1] (numeric) = -2.3874158884432965723120103252024
absolute error = 1.4e-30
relative error = 5.8640809369533998095301089579285e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5989
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = -2.3838765922433315886538773926802
y[1] (numeric) = -2.3838765922433315886538773926787
absolute error = 1.5e-30
relative error = 6.2922720281775775124273693485257e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5896
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = -2.3803419016580822057953516592556
y[1] (numeric) = -2.3803419016580822057953516592542
absolute error = 1.4e-30
relative error = 5.8815080263251158156346307872282e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5802
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = -2.3768119052446972730893537885603
y[1] (numeric) = -2.3768119052446972730893537885588
absolute error = 1.5e-30
relative error = 6.3109747838694546087152279569228e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5709
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = -2.3732866916080780572944239008123
y[1] (numeric) = -2.3732866916080780572944239008109
absolute error = 1.4e-30
relative error = 5.8989923339240401115082856079557e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5615
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = -2.3697663494000807990614036500826
y[1] (numeric) = -2.3697663494000807990614036500811
absolute error = 1.5e-30
relative error = 6.3297379523501679119228863181368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.552
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=389.6MB, alloc=44.3MB, time=4.30
x[1] = 4.35
y[1] (closed_form) = -2.366250967318718846825670216824
y[1] (numeric) = -2.3662509673187188468256702168225
absolute error = 1.5e-30
relative error = 6.3391416241012765285863420075815e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5426
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = -2.3627406341073643752857117999657
y[1] (numeric) = -2.3627406341073643752857117999642
absolute error = 1.5e-30
relative error = 6.3485597121695714877771368791905e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5331
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = -2.3592354385539496956525729129928
y[1] (numeric) = -2.3592354385539496956525729129913
absolute error = 1.5e-30
relative error = 6.3579919811623278427007204857500e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5236
Order of pole (three term test) = 32.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = -2.3557354694901681648583718478512
y[1] (numeric) = -2.3557354694901681648583718478497
absolute error = 1.5e-30
relative error = 6.3674381925600172326919904290056e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5141
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = -2.3522408157906747009157020361581
y[1] (numeric) = -2.3522408157906747009157020361566
absolute error = 1.5e-30
relative error = 6.3768981046942457710483057213718e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5046
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = -2.3487515663722859116232736765864
y[1] (numeric) = -2.3487515663722859116232736765848
absolute error = 1.6e-30
relative error = 6.8121295709075176546785257790593e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4951
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = -2.3452678101931798438166318785189
y[1] (numeric) = -2.3452678101931798438166318785174
absolute error = 1.5e-30
relative error = 6.3958580486227920985679247792131e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4855
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = -2.3417896362520953603662026638186
y[1] (numeric) = -2.3417896362520953603662026638171
absolute error = 1.5e-30
relative error = 6.4053575811389572108894525669395e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4759
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = -2.3383171335875311521282684400961
y[1] (numeric) = -2.3383171335875311521282684400947
absolute error = 1.4e-30
relative error = 5.9872118280725639008592639303143e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4663
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = -2.3348503912769443920577599800286
y[1] (numeric) = -2.3348503912769443920577599800271
absolute error = 1.5e-30
relative error = 6.4243944948423035693710442128209e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4567
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = -2.331389498435949038694972482518
y[1] (numeric) = -2.3313894984359490386949724825165
absolute error = 1.5e-30
relative error = 6.4339313572712738580621969537713e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4471
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = -2.3279345442175137962414689237959
y[1] (numeric) = -2.3279345442175137962414689237944
absolute error = 1.5e-30
relative error = 6.4434801387604883507462137773100e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4375
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = -2.3244856178111597384435246015749
y[1] (numeric) = -2.3244856178111597384435246015734
absolute error = 1.5e-30
relative error = 6.4530405716705079090701460484257e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4278
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = -2.3210428084421576035044925052102
y[1] (numeric) = -2.3210428084421576035044925052087
absolute error = 1.5e-30
relative error = 6.4626123850200469010311693669423e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4181
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = -2.3176062053707247672504298823242
y[1] (numeric) = -2.3176062053707247672504298823227
absolute error = 1.5e-30
relative error = 6.4721953044652798995042317558819e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4085
Order of pole (three term test) = 32.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = -2.3141758978912219017762220908267
y[1] (numeric) = -2.3141758978912219017762220908252
absolute error = 1.5e-30
relative error = 6.4817890522793253489301740096168e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3987
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = -2.3107519753313493268022704986616
y[1] (numeric) = -2.3107519753313493268022704986602
absolute error = 1.4e-30
relative error = 6.0586337908431197043822256872150e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.389
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = -2.3073345270513430609745767964646
y[1] (numeric) = -2.3073345270513430609745767964632
absolute error = 1.4e-30
relative error = 6.0676073780646331325922361566933e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3793
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = -2.3039236424431705803437565957192
y[1] (numeric) = -2.3039236424431705803437565957178
absolute error = 1.4e-30
relative error = 6.0765902749944670090413849628354e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3696
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = -2.3005194109297262912611505726609
y[1] (numeric) = -2.3005194109297262912611505726595
absolute error = 1.4e-30
relative error = 6.0855822096028627822362483450973e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3598
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = -2.2971219219640267249327716623727
y[1] (numeric) = -2.2971219219640267249327716623713
absolute error = 1.4e-30
relative error = 6.0945829066095352457828717749540e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.35
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = -2.2937312650284054608743318851117
y[1] (numeric) = -2.2937312650284054608743318851104
absolute error = 1.3e-30
relative error = 5.6676212240752661175715355836871e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3402
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = -2.2903475296337077865130322753616
y[1] (numeric) = -2.2903475296337077865130322753602
absolute error = 1.4e-30
relative error = 6.1126094703361464332318285584779e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3305
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = -2.2869708053184851001841740614532
y[1] (numeric) = -2.2869708053184851001841740614518
absolute error = 1.4e-30
relative error = 6.1216347700819689899624760446803e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3206
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = -2.2836011816481890647729586884774
y[1] (numeric) = -2.283601181648189064772958688476
absolute error = 1.4e-30
relative error = 6.1306676982429570035513615333654e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3108
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = -2.2802387482143655192540884688261
y[1] (numeric) = -2.2802387482143655192540884688247
absolute error = 1.4e-30
relative error = 6.1397079630206592360032181067860e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.301
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = -2.276883594633848155383958562862
y[1] (numeric) = -2.2768835946338481553839585628606
absolute error = 1.4e-30
relative error = 6.1487552692615267773198183987341e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2912
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = -2.2735358105479519668023446173072
y[1] (numeric) = -2.2735358105479519668023446173057
absolute error = 1.5e-30
relative error = 6.5976528411860832530247274467510e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2813
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = -2.2701954856216664778025387019458
y[1] (numeric) = -2.2701954856216664778025387019443
absolute error = 1.5e-30
relative error = 6.6073605092613535281680405392497e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2714
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = -2.2668627095428487590308691677129
y[1] (numeric) = -2.2668627095428487590308691677113
absolute error = 1.6e-30
relative error = 7.0582130680629842215232917833305e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2616
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = -2.2635375720214162373784576833481
y[1] (numeric) = -2.2635375720214162373784576833466
absolute error = 1.5e-30
relative error = 6.6267952365396296501836173887360e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2517
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = -2.2602201627885393073299189762699
y[1] (numeric) = -2.2602201627885393073299189762684
absolute error = 1.5e-30
relative error = 6.6365216304830227553818682991130e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2418
Order of pole (three term test) = 32.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = -2.2569105715958337510354956894998
y[1] (numeric) = -2.2569105715958337510354956894983
absolute error = 1.5e-30
relative error = 6.6462535949723892671573884916565e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2319
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = -2.2536088882145529743748422542616
y[1] (numeric) = -2.2536088882145529743748422542601
absolute error = 1.5e-30
relative error = 6.6559907881282448061571252518385e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.222
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = -2.2503152024347800662823277517938
y[1] (numeric) = -2.2503152024347800662823277517923
absolute error = 1.5e-30
relative error = 6.6657328643429180475405665730421e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2121
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = -2.247029604064619688605318383054
y[1] (numeric) = -2.2470296040646196886053183830525
absolute error = 1.5e-30
relative error = 6.6754794742653655732974391226468e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2022
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = -2.2437521829293898037684253670284
y[1] (numeric) = -2.2437521829293898037684253670269
absolute error = 1.5e-30
relative error = 6.6852302647863520411112290651068e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1922
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = -2.2404830288708132475181638335818
y[1] (numeric) = -2.2404830288708132475181638335802
absolute error = 1.6e-30
relative error = 7.1413172042922729847043104339818e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1823
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = -2.2372222317462091540238625520325
y[1] (numeric) = -2.2372222317462091540238625520309
absolute error = 1.6e-30
relative error = 7.1517258200637452569635305024047e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1723
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = -2.2339698814276842406119931293884
y[1] (numeric) = -2.2339698814276842406119931293869
absolute error = 1.5e-30
relative error = 6.7145041321746953307043155628450e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1624
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = -2.2307260678013239594123506104535
y[1] (numeric) = -2.230726067801323959412350610452
absolute error = 1.5e-30
relative error = 6.7242680383362745325244171667384e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1524
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = -2.227490880766383523195715204455
y[1] (numeric) = -2.2274908807663835231957152044534
absolute error = 1.6e-30
relative error = 7.1829699228645507197345790886246e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1425
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = -2.2242644102344788126837571386614
y[1] (numeric) = -2.2242644102344788126837571386599
absolute error = 1.5e-30
relative error = 6.7438025492745807074584274443916e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1325
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = -2.221046746128777172613013388475
y[1] (numeric) = -2.2210467461287771726130133884734
absolute error = 1.6e-30
relative error = 7.2038105581917876681539632170630e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1225
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = -2.2178379783831881038357662460808
y[1] (numeric) = -2.2178379783831881038357662460792
absolute error = 1.6e-30
relative error = 7.2142330305228417927310823139859e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1126
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = -2.2146381969415538587415893569213
y[1] (numeric) = -2.2146381969415538587415893569197
absolute error = 1.6e-30
relative error = 7.2246563895160042197561407851135e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1026
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = -2.2114474917568399472841969666007
y[1] (numeric) = -2.2114474917568399472841969665991
absolute error = 1.6e-30
relative error = 7.2350802176583094233054746227229e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09261
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
memory used=432.4MB, alloc=44.3MB, time=4.75
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = -2.2082659527903255608990366724942
y[1] (numeric) = -2.2082659527903255608990366724925
absolute error = 1.7e-30
relative error = 7.6983480991132895575126164279545e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08262
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = -2.2050936700107939215978049570901
y[1] (numeric) = -2.2050936700107939215978049570884
absolute error = 1.7e-30
relative error = 7.7094230649697457486567486144275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07263
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = -2.2019307333937225635267381872835
y[1] (numeric) = -2.2019307333937225635267381872818
absolute error = 1.7e-30
relative error = 7.7204971719518054711479440312353e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06264
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = -2.1987772329204735542761395894042
y[1] (numeric) = -2.1987772329204735542761395894026
absolute error = 1.6e-30
relative error = 7.2767717258689187963327600168786e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05265
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
TOP MAIN SOLVE Loop
x[1] = 4.859764792968356813380717148829
y[1] (closed_form) = -2.1957070969883162026828563988103
y[1] (numeric) = -2.1957070969883162026828563988087
absolute error = 1.6e-30
relative error = 7.2869464337688658503220376516355e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.0047647929683568133807171488289625
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 = 0.04288
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
SETTING H FOR POLE
TOP MAIN SOLVE Loop
x[1] = 4.8713869370181875689001279219295
y[1] (closed_form) = -2.1920649490121811447162015366007
y[1] (numeric) = -2.1920649490121811447162015365989
absolute error = 1.8e-30
relative error = 8.2114355270866453307432538717867e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.0034738855326024712699212208023156
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 = 0.03127
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE
SETTING H FOR POLE
TOP MAIN SOLVE Loop
x[1] = 4.8798600592489697482073893401738
y[1] (closed_form) = -2.1894179074901061470270630303204
y[1] (numeric) = -2.1894179074901061470270630303186
absolute error = 1.8e-30
relative error = 8.2213632849266082654337502143189e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.0025325987383926088085827449870271
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 = 0.02279
Order of pole (three term test) = 33
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
TOP MAIN SOLVE Loop
x[1] = 4.8905404048944713998984138670867
y[1] (closed_form) = -2.1860913446634875865799163738028
y[1] (numeric) = -2.1860913446634875865799163738012
absolute error = 1.6e-30
relative error = 7.3189988328062906086142617174592e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.0013459857157070880101303884232561
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 = 0.01211
Order of pole (three term test) = 33
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
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
TOP MAIN SOLVE Loop
x[1] = 4.9001602415214508977266667736652
y[1] (closed_form) = -2.1831047488291306369829037438072
y[1] (numeric) = -2.1831047488291306369829037438059
absolute error = 1.3e-30
relative error = 5.9548219145106612689672099232698e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.00027713109457283309093583370482944
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 = 0.002494
Order of pole (three term test) = 33
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
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
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
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
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memory used=474.6MB, alloc=44.3MB, time=5.19
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memory used=515.5MB, alloc=44.3MB, time=5.61
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memory used=556.3MB, alloc=44.3MB, time=6.03
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memory used=597.0MB, alloc=44.3MB, time=6.45
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memory used=637.8MB, alloc=44.3MB, time=6.88
SETTING H FOR POLE
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memory used=678.5MB, alloc=44.3MB, time=7.30
SETTING H FOR POLE
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memory used=719.0MB, alloc=44.3MB, time=7.70
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memory used=759.5MB, alloc=44.3MB, time=8.13
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memory used=800.0MB, alloc=44.3MB, time=8.55
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memory used=840.5MB, alloc=44.3MB, time=8.97
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memory used=880.9MB, alloc=44.3MB, time=9.37
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memory used=921.5MB, alloc=44.3MB, time=9.80
SETTING H FOR POLE
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memory used=961.9MB, alloc=44.3MB, time=10.22
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memory used=1002.5MB, alloc=44.3MB, time=10.64
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memory used=1043.0MB, alloc=44.3MB, time=11.06
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memory used=1083.4MB, alloc=44.3MB, time=11.47
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memory used=1123.9MB, alloc=44.3MB, time=11.89
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memory used=1164.4MB, alloc=44.3MB, time=12.31
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memory used=1205.0MB, alloc=44.3MB, time=12.72
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memory used=1245.5MB, alloc=44.3MB, time=13.14
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memory used=1286.0MB, alloc=44.3MB, time=13.56
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memory used=1326.5MB, alloc=44.3MB, time=13.98
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memory used=1367.0MB, alloc=44.3MB, time=14.39
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memory used=1407.5MB, alloc=44.3MB, time=14.81
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memory used=1448.0MB, alloc=44.3MB, time=15.23
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memory used=1488.5MB, alloc=44.3MB, time=15.66
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memory used=1529.0MB, alloc=44.3MB, time=16.08
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memory used=1569.6MB, alloc=44.3MB, time=16.50
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memory used=1610.1MB, alloc=44.3MB, time=16.91
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memory used=1650.5MB, alloc=44.3MB, time=17.33
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memory used=1691.1MB, alloc=44.3MB, time=17.75
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memory used=1731.7MB, alloc=44.3MB, time=18.17
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memory used=1772.3MB, alloc=44.3MB, time=18.58
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memory used=1812.8MB, alloc=44.3MB, time=19.00
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memory used=1853.3MB, alloc=44.3MB, time=19.42
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memory used=1893.9MB, alloc=44.3MB, time=19.84
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memory used=1934.4MB, alloc=44.3MB, time=20.25
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memory used=1974.9MB, alloc=44.3MB, time=20.67
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memory used=2015.4MB, alloc=44.3MB, time=21.09
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memory used=2055.9MB, alloc=44.3MB, time=21.52
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memory used=2096.4MB, alloc=44.3MB, time=21.94
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memory used=2136.9MB, alloc=44.3MB, time=22.36
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memory used=2177.3MB, alloc=44.3MB, time=22.76
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memory used=2217.8MB, alloc=44.3MB, time=23.19
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memory used=2258.4MB, alloc=44.3MB, time=23.61
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memory used=2298.8MB, alloc=44.3MB, time=24.03
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memory used=2339.4MB, alloc=44.3MB, time=24.44
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memory used=2379.8MB, alloc=44.3MB, time=24.86
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memory used=2420.3MB, alloc=44.3MB, time=25.28
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memory used=2460.8MB, alloc=44.3MB, time=25.70
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memory used=2501.2MB, alloc=44.3MB, time=26.13
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memory used=2541.9MB, alloc=44.3MB, time=26.55
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memory used=2582.4MB, alloc=44.3MB, time=26.97
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memory used=2622.9MB, alloc=44.3MB, time=27.39
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memory used=2663.4MB, alloc=44.3MB, time=27.81
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memory used=2704.0MB, alloc=44.3MB, time=28.22
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memory used=2744.4MB, alloc=44.3MB, time=28.64
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memory used=2784.9MB, alloc=44.3MB, time=29.06
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memory used=2825.3MB, alloc=44.3MB, time=29.48
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memory used=2865.9MB, alloc=44.3MB, time=29.89
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memory used=2906.5MB, alloc=44.3MB, time=30.31
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memory used=2947.0MB, alloc=44.3MB, time=30.73
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memory used=2987.5MB, alloc=44.3MB, time=31.16
SETTING H FOR POLE
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memory used=3028.1MB, alloc=44.3MB, time=31.58
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memory used=3068.6MB, alloc=44.3MB, time=32.00
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memory used=3109.1MB, alloc=44.3MB, time=32.41
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memory used=3149.6MB, alloc=44.3MB, time=32.83
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memory used=3190.1MB, alloc=44.3MB, time=33.31
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memory used=3230.6MB, alloc=44.3MB, time=33.73
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memory used=3271.1MB, alloc=44.3MB, time=34.16
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memory used=3311.5MB, alloc=44.3MB, time=34.56
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memory used=3352.0MB, alloc=44.3MB, time=34.98
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memory used=3392.4MB, alloc=44.3MB, time=35.41
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memory used=3433.0MB, alloc=44.3MB, time=35.83
SETTING H FOR POLE
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memory used=3473.5MB, alloc=44.3MB, time=36.25
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memory used=3513.9MB, alloc=44.3MB, time=36.66
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memory used=3554.4MB, alloc=44.3MB, time=37.08
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memory used=3594.9MB, alloc=44.3MB, time=37.50
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memory used=3635.3MB, alloc=44.3MB, time=37.92
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memory used=3675.9MB, alloc=44.3MB, time=38.34
SETTING H FOR POLE
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memory used=3716.4MB, alloc=44.3MB, time=38.75
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memory used=3756.9MB, alloc=44.3MB, time=39.17
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memory used=3797.4MB, alloc=44.3MB, time=39.59
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TOP MAIN SOLVE Loop
x[1] = 4.9100000517543902142652658335513
y[1] (closed_form) = -2.1800594126029087531590437557314
y[1] (numeric) = -2.1800594126029087531590437557311
absolute error = 3e-31
relative error = 1.3761092852135222756219693140408e-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 = 0.007346
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
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memory used=3837.9MB, alloc=44.3MB, time=40.02
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memory used=3878.4MB, alloc=44.3MB, time=40.44
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memory used=3918.8MB, alloc=44.3MB, time=40.86
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memory used=3959.4MB, alloc=44.3MB, time=41.26
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memory used=3999.9MB, alloc=44.3MB, time=41.70
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memory used=4040.5MB, alloc=44.3MB, time=42.13
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memory used=4081.1MB, alloc=44.3MB, time=42.55
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memory used=4121.6MB, alloc=44.3MB, time=42.97
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memory used=4162.1MB, alloc=44.3MB, time=43.39
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memory used=4202.6MB, alloc=44.3MB, time=43.80
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memory used=4243.1MB, alloc=44.3MB, time=44.22
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memory used=4283.6MB, alloc=44.3MB, time=44.64
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memory used=4324.2MB, alloc=44.3MB, time=45.06
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memory used=4364.6MB, alloc=44.3MB, time=45.48
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memory used=4405.1MB, alloc=44.3MB, time=45.89
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memory used=4445.7MB, alloc=44.3MB, time=46.31
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memory used=4486.3MB, alloc=44.3MB, time=46.73
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memory used=4526.8MB, alloc=44.3MB, time=47.16
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memory used=4567.4MB, alloc=44.3MB, time=47.58
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memory used=4607.9MB, alloc=44.3MB, time=47.98
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memory used=4648.5MB, alloc=44.3MB, time=48.41
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memory used=4688.9MB, alloc=44.3MB, time=48.83
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memory used=4729.3MB, alloc=44.3MB, time=49.25
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memory used=4769.9MB, alloc=44.3MB, time=49.67
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memory used=4810.4MB, alloc=44.3MB, time=50.08
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memory used=4850.9MB, alloc=44.3MB, time=50.50
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memory used=4891.4MB, alloc=44.3MB, time=50.92
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memory used=4931.8MB, alloc=44.3MB, time=51.34
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memory used=4972.4MB, alloc=44.3MB, time=51.75
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memory used=5012.8MB, alloc=44.3MB, time=52.17
SETTING H FOR POLE
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memory used=5053.4MB, alloc=44.3MB, time=52.58
SETTING H FOR POLE
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memory used=5094.0MB, alloc=44.3MB, time=53.00
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memory used=5134.6MB, alloc=44.3MB, time=53.42
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memory used=5175.2MB, alloc=44.3MB, time=53.83
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memory used=5215.6MB, alloc=44.3MB, time=54.25
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memory used=5256.1MB, alloc=44.3MB, time=54.67
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memory used=5296.6MB, alloc=44.3MB, time=55.08
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memory used=5337.1MB, alloc=44.3MB, time=55.50
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memory used=5377.6MB, alloc=44.3MB, time=55.92
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memory used=5418.0MB, alloc=44.3MB, time=56.33
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memory used=5458.6MB, alloc=44.3MB, time=56.75
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memory used=5499.1MB, alloc=44.3MB, time=57.17
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memory used=5539.7MB, alloc=44.3MB, time=57.59
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memory used=5580.3MB, alloc=44.3MB, time=58.01
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memory used=5620.8MB, alloc=44.3MB, time=58.42
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memory used=5661.3MB, alloc=44.3MB, time=58.84
SETTING H FOR POLE
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memory used=5701.8MB, alloc=44.3MB, time=59.27
SETTING H FOR POLE
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memory used=5742.3MB, alloc=44.3MB, time=59.69
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memory used=5782.9MB, alloc=44.3MB, time=60.11
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memory used=5823.5MB, alloc=44.3MB, time=60.53
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memory used=5864.0MB, alloc=44.3MB, time=60.95
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memory used=5904.5MB, alloc=44.3MB, time=61.38
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memory used=5945.0MB, alloc=44.3MB, time=61.78
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memory used=5985.5MB, alloc=44.3MB, time=62.22
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memory used=6025.9MB, alloc=44.3MB, time=62.62
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memory used=6066.5MB, alloc=44.3MB, time=63.05
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memory used=6107.0MB, alloc=44.3MB, time=63.47
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memory used=6147.5MB, alloc=44.3MB, time=63.89
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memory used=6188.1MB, alloc=44.3MB, time=64.30
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memory used=6228.6MB, alloc=44.3MB, time=64.72
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memory used=6269.2MB, alloc=44.3MB, time=65.14
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memory used=6309.6MB, alloc=44.3MB, time=65.58
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memory used=6350.1MB, alloc=44.3MB, time=66.00
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memory used=6390.7MB, alloc=44.3MB, time=66.41
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memory used=6431.2MB, alloc=44.3MB, time=66.83
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memory used=6471.8MB, alloc=44.3MB, time=67.25
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memory used=6512.3MB, alloc=44.3MB, time=67.67
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memory used=6552.9MB, alloc=44.3MB, time=68.09
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memory used=6593.5MB, alloc=44.3MB, time=68.51
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memory used=6634.0MB, alloc=44.3MB, time=68.92
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memory used=6674.5MB, alloc=44.3MB, time=69.34
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memory used=6715.0MB, alloc=44.3MB, time=69.75
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memory used=6755.5MB, alloc=44.3MB, time=70.17
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memory used=6796.1MB, alloc=44.3MB, time=70.59
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memory used=6836.6MB, alloc=44.3MB, time=71.02
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memory used=6877.2MB, alloc=44.3MB, time=71.44
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memory used=6917.7MB, alloc=44.3MB, time=71.84
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memory used=6958.2MB, alloc=44.3MB, time=72.27
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memory used=6998.8MB, alloc=44.3MB, time=72.69
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memory used=7039.4MB, alloc=44.3MB, time=73.11
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memory used=7079.9MB, alloc=44.3MB, time=73.53
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memory used=7120.4MB, alloc=44.3MB, time=73.95
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memory used=7160.9MB, alloc=44.3MB, time=74.38
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memory used=7201.5MB, alloc=44.3MB, time=74.78
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memory used=7242.0MB, alloc=44.3MB, time=75.20
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memory used=7282.6MB, alloc=44.3MB, time=75.62
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memory used=7323.0MB, alloc=44.3MB, time=76.05
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memory used=7363.6MB, alloc=44.3MB, time=76.47
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memory used=7404.2MB, alloc=44.3MB, time=76.88
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memory used=7444.6MB, alloc=44.3MB, time=77.30
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memory used=7485.2MB, alloc=44.3MB, time=77.72
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memory used=7525.7MB, alloc=44.3MB, time=78.14
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memory used=7566.2MB, alloc=44.3MB, time=78.56
SETTING H FOR POLE
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memory used=7606.8MB, alloc=44.3MB, time=78.98
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memory used=7647.3MB, alloc=44.3MB, time=79.41
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memory used=7687.8MB, alloc=44.3MB, time=79.81
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memory used=7728.3MB, alloc=44.3MB, time=80.23
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memory used=7768.9MB, alloc=44.3MB, time=80.66
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memory used=7809.5MB, alloc=44.3MB, time=81.08
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memory used=7850.0MB, alloc=44.3MB, time=81.50
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memory used=7890.6MB, alloc=44.3MB, time=81.92
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memory used=7931.1MB, alloc=44.3MB, time=82.34
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memory used=7971.6MB, alloc=44.3MB, time=82.75
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memory used=8012.1MB, alloc=44.3MB, time=83.17
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memory used=8052.7MB, alloc=44.3MB, time=83.59
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memory used=8093.1MB, alloc=44.3MB, time=84.02
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memory used=8133.7MB, alloc=44.3MB, time=84.44
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memory used=8174.3MB, alloc=44.3MB, time=84.84
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memory used=8214.9MB, alloc=44.3MB, time=85.26
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memory used=8255.4MB, alloc=44.3MB, time=85.69
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memory used=8296.0MB, alloc=44.3MB, time=86.11
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memory used=8336.5MB, alloc=44.3MB, time=86.53
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memory used=8377.0MB, alloc=44.3MB, time=86.94
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TOP MAIN SOLVE Loop
x[1] = 4.9200000517543902142652658335513
y[1] (closed_form) = -2.1769744849911096959472198560283
y[1] (numeric) = -2.1769744849911096959472198560208
absolute error = 7.5e-30
relative error = 3.4451483247543107590045971404862e-28 %
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 = 0.01735
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
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memory used=8417.7MB, alloc=44.3MB, time=87.36
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memory used=8498.7MB, alloc=44.3MB, time=88.20
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memory used=8539.2MB, alloc=44.3MB, time=88.63
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memory used=8579.7MB, alloc=44.3MB, time=89.05
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memory used=8620.3MB, alloc=44.3MB, time=89.45
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memory used=8660.8MB, alloc=44.3MB, time=89.87
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memory used=8701.4MB, alloc=44.3MB, time=90.30
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memory used=8741.9MB, alloc=44.3MB, time=90.72
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memory used=8782.5MB, alloc=44.3MB, time=91.14
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memory used=8823.1MB, alloc=44.3MB, time=91.55
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memory used=8863.6MB, alloc=44.3MB, time=91.97
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memory used=8904.2MB, alloc=44.3MB, time=92.39
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memory used=8944.7MB, alloc=44.3MB, time=92.81
SETTING H FOR POLE
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memory used=8985.2MB, alloc=44.3MB, time=93.23
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memory used=9025.8MB, alloc=44.3MB, time=93.66
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memory used=9066.4MB, alloc=44.3MB, time=94.08
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memory used=9107.0MB, alloc=44.3MB, time=94.48
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memory used=9147.5MB, alloc=44.3MB, time=94.91
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memory used=9188.0MB, alloc=44.3MB, time=95.33
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memory used=9228.5MB, alloc=44.3MB, time=95.75
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memory used=9269.1MB, alloc=44.3MB, time=96.16
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memory used=9309.7MB, alloc=44.3MB, time=96.58
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memory used=9350.2MB, alloc=44.3MB, time=97.00
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memory used=9390.8MB, alloc=44.3MB, time=97.42
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memory used=9431.4MB, alloc=44.3MB, time=97.83
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memory used=9471.9MB, alloc=44.3MB, time=98.25
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memory used=9512.4MB, alloc=44.3MB, time=98.67
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memory used=9552.9MB, alloc=44.3MB, time=99.09
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memory used=9593.5MB, alloc=44.3MB, time=99.50
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memory used=9634.0MB, alloc=44.3MB, time=99.92
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memory used=9674.6MB, alloc=44.3MB, time=100.34
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memory used=9715.2MB, alloc=44.3MB, time=100.77
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memory used=9755.6MB, alloc=44.3MB, time=101.19
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memory used=9796.2MB, alloc=44.3MB, time=101.59
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memory used=9836.7MB, alloc=44.3MB, time=102.02
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memory used=9877.2MB, alloc=44.3MB, time=102.44
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memory used=9917.7MB, alloc=44.3MB, time=102.86
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memory used=9958.2MB, alloc=44.3MB, time=103.27
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memory used=9998.8MB, alloc=44.3MB, time=103.69
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memory used=10039.4MB, alloc=44.3MB, time=104.11
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memory used=10079.9MB, alloc=44.3MB, time=104.53
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memory used=10120.5MB, alloc=44.3MB, time=104.95
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memory used=10160.9MB, alloc=44.3MB, time=105.36
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memory used=10201.5MB, alloc=44.3MB, time=105.78
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memory used=10242.1MB, alloc=44.3MB, time=106.20
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memory used=10282.6MB, alloc=44.3MB, time=106.63
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memory used=10323.2MB, alloc=44.3MB, time=107.05
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memory used=10363.7MB, alloc=44.3MB, time=107.47
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memory used=10404.3MB, alloc=44.3MB, time=107.89
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memory used=10444.8MB, alloc=44.3MB, time=108.31
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memory used=10485.4MB, alloc=44.3MB, time=108.73
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memory used=10525.9MB, alloc=44.3MB, time=109.16
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memory used=10566.4MB, alloc=44.3MB, time=109.58
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memory used=10607.0MB, alloc=44.3MB, time=109.98
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memory used=10647.6MB, alloc=44.3MB, time=110.41
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memory used=10688.1MB, alloc=44.3MB, time=110.83
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memory used=10728.7MB, alloc=44.3MB, time=111.25
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memory used=10769.1MB, alloc=44.3MB, time=111.66
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memory used=10809.7MB, alloc=44.3MB, time=112.08
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memory used=10850.3MB, alloc=44.3MB, time=112.50
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memory used=10890.8MB, alloc=44.3MB, time=112.92
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memory used=10931.3MB, alloc=44.3MB, time=113.34
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memory used=10971.8MB, alloc=44.3MB, time=113.75
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memory used=11012.4MB, alloc=44.3MB, time=114.17
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memory used=11053.0MB, alloc=44.3MB, time=114.59
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memory used=11093.5MB, alloc=44.3MB, time=115.02
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memory used=11134.0MB, alloc=44.3MB, time=115.44
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memory used=11174.5MB, alloc=44.3MB, time=115.84
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memory used=11215.1MB, alloc=44.3MB, time=116.27
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memory used=11255.6MB, alloc=44.3MB, time=116.69
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memory used=11296.2MB, alloc=44.3MB, time=117.11
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memory used=11336.7MB, alloc=44.3MB, time=117.53
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memory used=11377.2MB, alloc=44.3MB, time=117.95
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memory used=11417.7MB, alloc=44.3MB, time=118.38
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memory used=11458.3MB, alloc=44.3MB, time=118.80
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memory used=11498.8MB, alloc=44.3MB, time=119.22
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memory used=11539.3MB, alloc=44.3MB, time=119.63
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memory used=11579.9MB, alloc=44.3MB, time=120.05
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memory used=11620.5MB, alloc=44.3MB, time=120.48
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memory used=11661.1MB, alloc=44.3MB, time=120.91
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memory used=11701.6MB, alloc=44.3MB, time=121.33
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memory used=11742.2MB, alloc=44.3MB, time=121.73
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memory used=11782.6MB, alloc=44.3MB, time=122.16
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memory used=11823.2MB, alloc=44.3MB, time=122.58
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memory used=11863.8MB, alloc=44.3MB, time=123.00
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memory used=11904.3MB, alloc=44.3MB, time=123.42
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memory used=11944.9MB, alloc=44.3MB, time=123.84
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memory used=11985.4MB, alloc=44.3MB, time=124.27
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memory used=12026.0MB, alloc=44.3MB, time=124.70
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memory used=12066.6MB, alloc=44.3MB, time=125.13
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memory used=12107.0MB, alloc=44.3MB, time=125.56
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memory used=12147.5MB, alloc=44.3MB, time=125.98
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memory used=12188.1MB, alloc=44.3MB, time=126.41
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memory used=12228.5MB, alloc=44.3MB, time=126.83
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memory used=12269.1MB, alloc=44.3MB, time=127.25
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memory used=12309.6MB, alloc=44.3MB, time=127.66
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memory used=12350.1MB, alloc=44.3MB, time=128.08
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memory used=12390.6MB, alloc=44.3MB, time=128.50
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memory used=12431.0MB, alloc=44.3MB, time=128.92
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memory used=12471.6MB, alloc=44.3MB, time=129.34
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memory used=12512.2MB, alloc=44.3MB, time=129.75
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memory used=12552.7MB, alloc=44.3MB, time=130.17
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memory used=12593.2MB, alloc=44.3MB, time=130.59
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memory used=12633.7MB, alloc=44.3MB, time=131.00
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memory used=12674.2MB, alloc=44.3MB, time=131.42
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memory used=12714.8MB, alloc=44.3MB, time=131.84
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memory used=12755.3MB, alloc=44.3MB, time=132.26
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memory used=12795.7MB, alloc=44.3MB, time=132.67
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memory used=12836.2MB, alloc=44.3MB, time=133.09
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memory used=12876.7MB, alloc=44.3MB, time=133.52
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memory used=12917.3MB, alloc=44.3MB, time=133.95
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memory used=12957.9MB, alloc=44.3MB, time=134.36
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TOP MAIN SOLVE Loop
x[1] = 4.9300000517543902142652658335513
y[1] (closed_form) = -2.1738997134891509626586621756543
y[1] (numeric) = -2.173899713489150962658662175647
absolute error = 7.3e-30
relative error = 3.3580205906938362043173518856016e-28 %
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 = 0.02734
Order of pole (three term test) = 33
NO COMPLEX POLE (six term test) for Equation 1
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memory used=12998.6MB, alloc=44.3MB, time=134.78
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memory used=13039.1MB, alloc=44.3MB, time=135.20
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memory used=13079.6MB, alloc=44.3MB, time=135.62
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memory used=13120.2MB, alloc=44.3MB, time=136.05
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memory used=13160.6MB, alloc=44.3MB, time=136.47
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memory used=13201.1MB, alloc=44.3MB, time=136.88
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memory used=13241.7MB, alloc=44.3MB, time=137.30
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memory used=13282.4MB, alloc=44.3MB, time=137.72
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memory used=13322.9MB, alloc=44.3MB, time=138.14
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memory used=13363.5MB, alloc=44.3MB, time=138.56
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memory used=13404.0MB, alloc=44.3MB, time=138.98
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memory used=13444.5MB, alloc=44.3MB, time=139.39
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memory used=13485.1MB, alloc=44.3MB, time=139.81
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memory used=13525.7MB, alloc=44.3MB, time=140.23
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memory used=13566.3MB, alloc=44.3MB, time=140.66
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memory used=13606.7MB, alloc=44.3MB, time=141.08
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memory used=13647.2MB, alloc=44.3MB, time=141.48
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memory used=13687.8MB, alloc=44.3MB, time=141.91
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memory used=13728.3MB, alloc=44.3MB, time=142.33
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memory used=13768.8MB, alloc=44.3MB, time=142.73
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memory used=13809.4MB, alloc=44.3MB, time=143.16
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memory used=13849.9MB, alloc=44.3MB, time=143.58
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memory used=13890.4MB, alloc=44.3MB, time=144.00
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memory used=13930.9MB, alloc=44.3MB, time=144.41
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memory used=13971.5MB, alloc=44.3MB, time=144.83
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memory used=14012.0MB, alloc=44.3MB, time=145.25
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memory used=14052.5MB, alloc=44.3MB, time=145.67
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memory used=14093.1MB, alloc=44.3MB, time=146.09
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memory used=14133.7MB, alloc=44.3MB, time=146.50
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memory used=14174.3MB, alloc=44.3MB, time=146.92
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memory used=14214.9MB, alloc=44.3MB, time=147.34
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memory used=14255.4MB, alloc=44.3MB, time=147.77
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memory used=14296.0MB, alloc=44.3MB, time=148.19
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memory used=14336.5MB, alloc=44.3MB, time=148.59
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memory used=14377.0MB, alloc=44.3MB, time=149.01
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memory used=14417.6MB, alloc=44.3MB, time=149.44
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memory used=14458.1MB, alloc=44.3MB, time=149.86
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memory used=14498.7MB, alloc=44.3MB, time=150.28
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memory used=14539.2MB, alloc=44.3MB, time=150.69
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memory used=14579.7MB, alloc=44.3MB, time=151.11
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memory used=14620.3MB, alloc=44.3MB, time=151.53
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memory used=14660.9MB, alloc=44.3MB, time=151.95
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memory used=14701.4MB, alloc=44.3MB, time=152.38
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memory used=14741.9MB, alloc=44.3MB, time=152.80
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memory used=14782.4MB, alloc=44.3MB, time=153.22
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memory used=14822.9MB, alloc=44.3MB, time=153.64
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memory used=14863.5MB, alloc=44.3MB, time=154.06
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memory used=14904.1MB, alloc=44.3MB, time=154.48
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memory used=14944.6MB, alloc=44.3MB, time=154.91
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memory used=14985.2MB, alloc=44.3MB, time=155.33
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memory used=15025.8MB, alloc=44.3MB, time=155.73
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memory used=15066.3MB, alloc=44.3MB, time=156.16
SETTING H FOR POLE
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memory used=15106.9MB, alloc=44.3MB, time=156.58
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memory used=15147.5MB, alloc=44.3MB, time=156.98
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memory used=15188.1MB, alloc=44.3MB, time=157.41
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memory used=15228.6MB, alloc=44.3MB, time=157.83
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memory used=15269.2MB, alloc=44.3MB, time=158.25
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memory used=15309.8MB, alloc=44.3MB, time=158.67
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memory used=15350.3MB, alloc=44.3MB, time=159.09
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memory used=15390.9MB, alloc=44.3MB, time=159.52
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memory used=15431.4MB, alloc=44.3MB, time=159.92
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memory used=15472.0MB, alloc=44.3MB, time=160.34
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memory used=15512.6MB, alloc=44.3MB, time=160.76
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memory used=15553.2MB, alloc=44.3MB, time=161.19
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memory used=15593.8MB, alloc=44.3MB, time=161.61
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memory used=15634.3MB, alloc=44.3MB, time=162.03
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memory used=15674.8MB, alloc=44.3MB, time=162.45
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memory used=15715.3MB, alloc=44.3MB, time=162.87
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memory used=15755.8MB, alloc=44.3MB, time=163.30
SETTING H FOR POLE
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memory used=15796.3MB, alloc=44.3MB, time=163.70
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memory used=15836.8MB, alloc=44.3MB, time=164.12
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memory used=15877.3MB, alloc=44.3MB, time=164.55
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memory used=15917.9MB, alloc=44.3MB, time=164.97
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memory used=15958.4MB, alloc=44.3MB, time=165.39
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memory used=15998.9MB, alloc=44.3MB, time=165.80
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memory used=16039.4MB, alloc=44.3MB, time=166.22
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memory used=16079.9MB, alloc=44.3MB, time=166.64
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memory used=16120.5MB, alloc=44.3MB, time=167.06
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memory used=16161.1MB, alloc=44.3MB, time=167.48
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memory used=16201.6MB, alloc=44.3MB, time=167.89
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memory used=16242.1MB, alloc=44.3MB, time=168.31
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memory used=16282.6MB, alloc=44.3MB, time=168.73
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memory used=16323.2MB, alloc=44.3MB, time=169.16
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memory used=16363.7MB, alloc=44.3MB, time=169.56
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memory used=16404.3MB, alloc=44.3MB, time=169.98
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memory used=16444.8MB, alloc=44.3MB, time=170.41
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memory used=16485.3MB, alloc=44.3MB, time=170.83
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memory used=16525.9MB, alloc=44.3MB, time=171.25
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memory used=16566.5MB, alloc=44.3MB, time=171.67
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memory used=16607.1MB, alloc=44.3MB, time=172.08
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memory used=16647.6MB, alloc=44.3MB, time=172.50
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memory used=16688.2MB, alloc=44.3MB, time=172.92
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memory used=16728.6MB, alloc=44.3MB, time=173.34
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memory used=16769.1MB, alloc=44.3MB, time=173.77
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memory used=16809.7MB, alloc=44.3MB, time=174.17
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memory used=16850.3MB, alloc=44.3MB, time=174.59
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memory used=16890.8MB, alloc=44.3MB, time=175.01
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memory used=16931.2MB, alloc=44.3MB, time=175.44
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memory used=16971.8MB, alloc=44.3MB, time=175.86
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memory used=17012.4MB, alloc=44.3MB, time=176.28
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memory used=17052.9MB, alloc=44.3MB, time=176.70
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memory used=17093.5MB, alloc=44.3MB, time=177.13
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memory used=17134.0MB, alloc=44.3MB, time=177.53
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memory used=17174.5MB, alloc=44.3MB, time=177.95
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memory used=17215.1MB, alloc=44.3MB, time=178.38
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memory used=17255.6MB, alloc=44.3MB, time=178.80
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memory used=17296.2MB, alloc=44.3MB, time=179.22
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memory used=17336.8MB, alloc=44.3MB, time=179.64
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memory used=17377.3MB, alloc=44.3MB, time=180.06
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Finished!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;
Iterations = 38055
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 3 Minutes 0 Seconds
Expected Time Remaining = 2 Seconds
Optimized Time Remaining = 2 Seconds
Expected Total Time = 3 Minutes 2 Seconds
Time to Timeout = 0 Seconds
Percent Done = 98.77 %
> quit
memory used=17379.4MB, alloc=44.3MB, time=180.08