|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));
> end;
exact_soln_y :=
proc(x) return c(0.5)*c(x) + c(0.25)*ln(c(2.0)*c(x) + c(3.0)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> 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)*28*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
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)*28*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp2[1] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := neg( array_tmp5[2]) * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := neg( array_tmp5[3]) * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := neg( array_tmp5[4]) * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(array_tmp5[kkk-1]) * array_tmp4[2] / array_tmp4[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp6[kkk] := array_tmp5[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_tmp6[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
array_tmp1[1] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := array_const_0D2[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_const_0D2[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp2[2])/array_tmp4[1];
array_tmp6[2] := array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp5[3] := neg(array_tmp5[2])*array_tmp4[2]/array_tmp4[1];
array_tmp6[3] := array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp5[4] := neg(array_tmp5[3])*array_tmp4[2]/array_tmp4[1];
array_tmp6[4] := array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp5[5] := neg(array_tmp5[4])*array_tmp4[2]/array_tmp4[1];
array_tmp6[5] := array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp5[kkk] :=
neg(array_tmp5[kkk - 1])*array_tmp4[2]/array_tmp4[1];
array_tmp6[kkk] := array_tmp5[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_tmp6[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> 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 := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #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..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> 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..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_tmp6:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 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..(30) ,(0..30+ 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 <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_const_0D3);
> array_const_0D3[1] := c(0.3);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> 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/div_lin_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> 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,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> 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(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));");
> 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 := 1;
> array_given_rad_poles[1,1] := c(-1.5);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(1.0);
> array_given_ord_poles[1,2] := c(0.0);
> #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 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ");
> 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,"2015-05-02T21:27:07-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_lin_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ")
> ;
> 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,"div_lin_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_lin_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_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
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 := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
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 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_tmp6 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
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 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 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 <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 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 <= 30 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 <= 30 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 <= 30 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 <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_const_0D3);
array_const_0D3[1] := c(0.3);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
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/div_lin_linpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.1 * x + \
0.2 ) / ( 0.2 * x + 0.3 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
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, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
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(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));");
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 := 1;
array_given_rad_poles[1, 1] := c(-1.5);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(1.0);
array_given_ord_poles[1, 2] := c(0.);
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 ) = ( 0.1 * x +\
0.2 ) / ( 0.2 * x + 0.3 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-05-02T21:27:07-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_lin_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = (\
0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ");
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, "div_lin_lin diffeq.mxt");
logitem_str(html_log_file, "div_lin_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/div_lin_linpostode.ode#################
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#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 := 1;
array_given_rad_poles[1,1] := c(-1.5);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(1.0);
array_given_ord_poles[1,2] := c(0.0);
#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(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));
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) = 0.34078770245142021576704228815162
y[1] (numeric) = 0.34078770245142021576704228815162
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.6
Order of pole (given) = 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) = 1.397e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0.3473453398890792343233386968357
y[1] (numeric) = 0.3473453398890792343233386968357
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.61
Order of pole (given) = 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) = 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4.1MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 0.35389333245105950409486557030942
y[1] (numeric) = 0.35389333245105950409486557030943
absolute error = 1e-32
relative error = 2.8257102022070214012302967369336e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.62
Order of pole (given) = 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) = 4.947e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0.36043179884465406886154539455255
y[1] (numeric) = 0.36043179884465406886154539455255
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.63
Order of pole (three term test) = 3.283e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 0.3669608555990130910206192070108
y[1] (numeric) = 0.3669608555990130910206192070108
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.64
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0.37348061711810863785979934005082
y[1] (numeric) = 0.37348061711810863785979934005082
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 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) = 5.753e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0.37999119573209929356848838920975
y[1] (numeric) = 0.37999119573209929356848838920974
absolute error = 1e-32
relative error = 2.6316399201654613958100595723375e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.66
Order of pole (given) = 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) = 5.318e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0.38649270174715226216024999720855
y[1] (numeric) = 0.38649270174715226216024999720854
absolute error = 1e-32
relative error = 2.5873709787519115921874269106848e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.67
Order of pole (three term test) = 1.001e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 0.39298524349377821653338588920742
y[1] (numeric) = 0.39298524349377821653338588920741
absolute error = 1e-32
relative error = 2.5446248085796944295766088715830e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.68
Order of pole (three term test) = 2.636e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0.39946892737373185337205602380502
y[1] (numeric) = 0.39946892737373185337205602380501
absolute error = 1e-32
relative error = 2.5033236166186919093485788124559e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.69
Order of pole (three term test) = 1.732e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 0.40594385790552892641219382116172
y[1] (numeric) = 0.40594385790552892641219382116172
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.7
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0.4124101377686284460451917794556
y[1] (numeric) = 0.41241013776862844604519177945557
absolute error = 3e-32
relative error = 7.2743119658301631360143252414472e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.71
Order of pole (three term test) = 2.975e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0.4188678678463267459221389920879
y[1] (numeric) = 0.41886786784632674592213899208789
absolute error = 1e-32
relative error = 2.3873877104530673577731130442381e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.72
Order of pole (three term test) = 3.890e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0.4253171472674082220786874001326
y[1] (numeric) = 0.42531714726740822207868740013258
absolute error = 2e-32
relative error = 4.7023733062484469139585942688441e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.73
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 0.43175807344659574234424965070802
y[1] (numeric) = 0.43175807344659574234424965070798
absolute error = 4e-32
relative error = 9.2644474903947822548712865257441e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.74
Order of pole (three term test) = 4.635e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0.43819074212384199892203015549625
y[1] (numeric) = 0.43819074212384199892203015549621
absolute error = 4e-32
relative error = 9.1284447969225126835283763310228e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.75
Order of pole (three term test) = 8.618e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0.44461524740250143077803031897182
y[1] (numeric) = 0.44461524740250143077803031897178
absolute error = 4e-32
relative error = 8.9965425688131625049674596617487e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.76
Order of pole (three term test) = 1.120e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0.45103168178642077084813620568292
y[1] (numeric) = 0.45103168178642077084813620568288
absolute error = 4e-32
relative error = 8.8685566037335254934820245117692e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.77
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0.45744013621598477227907421855438
y[1] (numeric) = 0.45744013621598477227907421855434
absolute error = 4e-32
relative error = 8.7443135906014189808590357197060e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.78
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0.4638407001031522343897634105277
y[1] (numeric) = 0.46384070010315223438976341052769
absolute error = 1e-32
relative error = 2.1559125789901852086894597478469e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.79
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0.47023346136551607940174081551925
y[1] (numeric) = 0.47023346136551607940174081551924
absolute error = 1e-32
relative error = 2.1266032346913150087644878271472e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0.47661850645941992205508406268062
y[1] (numeric) = 0.47661850645941992205508406268059
absolute error = 3e-32
relative error = 6.2943422450916200395542029075398e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.81
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0.48299592041216232298933037963902
y[1] (numeric) = 0.48299592041216232298933037963901
absolute error = 1e-32
relative error = 2.0704108621593628565434977312802e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.82
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0.4893657868533187203819708881094
y[1] (numeric) = 0.48936578685331872038197088810938
absolute error = 2e-32
relative error = 4.0869224080012667671539176669274e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.83
Order of pole (three term test) = 3.368e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0.49572818804520989010992460206855
y[1] (numeric) = 0.49572818804520989010992460206853
absolute error = 2e-32
relative error = 4.0344689856885888855388629311106e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.84
Order of pole (three term test) = 8.655e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0.50208320491254469008752605408678
y[1] (numeric) = 0.50208320491254469008752605408676
absolute error = 2e-32
relative error = 3.9834035084849527845508944780878e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 4.442e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0.50843091707126379703072272375312
y[1] (numeric) = 0.50843091707126379703072272375312
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.86
Order of pole (three term test) = 1.423e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 0.51477140285661014142318185198192
y[1] (numeric) = 0.51477140285661014142318185198192
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.87
Order of pole (three term test) = 3.642e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0.5211047393504507867591660311945
y[1] (numeric) = 0.52110473935045078675916603119448
absolute error = 2e-32
relative error = 3.8380000199057293037635228198464e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.88
Order of pole (three term test) = 2.328e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 0.52743100240787408016808441657505
y[1] (numeric) = 0.52743100240787408016808441657504
absolute error = 1e-32
relative error = 1.8959825938079344140181769710711e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.89
Order of pole (three term test) = 2.971e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0.53375026668308502135206702466542
y[1] (numeric) = 0.5337502666830850213520670246654
absolute error = 2e-32
relative error = 3.7470707273435478010699995302763e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.9
Order of pole (three term test) = 7.574e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0.54006260565462095355779979107295
y[1] (numeric) = 0.54006260565462095355779979107294
absolute error = 1e-32
relative error = 1.8516371797078590615926207435277e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.91
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0.54636809164990887231997179444025
y[1] (numeric) = 0.54636809164990887231997179444024
absolute error = 1e-32
relative error = 1.8302679370975429620349750319382e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.92
Order of pole (three term test) = 6.131e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 0.55266679586918487330904506636812
y[1] (numeric) = 0.5526667958691848733090450663681
absolute error = 2e-32
relative error = 3.6188170068270140933515719544035e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.93
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 0.5589587884087955182288007388129
y[1] (numeric) = 0.55895878840879551822880073881287
absolute error = 3e-32
relative error = 5.3671219814616182189646688378084e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.94
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0.56524413828390018585768530595088
y[1] (numeric) = 0.56524413828390018585768530595084
absolute error = 4e-32
relative error = 7.0765882015939726460801759860451e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.95
Order of pole (three term test) = 5.004e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 0.57152291345059279260660473547305
y[1] (numeric) = 0.57152291345059279260660473547301
absolute error = 4e-32
relative error = 6.9988445010014342351911702528956e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.96
Order of pole (three term test) = 3.166e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0.57779518082746061204026163531308
y[1] (numeric) = 0.57779518082746061204026163531304
absolute error = 4e-32
relative error = 6.9228684016914074556008586792604e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.97
Order of pole (three term test) = 2.000e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 0.58406100631659729441272884633945
y[1] (numeric) = 0.58406100631659729441272884633942
absolute error = 3e-32
relative error = 5.1364497330845845093422266553630e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.98
Order of pole (three term test) = 2.525e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0.5903204548240865841978426259895
y[1] (numeric) = 0.59032045482408658419784262598946
absolute error = 4e-32
relative error = 6.7759806852567660183026534883786e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 1.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.99
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0.5965735902799726547086160607291
y[1] (numeric) = 0.59657359027997265470861606072905
absolute error = 5e-32
relative error = 8.3811956839281041501321801157075e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2
Order of pole (three term test) = 8.018e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0.60282047565773242311164161134392
y[1] (numeric) = 0.60282047565773242311164161134389
absolute error = 3e-32
relative error = 4.9766060065008987501166309917037e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.01
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 0.60906117299326467542066990011515
y[1] (numeric) = 0.60906117299326467542066990011512
absolute error = 3e-32
relative error = 4.9256136050445225251328557688846e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.02
Order of pole (three term test) = 6.336e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0.61529574340341031841746849697362
y[1] (numeric) = 0.6152957434034103184174684969736
absolute error = 2e-32
relative error = 3.2504694229433781326911711577402e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.03
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0.62152424710401758296512332745038
y[1] (numeric) = 0.62152424710401758296512332745033
absolute error = 5e-32
relative error = 8.0447384366698822487467234529208e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.04
Order of pole (three term test) = 1.994e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0.62774674342756552996219297958825
y[1] (numeric) = 0.62774674342756552996219297958823
absolute error = 2e-32
relative error = 3.1859982085765708026801519517768e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.05
Order of pole (three term test) = 1.248e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 0.63396329084035875539177091215028
y[1] (numeric) = 0.63396329084035875539177091215023
absolute error = 5e-32
relative error = 7.8868919892383378602479366413125e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.06
Order of pole (three term test) = 3.123e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0.64017394695930575374462312943618
y[1] (numeric) = 0.64017394695930575374462312943614
absolute error = 4e-32
relative error = 6.2483017607935705801717645757579e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.07
Order of pole (three term test) = 1.951e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 0.64637876856829297877591628487188
y[1] (numeric) = 0.64637876856829297877591628487183
absolute error = 5e-32
relative error = 7.7354025892199866016348455895150e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.08
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0.6525778116341662363630550554856
y[1] (numeric) = 0.65257781163416623636305505548557
absolute error = 3e-32
relative error = 4.5971529318281415290676551595090e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.09
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 0.65877113132233065547495966178488
y[1] (numeric) = 0.65877113132233065547495966178484
absolute error = 4e-32
relative error = 6.0719114876374823871932434043304e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.1
Order of pole (three term test) = 3.782e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 0.66495878201198010928080136938592
y[1] (numeric) = 0.66495878201198010928080136938589
absolute error = 3e-32
relative error = 4.5115578305813713490635274006769e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.11
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 0.67114081731096659859004564850872
y[1] (numeric) = 0.67114081731096659859004564850867
absolute error = 5e-32
relative error = 7.4500013574398626069343999579640e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.12
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0.67731729007031976352648724538125
y[1] (numeric) = 0.67731729007031976352648724538121
absolute error = 4e-32
relative error = 5.9056516918159817971894691024409e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.13
Order of pole (three term test) = 2.905e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 0.68348825239842635602572003764272
y[1] (numeric) = 0.68348825239842635602572003764268
absolute error = 4e-32
relative error = 5.8523317496147348363602518838099e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.14
Order of pole (three term test) = 9.009e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 0.68965375567487918486371276466538
y[1] (numeric) = 0.68965375567487918486371276466533
absolute error = 5e-32
relative error = 7.2500148934984278573615591998223e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.15
Order of pole (three term test) = 1.116e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 0.6958138505640047359546703218079
y[1] (numeric) = 0.69581385056400473595467032180785
absolute error = 5e-32
relative error = 7.1858299399288443052912322275983e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.16
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 0.70196858702807837310394157001875
y[1] (numeric) = 0.70196858702807837310394157001871
absolute error = 4e-32
relative error = 5.6982606827675639430083664207668e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.17
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 0.7081180143402357377939494464392
y[1] (numeric) = 0.70811801434023573779394944643917
absolute error = 3e-32
relative error = 4.2365819527909417279245247926469e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.18
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 0.71426218109708869046715082661262
y[1] (numeric) = 0.71426218109708869046715082661259
absolute error = 3e-32
relative error = 4.2001383797082405864259334532665e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.19
Order of pole (three term test) = 2.607e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0.72040113523105386971960409154928
y[1] (numeric) = 0.72040113523105386971960409154924
absolute error = 4e-32
relative error = 5.5524620997676275806773280574694e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.2
Order of pole (three term test) = 3.214e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 0.72653492402240168942106781788198
y[1] (numeric) = 0.72653492402240168942106781788193
absolute error = 5e-32
relative error = 6.8819816290700871868123404352435e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.21
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 0.7326635941110333466404555603754
y[1] (numeric) = 0.73266359411103334664045556037535
absolute error = 5e-32
relative error = 6.8244144245582133122611560246892e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.22
Order of pole (three term test) = 4.874e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 0.73878719150799317500433860545315
y[1] (numeric) = 0.7387871915079931750043386054531
absolute error = 5e-32
relative error = 6.7678487898445155978585634945600e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.23
Order of pole (three term test) = 2.397e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 0.74490576160672344839319064070588
y[1] (numeric) = 0.74490576160672344839319064070583
absolute error = 5e-32
relative error = 6.7122584596677799097381372438041e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.24
Order of pole (three term test) = 2.945e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 0.75101934919406851834331458809672
y[1] (numeric) = 0.75101934919406851834331458809667
absolute error = 5e-32
relative error = 6.6576180831633485955697138453005e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.25
Order of pole (three term test) = 7.230e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 0.7571279984610349548451532067909
y[1] (numeric) = 0.75712799846103495484515320679086
absolute error = 4e-32
relative error = 5.2831225474827782486520417271191e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.26
Order of pole (three term test) = 3.325e-29
NO COMPLEX POLE (six term test) for Equation 1
memory used=48.4MB, alloc=44.3MB, time=0.61
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 0.76323175301331415409865769723072
y[1] (numeric) = 0.76323175301331415409865769723069
absolute error = 3e-32
relative error = 3.9306540748019254198135679056759e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.27
Order of pole (three term test) = 2.716e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 0.76933065588157367790499653095405
y[1] (numeric) = 0.769330655881573677904996530954
absolute error = 5e-32
relative error = 6.4991560673875852280896736283144e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.28
Order of pole (three term test) = 4.986e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 0.77542474953152339745562120400552
y[1] (numeric) = 0.77542474953152339745562120400547
absolute error = 5e-32
relative error = 6.4480789438572525787398350556623e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.29
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 0.781514075873762329051498374646
y[1] (numeric) = 0.78151407587376232905149837464596
absolute error = 4e-32
relative error = 5.1182699371445722701875744729609e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.3
Order of pole (three term test) = 2.484e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 0.78759867627341187048594769260508
y[1] (numeric) = 0.78759867627341187048594769260503
absolute error = 5e-32
relative error = 6.3484108729815451195664372319686e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.31
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0.79367859155954097420405440220648
y[1] (numeric) = 0.79367859155954097420405440220643
absolute error = 5e-32
relative error = 6.2997793479287830839188481042384e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.32
Order of pole (three term test) = 7.398e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 0.79975386203438862667086852168958
y[1] (numeric) = 0.79975386203438862667086852168954
absolute error = 4e-32
relative error = 5.0015388357424449026265567005295e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.33
Order of pole (three term test) = 4.508e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 0.8058245274823888424106148122395
y[1] (numeric) = 0.80582452748238884241061481223945
absolute error = 5e-32
relative error = 6.2048247843998197822200047112997e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.34
Order of pole (three term test) = 5.490e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 0.81189062717900322570073980377195
y[1] (numeric) = 0.8118906271790032257007398037719
absolute error = 5e-32
relative error = 6.1584649860696259794713399607408e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.35
Order of pole (three term test) = 1.336e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 0.81795219989936600270794095718138
y[1] (numeric) = 0.81795219989936600270794095718133
absolute error = 5e-32
relative error = 6.1128266427000968758422655004612e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.36
Order of pole (three term test) = 8.121e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 0.82400928392674628173735999762335
y[1] (numeric) = 0.8240092839267462817373599976233
absolute error = 5e-32
relative error = 6.0678927986987288719962757492659e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.37
Order of pole (three term test) = 9.864e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 0.83006191706083215903834217371598
y[1] (numeric) = 0.83006191706083215903834217371594
absolute error = 4e-32
relative error = 4.8189176226318245085654147369164e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.38
Order of pole (three term test) = 2.395e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 0.83611013662584115208610320158785
y[1] (numeric) = 0.83611013662584115208610320158779
absolute error = 6e-32
relative error = 7.1760880979308074759658343298006e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.39
Order of pole (three term test) = 2.904e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0.84215397947846131126154556701772
y[1] (numeric) = 0.84215397947846131126154556701766
absolute error = 6e-32
relative error = 7.1245878381002820872315547382694e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.4
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 0.84819348201562723421191513270008
y[1] (numeric) = 0.84819348201562723421191513270001
absolute error = 7e-32
relative error = 8.2528339917979127199873006412582e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.41
Order of pole (three term test) = 4.261e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 0.85422868018213508473059212236948
y[1] (numeric) = 0.85422868018213508473059212236942
absolute error = 6e-32
relative error = 7.0238803018422478698402226585107e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.42
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 0.86025960947810059958936884917552
y[1] (numeric) = 0.86025960947810059958936884917546
absolute error = 6e-32
relative error = 6.9746387414841663637577329333711e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.43
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 0.86628630496626395224177563960785
y[1] (numeric) = 0.8662863049662639522417756396078
absolute error = 5e-32
relative error = 5.7717638745249660869568616009452e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.44
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 0.8723088012791452315481785080505
y[1] (numeric) = 0.87230880127914523154817850805044
absolute error = 6e-32
relative error = 6.8782981338737586286973682772697e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.45
Order of pole (three term test) = 9.085e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 0.8783271326260541865151224858769
y[1] (numeric) = 0.87832713262605418651512248587683
absolute error = 7e-32
relative error = 7.9696957317840645071463916591932e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.46
Order of pole (three term test) = 5.479e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 0.88434133279995778436094102138565
y[1] (numeric) = 0.8843413327999577843609410213856
absolute error = 5e-32
relative error = 5.6539254861799202834654512166601e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.47
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 0.89035143518420902889052747525158
y[1] (numeric) = 0.89035143518420902889052747525153
absolute error = 5e-32
relative error = 5.6157600273486685612854206816187e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.48
Order of pole (three term test) = 1.590e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 0.89635747275914038906299166807582
y[1] (numeric) = 0.89635747275914038906299166807578
absolute error = 4e-32
relative error = 4.4625053302532541028406472159177e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.49
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 0.90235947810852509365018983330655
y[1] (numeric) = 0.90235947810852509365018983330649
absolute error = 6e-32
relative error = 6.6492347512954157455124201634237e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.5
Order of pole (three term test) = 1.151e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 0.90835748342590945689995861277442
y[1] (numeric) = 0.90835748342590945689995861277437
absolute error = 5e-32
relative error = 5.5044408079760450489259120008102e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.51
Order of pole (three term test) = 2.765e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = 0.9143515205208193120278891680735
y[1] (numeric) = 0.91435152052081931202788916807346
absolute error = 4e-32
relative error = 4.3746851295457785212533254488492e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.52
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 0.9203416208248435440624864054662
y[1] (numeric) = 0.92034162082484354406248640546614
absolute error = 6e-32
relative error = 6.5193183316240575564448300413155e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.53
Order of pole (three term test) = 3.983e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 0.92632781539759763096148053531598
y[1] (numeric) = 0.92632781539759763096148053531593
absolute error = 5e-32
relative error = 5.3976571974726941407267064395060e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.54
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 0.93231013493257002190669710002782
y[1] (numeric) = 0.93231013493257002190669710002777
absolute error = 5e-32
relative error = 5.3630222526344503087580796868070e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.55
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = 0.93828860976285410417977654593872
y[1] (numeric) = 0.93828860976285410417977654593867
absolute error = 5e-32
relative error = 5.3288507906578074036759881132660e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.56
Order of pole (three term test) = 3.425e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 0.94426326986676843493326088171268
y[1] (numeric) = 0.94426326986676843493326088171263
absolute error = 5e-32
relative error = 5.2951334225946106249896587314793e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.57
Order of pole (three term test) = 4.098e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 0.950234144873367841416642270954
y[1] (numeric) = 0.95023414487336784141664227095395
absolute error = 5e-32
relative error = 5.2618610128625937960000409171616e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.58
Order of pole (three term test) = 4.900e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = 0.95620126406784792271367440664102
y[1] (numeric) = 0.95620126406784792271367440664097
absolute error = 5e-32
relative error = 5.2290246707362871027035032562843e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.59
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 0.96216465639684541771749005744932
y[1] (numeric) = 0.96216465639684541771749005744928
absolute error = 4e-32
relative error = 4.1572925937431207035131246513119e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.6
Order of pole (three term test) = 4.193e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 0.9681243504736368378387529295741
y[1] (numeric) = 0.96812435047363683783875292957406
absolute error = 4e-32
relative error = 4.1317006415994746679147964620066e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.61
Order of pole (three term test) = 8.339e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 0.9740803745832376987369763361793
y[1] (numeric) = 0.97408037458323769873697633617925
absolute error = 5e-32
relative error = 5.1330466463193659278994352601035e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.62
Order of pole (three term test) = 1.989e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 0.98003275668740462311679386907362
y[1] (numeric) = 0.98003275668740462311679386907359
absolute error = 3e-32
relative error = 3.0611221712019699753693212986263e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.63
Order of pole (three term test) = 2.369e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 0.9859815244295425262725335978379
y[1] (numeric) = 0.98598152442954252627253359783787
absolute error = 3e-32
relative error = 3.0426533618220730355098718037435e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.64
Order of pole (three term test) = 2.821e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 0.99192670513951903753161942108618
y[1] (numeric) = 0.99192670513951903753161942108614
absolute error = 4e-32
relative error = 4.0325560137403314150823322166577e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.65
Order of pole (three term test) = 3.357e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 0.99786832583838825397821537721968
y[1] (numeric) = 0.99786832583838825397821537721963
absolute error = 5e-32
relative error = 5.0106811395171840815757063271329e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.66
Order of pole (three term test) = 1.996e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = 1.0038064132430258677735774974204
y[1] (numeric) = 1.0038064132430258677735774974205
absolute error = 1e-31
relative error = 9.9620802059758875171807955765695e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.67
Order of pole (three term test) = 2.372e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 1.0097409937706776549714463628424
y[1] (numeric) = 1.0097409937706776549714463628424
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.68
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = 1.0156720935434232619003005981462
y[1] (numeric) = 1.0156720935434232619003005981462
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.69
Order of pole (three term test) = 3.344e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 1.0215997383925571748962440943854
y[1] (numeric) = 1.0215997383925571748962440943854
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.7
Order of pole (three term test) = 3.966e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = 1.0275239538628887103695298213238
y[1] (numeric) = 1.0275239538628887103695298213238
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.71
Order of pole (three term test) = 4.702e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 1.0334447652169628148249280789488
y[1] (numeric) = 1.0334447652169628148249280789488
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.72
Order of pole (three term test) = 5.570e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 1.0393621974392034184838336585051
y[1] (numeric) = 1.0393621974392034184838336585051
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.73
Order of pole (three term test) = 5.934e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 1.0452762752399810415284178653819
y[1] (numeric) = 1.0452762752399810415284178653818
absolute error = 1e-31
relative error = 9.5668487239932214849813665290801e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.74
Order of pole (three term test) = 2.340e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 1.0511870230596063086611778641268
y[1] (numeric) = 1.0511870230596063086611778641267
absolute error = 1e-31
relative error = 9.5130550326751530925354596514975e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.75
Order of pole (three term test) = 8.302e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 1.0570944650722509856044278809346
y[1] (numeric) = 1.0570944650722509856044278809346
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.76
Order of pole (three term test) = 3.270e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 1.0629986251897981103126616904035
y[1] (numeric) = 1.0629986251897981103126616904034
absolute error = 1e-31
relative error = 9.4073498902357496161231905163831e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.77
Order of pole (three term test) = 2.575e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = 1.0688995270656227519968165631058
y[1] (numeric) = 1.0688995270656227519968165631056
absolute error = 2e-31
relative error = 1.8710832490406877764319613021822e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.78
Order of pole (three term test) = 3.039e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 1.0747971940983048925252260026192
y[1] (numeric) = 1.074797194098304892525226002619
absolute error = 2e-31
relative error = 1.8608161716293731468736714708383e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.79
Order of pole (three term test) = 1.792e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = 1.0806916494352758873347644132833
y[1] (numeric) = 1.0806916494352758873347644132831
absolute error = 2e-31
relative error = 1.8506666550492141626261358662071e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.8
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 1.0865829159763999266219718841956
y[1] (numeric) = 1.0865829159763999266219718841954
absolute error = 2e-31
relative error = 1.8406326572904069713664157057734e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.81
Order of pole (three term test) = 7.469e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 1.0924710163774918822536693100606
y[1] (numeric) = 1.0924710163774918822536693100603
absolute error = 3e-31
relative error = 2.7460682755206217002983928497319e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 1.0983559730537728915068090897212
y[1] (numeric) = 1.0983559730537728915068090897209
absolute error = 3e-31
relative error = 2.7313549282743575044730190135841e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.83
Order of pole (three term test) = 6.900e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 1.1042378081832649953862919968797
y[1] (numeric) = 1.1042378081832649953862919968795
absolute error = 2e-31
relative error = 1.8112040587439021074803349256298e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.84
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 1.1101165437101261168465703035315
y[1] (numeric) = 1.1101165437101261168465703035313
absolute error = 2e-31
relative error = 1.8016126426832536716729691056677e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.85
Order of pole (three term test) = 4.770e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 1.1159922013479266327284780882695
y[1] (numeric) = 1.1159922013479266327284780882693
absolute error = 2e-31
relative error = 1.7921272187962819028187430255575e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.86
Order of pole (three term test) = 5.604e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 1.1218648025828687625883413321425
y[1] (numeric) = 1.1218648025828687625883413321423
absolute error = 2e-31
relative error = 1.7827460094972237478532192950933e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.87
Order of pole (three term test) = 6.580e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 1.1277343686769499678144750733064
y[1] (numeric) = 1.1277343686769499678144750733062
absolute error = 2e-31
relative error = 1.7734672770028157764833847031956e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.88
Order of pole (three term test) = 4.633e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 1.1336009206710715254700796119589
y[1] (numeric) = 1.1336009206710715254700796119587
absolute error = 2e-31
relative error = 1.7642893222211178808557261902332e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.89
Order of pole (three term test) = 5.434e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 1.1394644793880934131456281747839
y[1] (numeric) = 1.1394644793880934131456281747837
absolute error = 2e-31
relative error = 1.7552104836774068255976290902569e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.9
Order of pole (three term test) = 1.062e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 1.145325065435836613723304017679
y[1] (numeric) = 1.1453250654358366137233040176787
absolute error = 3e-31
relative error = 2.6193437047135558057137166356782e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
memory used=92.6MB, alloc=44.3MB, time=1.09
Radius of convergence (given) for eq 1 = 2.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.91
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 1.1511826992100339223269555781111
y[1] (numeric) = 1.1511826992100339223269555781108
absolute error = 3e-31
relative error = 2.6060155369418458704017726985251e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.92
Order of pole (three term test) = 4.369e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 1.1570374008972303118302723687255
y[1] (numeric) = 1.1570374008972303118302723687252
absolute error = 3e-31
relative error = 2.5928288901237205697860373228997e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.93
Order of pole (three term test) = 1.704e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 1.1628891904776338881011080143391
y[1] (numeric) = 1.1628891904776338881011080143388
absolute error = 3e-31
relative error = 2.5797814826774758650714742385708e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.94
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 1.1687380877279184416495147297588
y[1] (numeric) = 1.1687380877279184416495147297585
absolute error = 3e-31
relative error = 2.5668710821533509260605873398952e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.95
Order of pole (three term test) = 4.661e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 1.1745841122239785785002603118738
y[1] (numeric) = 1.1745841122239785785002603118735
absolute error = 3e-31
relative error = 2.5540955039139311290798829211265e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.96
Order of pole (three term test) = 2.723e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 1.1804272833436383899072321252056
y[1] (numeric) = 1.1804272833436383899072321252052
absolute error = 4e-31
relative error = 3.3886034798092224001605991773741e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.97
Order of pole (three term test) = 3.180e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 1.1862676202693145979477274021629
y[1] (numeric) = 1.1862676202693145979477274021626
absolute error = 3e-31
relative error = 2.5289403071786781619634632329176e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.98
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 1.1921051419906350920603723713662
y[1] (numeric) = 1.1921051419906350920603723713659
absolute error = 3e-31
relative error = 2.5165565471770839156309759161730e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 2.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.99
Order of pole (three term test) = 4.330e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 1.1979398673070137502031193395952
y[1] (numeric) = 1.1979398673070137502031193395948
absolute error = 4e-31
relative error = 3.3390657654562062397514656121016e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3
Order of pole (three term test) = 5.049e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 1.2037718148301824174898611172196
y[1] (numeric) = 1.2037718148301824174898611172192
absolute error = 4e-31
relative error = 3.3228888986442043916085015651031e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.01
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 1.209601002986680894898679408258
y[1] (numeric) = 1.2096010029866808948986794082576
absolute error = 4e-31
relative error = 3.3068755648543758881169548196973e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.02
Order of pole (three term test) = 2.742e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 1.2154274500203057709151731789812
y[1] (numeric) = 1.2154274500203057709151731789808
absolute error = 4e-31
relative error = 3.2910232527109480995792413600034e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.03
Order of pole (three term test) = 3.192e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 1.2212511739945189097648012824525
y[1] (numeric) = 1.221251173994518909764801282452
absolute error = 5e-31
relative error = 4.0941618779745307910677914681825e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.04
Order of pole (three term test) = 2.786e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 1.2270721927948163911833494121853
y[1] (numeric) = 1.2270721927948163911833494121848
absolute error = 5e-31
relative error = 4.0747398803096093251874810570817e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.05
Order of pole (three term test) = 2.160e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 1.2328905241310586784596266063164
y[1] (numeric) = 1.232890524131058678459626606316
absolute error = 4e-31
relative error = 3.2444080976445173507870990487327e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.06
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 1.238706185539762773744927944843
y[1] (numeric) = 1.2387061855397627737449279448426
absolute error = 4e-31
relative error = 3.2291757696010948146595398564331e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.07
Order of pole (three term test) = 4.377e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 1.2445191943863571023457524441035
y[1] (numeric) = 1.2445191943863571023457524441032
absolute error = 3e-31
relative error = 2.4105694902353264603403149102647e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.08
Order of pole (three term test) = 1.694e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 1.2503295678673998508862741910164
y[1] (numeric) = 1.250329567867399850886274191016
absolute error = 4e-31
relative error = 3.1991565286443011101664867286368e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.09
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 1.256137323012761467832101247829
y[1] (numeric) = 1.2561373230127614678321012478287
absolute error = 3e-31
relative error = 2.3882739132411895695912906115452e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.1
Order of pole (three term test) = 6.846e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 1.2619424766877720188943111943805
y[1] (numeric) = 1.2619424766877720188943111943802
absolute error = 3e-31
relative error = 2.3772874401328640417423679301847e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.11
Order of pole (three term test) = 5.292e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 1.267745045595334074270419563738
y[1] (numeric) = 1.2677450455953340742704195637376
absolute error = 4e-31
relative error = 3.1552085444132789665777022027691e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.12
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 1.2735450462780017895150036303367
y[1] (numeric) = 1.2735450462780017895150036303363
absolute error = 4e-31
relative error = 3.1408390395692694849689343348709e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.13
Order of pole (three term test) = 3.554e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 1.2793424951200268270557316424878
y[1] (numeric) = 1.2793424951200268270557316424874
absolute error = 4e-31
relative error = 3.1266060615181264615014305349253e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.14
Order of pole (three term test) = 4.115e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 1.285137408349371750969462940651
y[1] (numeric) = 1.2851374083493717509694629406506
absolute error = 4e-31
relative error = 3.1125076384925974829564785708286e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.15
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 1.2909298020396915135971647491218
y[1] (numeric) = 1.2909298020396915135971647491214
absolute error = 4e-31
relative error = 3.0985418368062543067334196689985e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.16
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 1.296719692112283638895252845347
y[1] (numeric) = 1.2967196921122836388952528453466
absolute error = 4e-31
relative error = 3.0847067599353136838687553693839e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.17
Order of pole (three term test) = 3.187e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 1.3025070943380076940845489273748
y[1] (numeric) = 1.3025070943380076940845489273744
absolute error = 4e-31
relative error = 3.0710005476269430486220676242986e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.18
Order of pole (three term test) = 1.473e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 1.3082920243391746281566162056041
y[1] (numeric) = 1.3082920243391746281566162056037
absolute error = 4e-31
relative error = 3.0574213750331632702860815005984e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.19
Order of pole (three term test) = 2.554e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 1.3140744975914065431213503185162
y[1] (numeric) = 1.3140744975914065431213503185157
absolute error = 5e-31
relative error = 3.8049593148368681603710829550720e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.2
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 1.3198545294254674515202233165088
y[1] (numeric) = 1.3198545294254674515202233165083
absolute error = 5e-31
relative error = 3.7882962769969047379937254835898e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.21
Order of pole (three term test) = 3.404e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 1.3256321350290655616776467272002
y[1] (numeric) = 1.3256321350290655616776467271997
absolute error = 5e-31
relative error = 3.7717854507882542673463957865513e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.22
Order of pole (three term test) = 2.618e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 1.3314073294486276204099528154626
y[1] (numeric) = 1.331407329448627620409952815462
absolute error = 6e-31
relative error = 4.5065096663428801750528318125956e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.23
Order of pole (three term test) = 3.020e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 1.337180127591045831449173600674
y[1] (numeric) = 1.3371801275910458314491736006734
absolute error = 6e-31
relative error = 4.4870544186213030597846176853139e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.24
Order of pole (three term test) = 1.741e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 1.3429505442253978566590638300268
y[1] (numeric) = 1.3429505442253978566590638300262
absolute error = 6e-31
relative error = 4.4677743538655383549272190213726e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.25
Order of pole (three term test) = 2.006e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 1.3487185939846403962158534249171
y[1] (numeric) = 1.3487185939846403962158534249165
absolute error = 6e-31
relative error = 4.4486670731465646002735469384105e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.26
Order of pole (three term test) = 2.310e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 1.3544842913672768332884527253053
y[1] (numeric) = 1.3544842913672768332884527253047
absolute error = 6e-31
relative error = 4.4297302214877165466733605429321e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.27
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 1.3602476507389994183749272373754
y[1] (numeric) = 1.3602476507389994183749272373748
absolute error = 6e-31
relative error = 4.4109614868588834001933992789401e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.28
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 1.3660086863343064583268881563262
y[1] (numeric) = 1.3660086863343064583268881563257
absolute error = 5e-31
relative error = 3.6602988326652107839039394995449e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.29
Order of pole (three term test) = 3.521e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 1.3717674122580949652141073704154
y[1] (numeric) = 1.3717674122580949652141073704149
absolute error = 5e-31
relative error = 3.6449327745506037741801975803710e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.3
Order of pole (three term test) = 8.097e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 1.3775238424872292105414665129165
y[1] (numeric) = 1.377523842487229210541466512916
absolute error = 5e-31
relative error = 3.6297012405767881657124812827877e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.31
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 1.3832779908720856209227964195743
y[1] (numeric) = 1.3832779908720856209227964195737
absolute error = 6e-31
relative error = 4.3375229271285583202464067042707e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.32
Order of pole (three term test) = 5.346e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 1.3890298711380744421349588392415
y[1] (numeric) = 1.3890298711380744421349588392409
absolute error = 6e-31
relative error = 4.3195615333196667813195354896542e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.33
Order of pole (three term test) = 4.297e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 1.3947794968871385895145580275731
y[1] (numeric) = 1.3947794968871385895145580275726
absolute error = 5e-31
relative error = 3.5847960277298119302596804145116e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.34
Order of pole (three term test) = 7.047e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 1.4005268815992300939130201354198
y[1] (numeric) = 1.4005268815992300939130201354193
absolute error = 5e-31
relative error = 3.5700849913645446376456663223482e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.35
Order of pole (three term test) = 3.234e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 1.406272038633764543887693919572
y[1] (numeric) = 1.4062720386337645438876939195715
absolute error = 5e-31
relative error = 3.5554998340560407767822671426696e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.36
Order of pole (three term test) = 4.637e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 1.4120149812310539164715289416845
y[1] (numeric) = 1.412014981231053916471528941684
absolute error = 5e-31
relative error = 3.5410389170522753043205639198564e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.37
Order of pole (three term test) = 3.190e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 1.4177557225137181807263640541696
y[1] (numeric) = 1.4177557225137181807263640541691
absolute error = 5e-31
relative error = 3.5267006301585357088112216814175e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.38
Order of pole (three term test) = 2.437e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 1.423494275488076050339656485657
y[1] (numeric) = 1.4234942754880760503396564856566
absolute error = 4e-31
relative error = 2.8099867128924791662154907382415e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.39
Order of pole (three term test) = 4.188e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 1.4292306530455152537665018515263
y[1] (numeric) = 1.4292306530455152537665018515259
absolute error = 4e-31
relative error = 2.7987085159952947578406047193101e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.4
Order of pole (three term test) = 4.795e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 1.4349648679638426828430892786492
y[1] (numeric) = 1.4349648679638426828430892786488
absolute error = 4e-31
relative error = 2.7875246908837836539500592747369e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.41
Order of pole (three term test) = 1.830e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 1.4406969329086147733994998098201
y[1] (numeric) = 1.4406969329086147733994998098197
absolute error = 4e-31
relative error = 2.7764340359387195651894965033695e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.42
Order of pole (three term test) = 4.187e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 1.4464268604344484641743268606048
y[1] (numeric) = 1.4464268604344484641743268606043
absolute error = 5e-31
relative error = 3.4567942125315628219175637388751e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.43
Order of pole (three term test) = 2.394e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 1.4521546629863130732764470224524
y[1] (numeric) = 1.4521546629863130732764470224521
absolute error = 3e-31
relative error = 2.0658956490423608290041690357462e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.44
Order of pole (three term test) = 5.475e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 1.4578803529008034245460016535121
y[1] (numeric) = 1.4578803529008034245460016535118
absolute error = 3e-31
relative error = 2.0577820354261437330344706039747e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.45
Order of pole (three term test) = 3.128e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 1.4636039424073945494329954304972
y[1] (numeric) = 1.4636039424073945494329954304969
absolute error = 3e-31
relative error = 2.0497348449782661191909857113269e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.46
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 1.4693254436296782834337315146188
y[1] (numeric) = 1.4693254436296782834337315146186
absolute error = 2e-31
relative error = 1.3611688334065699191169972768556e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.47
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 1.4750448685865820696985576810726
y[1] (numeric) = 1.4750448685865820696985576810723
absolute error = 3e-31
relative error = 2.0338364370398175666428904257823e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.48
Order of pole (three term test) = 4.659e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 1.480762229193570276145182683647
y[1] (numeric) = 1.4807622291935702761451826836468
absolute error = 2e-31
relative error = 1.3506557370045891385381538136229e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.49
Order of pole (three term test) = 5.316e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 1.4864775372638283262763381858608
y[1] (numeric) = 1.4864775372638283262763381858605
absolute error = 3e-31
relative error = 2.0181939684888378257360703774854e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.5
Order of pole (three term test) = 1.213e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 1.4921908045094299379051180911056
y[1] (numeric) = 1.4921908045094299379051180911053
absolute error = 3e-31
relative error = 2.0104667519287352794895256098515e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.51
Order of pole (three term test) = 1.383e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 1.4979020425424877581323383493364
y[1] (numeric) = 1.4979020425424877581323383493361
absolute error = 3e-31
relative error = 2.0028011944678989028498434459691e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.52
Order of pole (three term test) = 3.153e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 1.5036112628762876771942423323194
y[1] (numeric) = 1.5036112628762876771942423323191
absolute error = 3e-31
relative error = 1.9951965471855010967062341177951e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.53
Order of pole (three term test) = 3.592e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 1.5093184769264070982024442360474
y[1] (numeric) = 1.5093184769264070982024442360472
absolute error = 2e-31
relative error = 1.3251013822296949564834853243578e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.54
Order of pole (three term test) = 2.046e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 1.5150236960118174343278657694572
y[1] (numeric) = 1.5150236960118174343278657694569
absolute error = 3e-31
relative error = 1.9801670481440440162926362205564e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.55
Order of pole (three term test) = 3.494e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 1.5207269313559710996333822489189
y[1] (numeric) = 1.5207269313559710996333822489187
absolute error = 2e-31
relative error = 1.3151605056515178323022900207048e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
memory used=136.8MB, alloc=44.3MB, time=1.58
Radius of convergence (given) for eq 1 = 3.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.56
Order of pole (three term test) = 3.976e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 1.5264281940878732545328454525821
y[1] (numeric) = 1.5264281940878732545328454525818
absolute error = 3e-31
relative error = 1.9653725026958564693667807861707e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.57
Order of pole (three term test) = 3.016e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 1.5321274952431385617440714408922
y[1] (numeric) = 1.532127495243138561744071440892
absolute error = 2e-31
relative error = 1.3053743935863595655959904955905e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.58
Order of pole (three term test) = 1.715e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 1.5378248457650332036073355244235
y[1] (numeric) = 1.5378248457650332036073355244233
absolute error = 2e-31
relative error = 1.3005382280743715471461614643730e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.59
Order of pole (three term test) = 1.950e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 1.5435202565055024067560488458838
y[1] (numeric) = 1.5435202565055024067560488458836
absolute error = 2e-31
relative error = 1.2957393928395589635792777697174e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 1.5492137382261837153498260189663
y[1] (numeric) = 1.5492137382261837153498260189661
absolute error = 2e-31
relative error = 1.2909774491736413481979234928314e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.61
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 1.5549053015994062494093920930452
y[1] (numeric) = 1.554905301599406249409392093045
absolute error = 2e-31
relative error = 1.2862519652758020494384897970271e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.62
Order of pole (three term test) = 2.859e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 1.5605949572091761802250954012356
y[1] (numeric) = 1.5605949572091761802250954012354
absolute error = 2e-31
relative error = 1.2815625161166835989968214806421e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.63
Order of pole (three term test) = 3.246e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 1.5662827155521486503436384100036
y[1] (numeric) = 1.5662827155521486503436384100034
absolute error = 2e-31
relative error = 1.2769086833055912220168664758971e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.64
Order of pole (three term test) = 3.684e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 1.5719685870385863612685293506886
y[1] (numeric) = 1.5719685870385863612685293506883
absolute error = 3e-31
relative error = 1.9084350824412246568966503849021e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.65
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 1.577652581993305047736278918474
y[1] (numeric) = 1.5776525819933050477362789184737
absolute error = 3e-31
relative error = 1.9015593383744931803984777905742e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.66
Order of pole (three term test) = 4.740e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 1.583334710656606053250170287812
y[1] (numeric) = 1.5833347106566060532501702878118
absolute error = 2e-31
relative error = 1.2631567959314197069470799060201e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.67
Order of pole (three term test) = 5.374e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 1.5890149831851962174642326324331
y[1] (numeric) = 1.5890149831851962174642326324329
absolute error = 2e-31
relative error = 1.2586413729032184831163012589229e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.68
Order of pole (three term test) = 4.263e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 1.594693409653095282009625764743
y[1] (numeric) = 1.5946934096530952820096257647427
absolute error = 3e-31
relative error = 1.8812393541230039996305211246572e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.69
Order of pole (three term test) = 6.900e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 1.6003700000525310174418340844513
y[1] (numeric) = 1.6003700000525310174418340844511
absolute error = 2e-31
relative error = 1.2497110042892277469812796958813e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.7
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 1.6060447642948222701577677736404
y[1] (numeric) = 1.6060447642948222701577677736402
absolute error = 2e-31
relative error = 1.2452953021382031740223721554814e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.71
Order of pole (three term test) = 1.770e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 1.6117177122112501243850307541177
y[1] (numeric) = 1.6117177122112501243850307541174
absolute error = 3e-31
relative error = 1.8613681398860160624224409977548e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.72
Order of pole (three term test) = 1.001e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 1.6173888535539173706792459542978
y[1] (numeric) = 1.6173888535539173706792459542975
absolute error = 3e-31
relative error = 1.8548415202738948653204232748818e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.73
Order of pole (three term test) = 2.266e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 1.6230581979965964687774898823465
y[1] (numeric) = 1.6230581979965964687774898823461
absolute error = 4e-31
relative error = 2.4644834085046086229301086295813e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.74
Order of pole (three term test) = 2.563e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 1.6287257551355661891446931121726
y[1] (numeric) = 1.6287257551355661891446931121723
absolute error = 3e-31
relative error = 1.8419307182566757359696783689866e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.75
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 1.634391534490437114113474061559
y[1] (numeric) = 1.6343915344904371141134740615587
absolute error = 3e-31
relative error = 1.8355454838643213200035835984809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.76
Order of pole (three term test) = 1.638e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 1.6400555455049661761545021715042
y[1] (numeric) = 1.6400555455049661761545021715039
absolute error = 3e-31
relative error = 1.8292063389086695046317548930989e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.77
Order of pole (three term test) = 7.403e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 1.6457177975478604075223924469396
y[1] (numeric) = 1.6457177975478604075223924469393
absolute error = 3e-31
relative error = 1.8229127767045094811458075584899e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.78
Order of pole (three term test) = 2.091e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 1.6513782999135700722996214489358
y[1] (numeric) = 1.6513782999135700722996214489355
absolute error = 3e-31
relative error = 1.8166642980333544191145552626166e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.79
Order of pole (three term test) = 2.361e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 1.65703706182307134870637505503
y[1] (numeric) = 1.6570370618230713487063750550297
absolute error = 3e-31
relative error = 1.8104604110057752701850875742904e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.8
Order of pole (three term test) = 2.665e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 1.6626940924246387264559838141821
y[1] (numeric) = 1.6626940924246387264559838141818
absolute error = 3e-31
relative error = 1.8043006309267766845108423382680e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.81
Order of pole (three term test) = 3.007e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 1.6683494007946072809121078214375
y[1] (numeric) = 1.6683494007946072809121078214372
absolute error = 3e-31
relative error = 1.7981844801641367927116605075952e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.82
Order of pole (three term test) = 3.393e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 1.6740029959381249828435759373105
y[1] (numeric) = 1.6740029959381249828435759373102
absolute error = 3e-31
relative error = 1.7921114880196348997857107571787e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.83
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 1.6796548867898951996742798248048
y[1] (numeric) = 1.6796548867898951996742798248045
absolute error = 3e-31
relative error = 1.7860811906030933555204709663427e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.84
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 1.685305082214909541287326216681
y[1] (numeric) = 1.6853050822149095412873262166807
absolute error = 3e-31
relative error = 1.7800931307091620114337099963967e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.85
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 1.6909535910091712006633530967327
y[1] (numeric) = 1.6909535910091712006633530967324
absolute error = 3e-31
relative error = 1.7741468576967757497501925930338e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.86
Order of pole (three term test) = 5.479e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 1.6966004219004089369111455498201
y[1] (numeric) = 1.6966004219004089369111455498199
absolute error = 2e-31
relative error = 1.1788279515808117186103055672549e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.87
Order of pole (three term test) = 1.851e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 1.7022455835487818455831087691774
y[1] (numeric) = 1.7022455835487818455831087691772
absolute error = 2e-31
relative error = 1.1749186012458144833960760465772e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.88
Order of pole (three term test) = 1.390e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 1.7078890845475750585574673614304
y[1] (numeric) = 1.7078890845475750585574673614302
absolute error = 2e-31
relative error = 1.1710362330290353715535604194841e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.89
Order of pole (three term test) = 2.347e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 1.7135309334238865132119933363154
y[1] (numeric) = 1.7135309334238865132119933363152
absolute error = 2e-31
relative error = 1.1671805632383339652031202204607e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.9
Order of pole (three term test) = 8.803e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 1.7191711386393049281093841654432
y[1] (numeric) = 1.7191711386393049281093841654429
absolute error = 3e-31
relative error = 1.7450269682717275000577090001959e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.91
Order of pole (three term test) = 2.971e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 1.7248097085905791199609127658376
y[1] (numeric) = 1.7248097085905791199609127658373
absolute error = 3e-31
relative error = 1.7393223061409117272378635373463e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.92
Order of pole (three term test) = 1.114e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 1.7304466516102787942314796150454
y[1] (numeric) = 1.730446651610278794231479615045
absolute error = 4e-31
relative error = 2.3115419341461772551425329598005e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.93
Order of pole (three term test) = 1.252e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 1.7360819759674469393945696656776
y[1] (numeric) = 1.7360819759674469393945696656772
absolute error = 4e-31
relative error = 2.3040386660145842734859587198357e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.94
Order of pole (three term test) = 5.630e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 1.7417156898682439525387385216992
y[1] (numeric) = 1.7417156898682439525387385216988
absolute error = 4e-31
relative error = 2.2965860750227203292286847078789e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.95
Order of pole (three term test) = 1.582e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 1.747347801456583621767036876704
y[1] (numeric) = 1.7473478014565836217670368767036
absolute error = 4e-31
relative error = 2.2891836397227916521042510425998e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.96
Order of pole (three term test) = 1.777e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 1.7529783188147610886161703105666
y[1] (numeric) = 1.7529783188147610886161703105662
absolute error = 4e-31
relative error = 2.2818308458626657217941572720439e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.97
Order of pole (three term test) = 1.995e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 1.758607249964072911552150656354
y[1] (numeric) = 1.7586072499640729115521506563537
absolute error = 3e-31
relative error = 1.7058953896961859190267714951030e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.98
Order of pole (three term test) = 4.480e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 1.7642346028654293494727186560858
y[1] (numeric) = 1.7642346028654293494727186560854
absolute error = 4e-31
relative error = 2.2672721606884321436168073350925e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 3.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.99
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 1.7698603854199589820629240910936
y[1] (numeric) = 1.7698603854199589820629240910933
absolute error = 3e-31
relative error = 1.6950489568069229175681805353360e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 1.7754846054696057818079820748597
y[1] (numeric) = 1.7754846054696057818079820748594
absolute error = 3e-31
relative error = 1.6896795335527658498852525465782e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.01
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 1.7811072707977187504659496417085
y[1] (numeric) = 1.7811072707977187504659496417081
absolute error = 4e-31
relative error = 2.2457939875841885853514025901782e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.02
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 1.7867283891296342308409752445493
y[1] (numeric) = 1.7867283891296342308409752445489
absolute error = 4e-31
relative error = 2.2387286306837676467341562176006e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.03
Order of pole (three term test) = 3.978e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 1.7923479681332510027749779304797
y[1] (numeric) = 1.7923479681332510027749779304793
absolute error = 4e-31
relative error = 2.2317095068130333441562569758831e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.04
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 1.7979660154195982703907473732514
y[1] (numeric) = 1.7979660154195982703907473732511
absolute error = 3e-31
relative error = 1.6685521162644881349209481913307e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.05
Order of pole (three term test) = 4.996e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 1.8035825385433966457717765273382
y[1] (numeric) = 1.8035825385433966457717765273378
absolute error = 4e-31
relative error = 2.2178081205146656317576982289750e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.06
Order of pole (three term test) = 5.596e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 1.8091975450036122324528221152715
y[1] (numeric) = 1.8091975450036122324528221152711
absolute error = 4e-31
relative error = 2.2109249545726161291736323548120e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.07
Order of pole (three term test) = 6.893e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 1.8148110422440039103194313578149
y[1] (numeric) = 1.8148110422440039103194313578145
absolute error = 4e-31
relative error = 2.2040862144270523702261265829760e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.08
Order of pole (three term test) = 4.910e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 1.8204230376536639217736928553044
y[1] (numeric) = 1.820423037653663921773692855304
absolute error = 4e-31
relative error = 2.1972914631730788434877565633912e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.09
Order of pole (three term test) = 3.925e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 1.8260335385675518573165010099528
y[1] (numeric) = 1.8260335385675518573165010099523
absolute error = 5e-31
relative error = 2.7381753370873429717794385140996e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.1
Order of pole (three term test) = 3.514e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 1.831642552267022137022921144248
y[1] (numeric) = 1.8316425522670221370229211442475
absolute error = 5e-31
relative error = 2.7297902605568455755125710620194e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.11
Order of pole (three term test) = 9.826e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 1.8372500859803450827460789425148
y[1] (numeric) = 1.8372500859803450827460789425143
absolute error = 5e-31
relative error = 2.7214585745043149466435002608341e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.12
Order of pole (three term test) = 2.198e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 1.8428561468832216742756630823131
y[1] (numeric) = 1.8428561468832216742756630823126
absolute error = 5e-31
relative error = 2.7131797609142633691791486370492e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.13
Order of pole (three term test) = 3.685e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 1.8484607420992920810989311598007
y[1] (numeric) = 1.8484607420992920810989311598003
absolute error = 4e-31
relative error = 2.1639626468113195370084590816806e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.14
Order of pole (three term test) = 4.119e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 1.8540638787006380598643701921518
y[1] (numeric) = 1.8540638787006380598643701921513
absolute error = 5e-31
relative error = 2.6967787126644695867782998663212e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.15
Order of pole (three term test) = 4.602e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 1.8596655637082793061302243152364
y[1] (numeric) = 1.859665563708279306130224315236
absolute error = 4e-31
relative error = 2.1509243802007989177636857425336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.16
Order of pole (three term test) = 1.714e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 1.8652658040926638474913198419719
y[1] (numeric) = 1.8652658040926638474913198419715
absolute error = 4e-31
relative error = 2.1444664836633039377842883943886e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.17
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 1.8708646067741525637173630858502
y[1] (numeric) = 1.8708646067741525637173630858498
absolute error = 4e-31
relative error = 2.1380488922162141586518151853390e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.18
Order of pole (three term test) = 4.274e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 1.8764619786234979181035457834437
y[1] (numeric) = 1.8764619786234979181035457834433
absolute error = 4e-31
relative error = 2.1316712225281803342100221859707e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.19
Order of pole (three term test) = 2.385e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 1.8820579264623169828292676921494
y[1] (numeric) = 1.882057926462316982829267692149
absolute error = 4e-31
relative error = 2.1253330961596675189030694323253e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.2
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=181.0MB, alloc=44.3MB, time=2.06
x[1] = 2.71
y[1] (closed_form) = 1.8876524570635588397424913601216
y[1] (numeric) = 1.8876524570635588397424913601213
absolute error = 3e-31
relative error = 1.5892756046135814112627800937355e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.21
Order of pole (three term test) = 2.969e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 1.8932455771519664366351093997505
y[1] (numeric) = 1.8932455771519664366351093997501
absolute error = 4e-31
relative error = 2.1127739836145563414643756268100e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.22
Order of pole (three term test) = 3.311e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 1.8988372934045329777481725889267
y[1] (numeric) = 1.8988372934045329777481725889262
absolute error = 5e-31
relative error = 2.6331903304022519399005097318858e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.23
Order of pole (three term test) = 3.692e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 1.9044276124509529259443536788732
y[1] (numeric) = 1.9044276124509529259443536788728
absolute error = 4e-31
relative error = 2.1003686219672562825465669051728e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.24
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 1.9100165408740676927080756241038
y[1] (numeric) = 1.9100165408740676927080756241033
absolute error = 5e-31
relative error = 2.6177783767840484220012436936585e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.25
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 1.9156040852103060908807952757458
y[1] (numeric) = 1.9156040852103060908807952757454
absolute error = 4e-31
relative error = 2.0881141520226278257154867521224e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.26
Order of pole (three term test) = 5.111e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 1.9211902519501196238094977647396
y[1] (numeric) = 1.9211902519501196238094977647392
absolute error = 4e-31
relative error = 2.0820426274491908412524192499879e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.27
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 1.9267750475384126833800280680073
y[1] (numeric) = 1.9267750475384126833800280680069
absolute error = 4e-31
relative error = 2.0760077857092214446653396981456e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.28
Order of pole (three term test) = 1.268e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 1.9323584783749677282229813671356
y[1] (numeric) = 1.9323584783749677282229813671352
absolute error = 4e-31
relative error = 2.0700092890444592338660934158378e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.29
Order of pole (three term test) = 2.823e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 1.9379405508148655122180207950299
y[1] (numeric) = 1.9379405508148655122180207950295
absolute error = 4e-31
relative error = 2.0640468038702629159198353645501e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.3
Order of pole (three term test) = 7.856e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 1.9435212711689004322822290046036
y[1] (numeric) = 1.9435212711689004322822290046032
absolute error = 4e-31
relative error = 2.0581200007110097855940620579406e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.31
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 1.9491006457039910633089783521724
y[1] (numeric) = 1.949100645703991063308978352172
absolute error = 4e-31
relative error = 2.0522285541366948950038754497571e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.32
Order of pole (three term test) = 2.918e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 1.9546786806435859470253834465155
y[1] (numeric) = 1.9546786806435859470253834465151
absolute error = 4e-31
relative error = 2.0463721427007039574267031592926e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.33
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 1.9602553821680647004582496003833
y[1] (numeric) = 1.9602553821680647004582496003829
absolute error = 4e-31
relative error = 2.0405504488787346688887951711452e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.34
Order of pole (three term test) = 1.203e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 1.96583075641513450864013145365
y[1] (numeric) = 1.9658307564151345086401314536497
absolute error = 3e-31
relative error = 1.5260723692566313154372924609087e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.35
Order of pole (three term test) = 2.674e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 1.9714048094802220651482574768038
y[1] (numeric) = 1.9714048094802220651482574768035
absolute error = 3e-31
relative error = 1.5217574724244362355806471766194e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.36
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 1.9769775474168610230492573689469
y[1] (numeric) = 1.9769775474168610230492573689466
absolute error = 3e-31
relative error = 1.5174679165779249853316118892500e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.37
Order of pole (three term test) = 3.302e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 1.9825489762370750178214588569772
y[1] (numeric) = 1.9825489762370750178214588569769
absolute error = 3e-31
relative error = 1.5132034748993042072624963918724e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.38
Order of pole (three term test) = 1.834e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 1.988119101911756322843615335458
y[1] (numeric) = 1.9881191019117563228436153354577
absolute error = 3e-31
relative error = 1.5089639232957566167421404008566e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.39
Order of pole (three term test) = 2.037e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 1.9936879303710401970739121219138
y[1] (numeric) = 1.9936879303710401970739121219134
absolute error = 4e-31
relative error = 2.0063320538112352214311556890782e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.4
Order of pole (three term test) = 4.524e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 1.9992554675046749835956112932052
y[1] (numeric) = 1.9992554675046749835956112932048
absolute error = 4e-31
relative error = 2.0007448097628606589444548756106e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.41
Order of pole (three term test) = 2.511e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 2.0048217191623880167753758482465
y[1] (numeric) = 2.0048217191623880167753758482461
absolute error = 4e-31
relative error = 1.9951898773678464288045405361337e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.42
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 2.0103866911542473948668141174837
y[1] (numeric) = 2.0103866911542473948668141174833
absolute error = 4e-31
relative error = 1.9896669718318877653883098084106e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.43
Order of pole (three term test) = 3.092e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 2.01595038925101967399476359074
y[1] (numeric) = 2.0159503892510196739947635907395
absolute error = 5e-31
relative error = 2.4802197646627781390502165563677e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.44
Order of pole (three term test) = 3.430e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 2.0215128191845235385749560214964
y[1] (numeric) = 2.0215128191845235385749560214959
absolute error = 5e-31
relative error = 2.4733951486971007799818861497172e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.45
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 2.0270739866479795023586466358177
y[1] (numeric) = 2.0270739866479795023586466358173
absolute error = 4e-31
relative error = 1.9732876186796223188458891634881e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.46
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 2.032633897296355693442230681029
y[1] (numeric) = 2.0326338972963556934422306810286
absolute error = 4e-31
relative error = 1.9678900392837464241058097205319e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.47
Order of pole (three term test) = 4.675e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 2.0381925567467097757474986710704
y[1] (numeric) = 2.03819255674670977574749867107
absolute error = 4e-31
relative error = 1.9625231123327509625595592574632e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.48
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 2.0437499705785270586586927507289
y[1] (numeric) = 2.0437499705785270586586927507285
absolute error = 4e-31
relative error = 1.9571865725178283960806480052573e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.49
Order of pole (three term test) = 5.741e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 2.0493061443340548456976226184613
y[1] (numeric) = 2.0493061443340548456976226184609
absolute error = 4e-31
relative error = 1.9518801576129783833451217085146e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.5
Order of pole (three term test) = 2.544e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 2.054861083518633072327489040773
y[1] (numeric) = 2.0548610835186330723274890407726
absolute error = 4e-31
relative error = 1.9466036084301213027333924854621e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.51
Order of pole (three term test) = 5.635e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 2.0604147936010212821994612371554
y[1] (numeric) = 2.060414793601021282199461237155
absolute error = 4e-31
relative error = 1.9413566687749961838515964397479e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.52
Order of pole (three term test) = 4.679e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 2.0659672800137219903931826871241
y[1] (numeric) = 2.0659672800137219903931826871237
absolute error = 4e-31
relative error = 1.9361390854038270722613879783748e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.53
Order of pole (three term test) = 3.453e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 2.0715185481533004814529657275953
y[1] (numeric) = 2.0715185481533004814529657275949
absolute error = 4e-31
relative error = 1.9309506079807422231850831254802e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.54
Order of pole (three term test) = 8.599e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 2.077068603380701089285212182581
y[1] (numeric) = 2.0770686033807010892852121825806
absolute error = 4e-31
relative error = 1.9257909890359308814502238191722e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.55
Order of pole (three term test) = 1.057e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 2.0826174510215600052593045613186
y[1] (numeric) = 2.0826174510215600052593045613181
absolute error = 5e-31
relative error = 2.4008249799056534462922659644767e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.56
Order of pole (three term test) = 1.170e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 2.0881650963665146601435951483107
y[1] (numeric) = 2.0881650963665146601435951483103
absolute error = 4e-31
relative error = 1.9155573507861756485326480898108e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.57
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 2.09371154467150972480992923437
y[1] (numeric) = 2.0937115446715097248099292343697
absolute error = 3e-31
relative error = 1.4328621378790177507385868960564e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.58
Order of pole (three term test) = 4.291e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 2.0992568011580997739541298851826
y[1] (numeric) = 2.0992568011580997739541298851821
absolute error = 5e-31
relative error = 2.3817953083403818874403534838362e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.59
Order of pole (three term test) = 1.581e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 2.1048008710137486564058064050106
y[1] (numeric) = 2.1048008710137486564058064050101
absolute error = 5e-31
relative error = 2.3755216319308240011166465312306e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.6
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 2.110343759392125614938493601341
y[1] (numeric) = 2.1103437593921256149384936013405
absolute error = 5e-31
relative error = 2.3692822450121709023007316699192e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.61
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 2.1158854714133981978402557229696
y[1] (numeric) = 2.1158854714133981978402557229691
absolute error = 5e-31
relative error = 2.3630768619343236106177430384646e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.62
Order of pole (three term test) = 2.134e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 2.121426012164522003865274098337
y[1] (numeric) = 2.1214260121645220038652740983366
absolute error = 4e-31
relative error = 1.8855241601938978142540621612861e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.63
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 2.126965386699527301558362432571
y[1] (numeric) = 2.1269653866995273015583624325706
absolute error = 4e-31
relative error = 1.8806135845054412436765951635596e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.64
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 2.1325036000398025633266045266951
y[1] (numeric) = 2.1325036000398025633266045266947
absolute error = 4e-31
relative error = 1.8757295415235599865528600413775e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.65
Order of pole (three term test) = 2.874e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 2.1380406571743749540251765520541
y[1] (numeric) = 2.1380406571743749540251765520537
absolute error = 4e-31
relative error = 1.8708718127401666214743243443607e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.66
Order of pole (three term test) = 3.173e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 2.1435765630601878132276951252059
y[1] (numeric) = 2.1435765630601878132276951252055
absolute error = 4e-31
relative error = 1.8660401820635539025748270465216e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.67
Order of pole (three term test) = 3.501e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 2.149111322622375169764922842604
y[1] (numeric) = 2.1491113226223751697649228426036
absolute error = 4e-31
relative error = 1.8612344357849015613049994940008e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.68
Order of pole (three term test) = 3.863e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 2.1546449407545333265391684879741
y[1] (numeric) = 2.1546449407545333265391684879736
absolute error = 5e-31
relative error = 2.3205679531816755584916190154468e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.69
Order of pole (three term test) = 8.524e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 2.1601774223189895530550478341365
y[1] (numeric) = 2.160177422318989553055047834136
absolute error = 5e-31
relative error = 2.3146246916294539921947867452911e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.7
Order of pole (three term test) = 4.701e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 2.1657087721470679225502349213538
y[1] (numeric) = 2.1657087721470679225502349213534
absolute error = 4e-31
relative error = 1.8469704013039708462096266116962e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.71
Order of pole (three term test) = 5.183e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 2.1712389950393523300622489875459
y[1] (numeric) = 2.1712389950393523300622489875455
absolute error = 4e-31
relative error = 1.8422661020453450985895814316258e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.72
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 2.1767680957659467272290088258501
y[1] (numeric) = 2.1767680957659467272290088258497
absolute error = 4e-31
relative error = 1.8375866532500360434322827659978e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.73
Order of pole (three term test) = 1.260e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 2.1822960790667326090916680279879
y[1] (numeric) = 2.1822960790667326090916680279875
absolute error = 4e-31
relative error = 1.8329318548336555367287170277952e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.74
Order of pole (three term test) = 2.777e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 2.1878229496516237876479488276074
y[1] (numeric) = 2.187822949651623787647948827607
absolute error = 4e-31
relative error = 1.8283015088752665085168365275692e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.75
Order of pole (three term test) = 7.648e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 2.1933487122008184863926502040805
y[1] (numeric) = 2.1933487122008184863926502040801
absolute error = 4e-31
relative error = 1.8236954195880587574335133436690e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.76
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 2.1988733713650487895790522062409
y[1] (numeric) = 2.1988733713650487895790522062405
absolute error = 4e-31
relative error = 1.8191133932905019739184698623701e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.77
Order of pole (three term test) = 1.856e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 2.2043969317658274794404112319524
y[1] (numeric) = 2.204396931765827479440411231952
absolute error = 4e-31
relative error = 1.8145552383779669377010246903557e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.78
Order of pole (three term test) = 3.065e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 2.2099193979956922941244817608723
y[1] (numeric) = 2.2099193979956922941244817608719
absolute error = 4e-31
relative error = 1.8100207652948060312403622132604e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.79
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 2.2154407746184476386158535973822
y[1] (numeric) = 2.2154407746184476386158535973819
absolute error = 3e-31
relative error = 1.3541323398801633015479350071114e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.8
Order of pole (three term test) = 3.714e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 2.2209610661694037804507080811716
y[1] (numeric) = 2.2209610661694037804507080811712
absolute error = 4e-31
relative error = 1.8010221164745532935847850544857e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.81
Order of pole (three term test) = 2.725e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 2.2264802771556135615662231630646
y[1] (numeric) = 2.2264802771556135615662231630642
absolute error = 4e-31
relative error = 1.7965575716260572461026584520292e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.82
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 2.2319984120561066571721500060664
y[1] (numeric) = 2.2319984120561066571721500060659
absolute error = 5e-31
relative error = 2.2401449629142088092802163682525e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.83
Order of pole (three term test) = 1.649e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 2.237515475322121412084900152734
y[1] (numeric) = 2.2375154753221214120849001527336
absolute error = 4e-31
relative error = 1.7876971328764304859959535389170e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.84
Order of pole (three term test) = 1.814e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 2.2430314713773342845246825417549
y[1] (numeric) = 2.2430314713773342845246825417545
absolute error = 4e-31
relative error = 1.7833008814378331287400913630199e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.85
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=225.2MB, alloc=44.3MB, time=2.55
x[1] = 3.36
y[1] (closed_form) = 2.2485464046180869269436768795401
y[1] (numeric) = 2.2485464046180869269436768795397
absolute error = 4e-31
relative error = 1.7789270400578615110287157758045e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.86
Order of pole (three term test) = 4.385e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 2.254060279413610933027790010835
y[1] (numeric) = 2.2540602794136109330277900108346
absolute error = 4e-31
relative error = 1.7745754346199612875386824741086e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.87
Order of pole (three term test) = 2.410e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 2.2595731001062502795960836699724
y[1] (numeric) = 2.259573100106250279596083669972
absolute error = 4e-31
relative error = 1.7702458928245830501936712223693e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.88
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 2.2650848710116814917103567037832
y[1] (numeric) = 2.2650848710116814917103567037827
absolute error = 5e-31
relative error = 2.2074228052067608414129595245216e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.89
Order of pole (three term test) = 2.910e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 2.270595596419131558902486538415
y[1] (numeric) = 2.2705955964191315589024865384146
absolute error = 4e-31
relative error = 1.7616523199059511947162416491377e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.9
Order of pole (three term test) = 3.196e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 2.2761052805915936300288598842761
y[1] (numeric) = 2.2761052805915936300288598842757
absolute error = 4e-31
relative error = 1.7573879530565213931942132750881e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.91
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 2.2816139277660405138694305162414
y[1] (numeric) = 2.281613927766040513869430516241
absolute error = 4e-31
relative error = 1.7531449783515543556269516334759e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.92
Order of pole (three term test) = 3.855e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 2.2871215421536360122035139655811
y[1] (numeric) = 2.2871215421536360122035139655806
absolute error = 5e-31
relative error = 2.1861540402841118494384540366421e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.93
Order of pole (three term test) = 8.465e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 2.2926281279399441117152490517502
y[1] (numeric) = 2.2926281279399441117152490517497
absolute error = 5e-31
relative error = 2.1809031909997468540168489360745e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.94
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 2.2981336892851360607086106492814
y[1] (numeric) = 2.2981336892851360607086106492809
absolute error = 5e-31
relative error = 2.1756784748041851669343055495895e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.95
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 2.3036382303241953562448355056161
y[1] (numeric) = 2.3036382303241953562448355056155
absolute error = 6e-31
relative error = 2.6045756321536687968003221173758e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.96
Order of pole (three term test) = 1.119e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 2.3091417551671206669540141220114
y[1] (numeric) = 2.3091417551671206669540141220108
absolute error = 6e-31
relative error = 2.5983679809062908786381482399747e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.97
Order of pole (three term test) = 1.228e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 2.3146442678991267164172996984404
y[1] (numeric) = 2.3146442678991267164172996984398
absolute error = 6e-31
relative error = 2.5921909829564716577537982219577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.98
Order of pole (three term test) = 6.733e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 2.3201457725808431516665850875184
y[1] (numeric) = 2.3201457725808431516665850875179
absolute error = 5e-31
relative error = 2.1550370063335233891860454129348e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 4.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.99
Order of pole (three term test) = 1.477e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 2.3256462732485114210044978636711
y[1] (numeric) = 2.3256462732485114210044978636705
absolute error = 6e-31
relative error = 2.5799280264659828687772281974088e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5
Order of pole (three term test) = 5.667e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 2.3311457739141796850090613064392
y[1] (numeric) = 2.3311457739141796850090613064386
absolute error = 6e-31
relative error = 2.5738416134849951678766478399969e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.01
Order of pole (three term test) = 2.663e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 2.336644278565895784254266643139
y[1] (numeric) = 2.3366442785658957842542666431383
absolute error = 7e-31
relative error = 2.9957491023392813633495209624510e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.02
Order of pole (three term test) = 2.918e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 2.3421417911678982869500025819313
y[1] (numeric) = 2.3421417911678982869500025819306
absolute error = 7e-31
relative error = 2.9887174322223600436803167483880e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.03
Order of pole (three term test) = 1.066e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 2.347638315660805639382197198438
y[1] (numeric) = 2.3476383156608056393821971984374
absolute error = 6e-31
relative error = 2.5557599567082970392310866433679e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.04
Order of pole (three term test) = 1.168e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 2.3531338559618034417165517030572
y[1] (numeric) = 2.3531338559618034417165517030565
absolute error = 7e-31
relative error = 2.9747564008163356501564193412547e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.05
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 2.3586284159648298714167944358308
y[1] (numeric) = 2.3586284159648298714167944358301
absolute error = 7e-31
relative error = 2.9678265353792713912855438320558e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.06
Order of pole (three term test) = 4.204e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 2.3641219995407592762208673330356
y[1] (numeric) = 2.364121999540759276220867333035
absolute error = 6e-31
relative error = 2.5379400898792555730136711823146e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.07
Order of pole (three term test) = 6.139e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 2.3696146105375839583157885656805
y[1] (numeric) = 2.3696146105375839583157885656799
absolute error = 6e-31
relative error = 2.5320573114793576529360161781853e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.08
Order of pole (three term test) = 5.041e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 2.3751062527805941710540282670373
y[1] (numeric) = 2.3751062527805941710540282670367
absolute error = 6e-31
relative error = 2.5262027721815204253584600660981e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.09
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 2.3805969300725563492610051303924
y[1] (numeric) = 2.3805969300725563492610051303918
absolute error = 6e-31
relative error = 2.5203762653836282563884839226264e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.1
Order of pole (three term test) = 2.013e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 2.3860866461938895938946777032428
y[1] (numeric) = 2.3860866461938895938946777032422
absolute error = 6e-31
relative error = 2.5145775865142030441312408163596e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.11
Order of pole (three term test) = 4.406e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 2.3915754049028404315340845763032
y[1] (numeric) = 2.3915754049028404315340845763026
absolute error = 6e-31
relative error = 2.5088065330073732549158180463316e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.12
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 2.3970632099356558688940030886862
y[1] (numeric) = 2.3970632099356558688940030886856
absolute error = 6e-31
relative error = 2.5030629042782135927401909324431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.13
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 2.4025500650067547622875689120772
y[1] (numeric) = 2.4025500650067547622875689120766
absolute error = 6e-31
relative error = 2.4973465016984489012225163205204e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.14
Order of pole (three term test) = 5.767e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 2.4080359738088975216876527150923
y[1] (numeric) = 2.4080359738088975216876527150916
absolute error = 7e-31
relative error = 2.9069333166679353607962228389288e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.15
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 2.4135209400133541687709503013186
y[1] (numeric) = 2.4135209400133541687709503013179
absolute error = 7e-31
relative error = 2.9003270217996403807708169081130e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.16
Order of pole (three term test) = 3.448e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 2.4190049672700707680660358649567
y[1] (numeric) = 2.4190049672700707680660358649561
absolute error = 6e-31
relative error = 2.4803586934222808574283408773173e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.17
Order of pole (three term test) = 7.538e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 2.4244880592078342500679824370056
y[1] (numeric) = 2.424488059207834250067982437005
absolute error = 6e-31
relative error = 2.4747492474598582240523530151475e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.18
Order of pole (three term test) = 4.119e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 2.4299702194344356449274987093632
y[1] (numeric) = 2.4299702194344356449274987093626
absolute error = 6e-31
relative error = 2.4691660630295593960012480449657e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.19
Order of pole (three term test) = 4.501e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 2.4354514515368317450717980878139
y[1] (numeric) = 2.4354514515368317450717980878132
absolute error = 7e-31
relative error = 2.8742104448778160395251717500961e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.2
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 2.4409317590813052148675362296518
y[1] (numeric) = 2.4409317590813052148675362296511
absolute error = 7e-31
relative error = 2.8677573528866672311733367887009e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.21
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 2.4464111456136231651930609599386
y[1] (numeric) = 2.4464111456136231651930609599379
absolute error = 7e-31
relative error = 2.8613342497849923018445129415370e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.22
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 2.4518896146591942105478480972506
y[1] (numeric) = 2.4518896146591942105478480972499
absolute error = 7e-31
relative error = 2.8549409231756872526099203900719e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.23
Order of pole (three term test) = 1.922e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 2.4573671697232240260912843665438
y[1] (numeric) = 2.4573671697232240260912843665431
absolute error = 7e-31
relative error = 2.8485771626827820437007192910974e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.24
Order of pole (three term test) = 1.399e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 2.4628438142908694217708414647269
y[1] (numeric) = 2.4628438142908694217708414647262
absolute error = 7e-31
relative error = 2.8422427599273164838570558579826e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.25
Order of pole (three term test) = 2.291e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 2.4683195518273909504711018994382
y[1] (numeric) = 2.4683195518273909504711018994375
absolute error = 7e-31
relative error = 2.8359375085035620533245086172280e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.26
Order of pole (three term test) = 8.337e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 2.4737943857783040668899870386262
y[1] (numeric) = 2.4737943857783040668899870386256
absolute error = 6e-31
relative error = 2.4254238891047861777637659215999e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.27
Order of pole (three term test) = 9.098e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 2.4792683195695288536268416282024
y[1] (numeric) = 2.4792683195695288536268416282018
absolute error = 6e-31
relative error = 2.4200688375035461296025063670861e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.28
Order of pole (three term test) = 9.927e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 2.4847413566075383307486887189274
y[1] (numeric) = 2.4847413566075383307486887189268
absolute error = 6e-31
relative error = 2.4147382519490507297757824199671e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.29
Order of pole (three term test) = 2.166e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 2.4902135002795053648859274514507
y[1] (numeric) = 2.4902135002795053648859274514501
absolute error = 6e-31
relative error = 2.4094319620894155622674046964662e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.3
Order of pole (three term test) = 2.362e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 2.4956847539534481936969475149136
y[1] (numeric) = 2.495684753953448193696947514913
absolute error = 6e-31
relative error = 2.4041497991664685690403989131748e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.31
Order of pole (three term test) = 2.576e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 2.5011551209783745813325234075842
y[1] (numeric) = 2.5011551209783745813325234075836
absolute error = 6e-31
relative error = 2.3988915959970469321008288053092e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.32
Order of pole (three term test) = 1.405e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 2.506624604684424620325375006673
y[1] (numeric) = 2.5066246046844246203253750066724
absolute error = 6e-31
relative error = 2.3936571869545576712249975526952e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.33
Order of pole (three term test) = 3.063e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 2.512093208383012195127885527785
y[1] (numeric) = 2.5120932083830121951278855277843
absolute error = 7e-31
relative error = 2.7865208092759305561840816030064e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.34
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 2.5175609353669651223216018405847
y[1] (numeric) = 2.517560935366965122321601840584
absolute error = 7e-31
relative error = 2.7804689458210332744877014083462e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.35
Order of pole (three term test) = 1.819e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 2.5230277889106639823257543932069
y[1] (numeric) = 2.5230277889106639823257543932062
absolute error = 7e-31
relative error = 2.7744442731731869175319690990879e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.36
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 2.5284937722701796572385747197584
y[1] (numeric) = 2.5284937722701796572385747197576
absolute error = 8e-31
relative error = 3.1639389773213837489268460437016e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.37
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 2.5339588886834095892546086285107
y[1] (numeric) = 2.5339588886834095892546086285099
absolute error = 8e-31
relative error = 3.1571151512077717778993402030920e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.38
Order of pole (three term test) = 2.353e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 2.5394231413702127739134745692352
y[1] (numeric) = 2.5394231413702127739134745692344
absolute error = 8e-31
relative error = 3.1503217678340085031186107036151e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.39
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 2.5448865335325435022505521247499
y[1] (numeric) = 2.5448865335325435022505521247491
absolute error = 8e-31
relative error = 3.1435586202325658983914454980731e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.4
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 2.5503490683545838657378587061685
y[1] (numeric) = 2.5503490683545838657378587061677
absolute error = 8e-31
relative error = 3.1368255033266419853414885244271e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.41
Order of pole (three term test) = 3.039e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 2.5558107490028750377238378516884
y[1] (numeric) = 2.5558107490028750377238378516876
absolute error = 8e-31
relative error = 3.1301222139084918531089526427492e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.42
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 2.5612715786264473449038953719112
y[1] (numeric) = 2.5612715786264473449038953719105
absolute error = 7e-31
relative error = 2.7330174817907999504440770998420e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.43
Order of pole (three term test) = 3.601e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 2.5667315603569491421792361093134
y[1] (numeric) = 2.5667315603569491421792361093127
absolute error = 7e-31
relative error = 2.7272037746816527054661724538748e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.44
Order of pole (three term test) = 3.919e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 2.5721906973087745040898312493812
y[1] (numeric) = 2.5721906973087745040898312493806
absolute error = 6e-31
relative error = 2.3326419795692697155958092894622e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.45
Order of pole (three term test) = 4.265e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 2.5776489925791897458381416888696
y[1] (numeric) = 2.577648992579189745838141688869
absolute error = 6e-31
relative error = 2.3277024983903698946960712667306e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.46
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 2.5831064492484587867534954584218
y[1] (numeric) = 2.5831064492484587867534954584211
absolute error = 7e-31
relative error = 2.7099154206504393665352207645147e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.47
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 2.5885630703799673688827258957464
y[1] (numeric) = 2.5885630703799673688827258957458
absolute error = 6e-31
relative error = 2.3178882788895223207005878492284e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.48
Order of pole (three term test) = 5.490e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 2.59401885902034614323078219734
y[1] (numeric) = 2.5940188590203461432307821973394
absolute error = 6e-31
relative error = 2.3130132532135685221151351869395e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.49
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 2.5994738181995926360154858944913
y[1] (numeric) = 2.5994738181995926360154858944907
absolute error = 6e-31
relative error = 2.3081594274935329914227168276583e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.5
Order of pole (three term test) = 1.298e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 2.6049279509311921071433871690848
y[1] (numeric) = 2.6049279509311921071433871690842
absolute error = 6e-31
relative error = 2.3033266612441854266550766755837e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.51
Order of pole (three term test) = 2.823e-29
NO COMPLEX POLE (six term test) for Equation 1
memory used=269.6MB, alloc=44.3MB, time=3.05
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 2.6103812602122373129587359112992
y[1] (numeric) = 2.6103812602122373129587359112985
absolute error = 7e-31
relative error = 2.6816006177698595225342825087174e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.52
Order of pole (three term test) = 3.835e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = 2.6158337490235471851648868742535
y[1] (numeric) = 2.6158337490235471851648868742528
absolute error = 7e-31
relative error = 2.6760110433673388134188137785946e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.53
Order of pole (three term test) = 1.667e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 2.621285420329784437666969720768
y[1] (numeric) = 2.6212854203297844376669697207674
absolute error = 6e-31
relative error = 2.2889533331494816051665835788827e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.54
Order of pole (three term test) = 9.059e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 2.6267362770795721129363373633174
y[1] (numeric) = 2.6267362770795721129363373633168
absolute error = 6e-31
relative error = 2.2842034247423008834917145551561e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.55
Order of pole (three term test) = 1.969e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 2.6321863222056090793511245934703
y[1] (numeric) = 2.6321863222056090793511245934697
absolute error = 6e-31
relative error = 2.2794738918680998569857605450002e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.56
Order of pole (three term test) = 2.139e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 2.6376355586247844908231690372336
y[1] (numeric) = 2.6376355586247844908231690372329
absolute error = 7e-31
relative error = 2.6538920348987384315040113499030e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.57
Order of pole (three term test) = 2.323e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 2.6430839892382912198795340329838
y[1] (numeric) = 2.6430839892382912198795340329831
absolute error = 7e-31
relative error = 2.6484213246728212282280001222567e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.58
Order of pole (three term test) = 3.784e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 2.6485316169317382752268947917502
y[1] (numeric) = 2.6485316169317382752268947917495
absolute error = 7e-31
relative error = 2.6429739238338169170405028765197e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.59
Order of pole (three term test) = 2.739e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 2.6539784445752622146890724436479
y[1] (numeric) = 2.6539784445752622146890724436472
absolute error = 7e-31
relative error = 2.6375496810488477837566728849453e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.6
Order of pole (three term test) = 2.974e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 2.6594244750236375642719931612126
y[1] (numeric) = 2.6594244750236375642719931612119
absolute error = 7e-31
relative error = 2.6321484463053918543511296216849e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.61
Order of pole (three term test) = 3.228e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 2.6648697111163862539762799145602
y[1] (numeric) = 2.6648697111163862539762799145595
absolute error = 7e-31
relative error = 2.6267700708968281982140443023110e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.62
Order of pole (three term test) = 3.504e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 2.6703141556778860808455215501768
y[1] (numeric) = 2.6703141556778860808455215501761
absolute error = 7e-31
relative error = 2.6214144074081724144888445414283e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.63
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 2.6757578115174782096079773404251
y[1] (numeric) = 2.6757578115174782096079773404245
absolute error = 6e-31
relative error = 2.2423554083159994699534754009946e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.64
Order of pole (three term test) = 1.031e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 2.6812006814295737211410350097329
y[1] (numeric) = 2.6812006814295737211410350097323
absolute error = 6e-31
relative error = 2.2378033996324717726109739280514e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.65
Order of pole (three term test) = 6.714e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 2.6866427681937592188611171200857
y[1] (numeric) = 2.686642768193759218861117120085
absolute error = 7e-31
relative error = 2.6054822333920219190456373276471e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.66
Order of pole (three term test) = 2.428e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 2.6920840745749015030168957258057
y[1] (numeric) = 2.692084074574901503016895725805
absolute error = 7e-31
relative error = 2.6002159687770330501875514945461e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.67
Order of pole (three term test) = 2.633e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 2.6975246033232513227406000272442
y[1] (numeric) = 2.6975246033232513227406000272436
absolute error = 6e-31
relative error = 2.2242614553388021656686258396395e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.68
Order of pole (three term test) = 2.855e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = 2.7029643571745462155908585053684
y[1] (numeric) = 2.7029643571745462155908585053677
absolute error = 7e-31
relative error = 2.5897492807922990542448194812084e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.69
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 2.708403338850112444200878333896
y[1] (numeric) = 2.7084033388501124442008783338953
absolute error = 7e-31
relative error = 2.5845485787105624555970243638406e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.7
Order of pole (three term test) = 3.357e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 2.7138415510569660395278038520073
y[1] (numeric) = 2.7138415510569660395278038520066
absolute error = 7e-31
relative error = 2.5793694540765263482850501751521e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.71
Order of pole (three term test) = 7.277e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 2.719278996487912960082786118634
y[1] (numeric) = 2.7192789964879129600827861186334
absolute error = 6e-31
relative error = 2.2064672318468627047726169003157e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.72
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 2.7247156778216483764066111003036
y[1] (numeric) = 2.724715677821648376406611100303
absolute error = 6e-31
relative error = 2.2020646223157019617103580106282e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.73
Order of pole (three term test) = 4.273e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 2.730151597722855089942649362507
y[1] (numeric) = 2.7301515977228550899426493625065
absolute error = 5e-31
relative error = 1.8314001333004231310171244698615e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.74
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 2.735586758842301095347380177588
y[1] (numeric) = 2.7355867588423010953473801775874
absolute error = 6e-31
relative error = 2.1933137308133472994737564875001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.75
Order of pole (three term test) = 5.016e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 2.7410211638169362951687831036709
y[1] (numeric) = 2.7410211638169362951687831036703
absolute error = 6e-31
relative error = 2.1889652218682103117325223459713e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.76
Order of pole (three term test) = 5.434e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 2.74645481526998837571445612984
y[1] (numeric) = 2.7464548152699883757144561298394
absolute error = 6e-31
relative error = 2.1846345210708205567643246928581e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.77
Order of pole (three term test) = 5.885e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 2.7518877158110578528243876423235
y[1] (numeric) = 2.7518877158110578528243876423228
absolute error = 7e-31
relative error = 2.5437084368600065853301153434507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.78
Order of pole (three term test) = 2.549e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 2.7573198680362122961578563755988
y[1] (numeric) = 2.757319868036212296157856375598
absolute error = 8e-31
relative error = 2.9013681338674975949048734357518e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.79
Order of pole (three term test) = 2.070e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 2.7627512745280797404999362051485
y[1] (numeric) = 2.7627512745280797404999362051477
absolute error = 8e-31
relative error = 2.8956642147840552920081232568920e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.8
Order of pole (three term test) = 2.988e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 2.768181937855941292490518544706
y[1] (numeric) = 2.7681819378559412924905185447052
absolute error = 8e-31
relative error = 2.8899834546988967750456108640411e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.81
Order of pole (three term test) = 1.617e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 2.7736118605758229410776120480435
y[1] (numeric) = 2.7736118605758229410776120480427
absolute error = 8e-31
relative error = 2.8843257103534086728481639976188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.82
Order of pole (three term test) = 1.750e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 2.7790410452305865798969154822709
y[1] (numeric) = 2.7790410452305865798969154822701
absolute error = 8e-31
relative error = 2.8786908396799920328983880839393e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.83
Order of pole (three term test) = 9.471e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 2.7844694943500202496812636084756
y[1] (numeric) = 2.7844694943500202496812636084748
absolute error = 8e-31
relative error = 2.8730787017896358664311051506161e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.84
Order of pole (three term test) = 4.099e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 2.7898972104509276087064966151815
y[1] (numeric) = 2.7898972104509276087064966151807
absolute error = 8e-31
relative error = 2.8674891569596465424833263475721e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.85
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 2.79532419603721663918458039909
y[1] (numeric) = 2.7953241960372166391845803990892
absolute error = 8e-31
relative error = 2.8619220666215307496562584124826e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.86
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 2.8007504535999875974203874274148
y[1] (numeric) = 2.8007504535999875974203874274139
absolute error = 9e-31
relative error = 3.2134244550176585053084832049465e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.87
Order of pole (three term test) = 1.297e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 2.8061759856176202154554160447037
y[1] (numeric) = 2.8061759856176202154554160447028
absolute error = 9e-31
relative error = 3.2072115384520908151846090686847e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.88
Order of pole (three term test) = 2.806e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 2.8116007945558601618298602421299
y[1] (numeric) = 2.811600794555860161829860242129
absolute error = 9e-31
relative error = 3.2010234231782901545058186628146e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.89
Order of pole (three term test) = 3.034e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 2.8170248828679047690038227601234
y[1] (numeric) = 2.8170248828679047690038227601224
absolute error = 1.0e-30
relative error = 3.5498443981862823736296058651343e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.9
Order of pole (three term test) = 1.640e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 2.8224482529944880348890729445437
y[1] (numeric) = 2.8224482529944880348890729445427
absolute error = 1.0e-30
relative error = 3.5430233271382244260994735014159e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.91
Order of pole (three term test) = 3.546e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 2.8278709073639649058545683422384
y[1] (numeric) = 2.8278709073639649058545683422374
absolute error = 1.0e-30
relative error = 3.5362293144143643295733411401999e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.92
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 2.8332928483923948484819672389349
y[1] (numeric) = 2.8332928483923948484819672389339
absolute error = 1.0e-30
relative error = 3.5294621964947893081977651845073e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.93
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 2.8387140784836247172615401555701
y[1] (numeric) = 2.8387140784836247172615401555691
absolute error = 1.0e-30
relative error = 3.5227218111877502937699045080723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.94
Order of pole (three term test) = 2.238e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 2.844134600029370925334223976658
y[1] (numeric) = 2.844134600029370925334223976657
absolute error = 1.0e-30
relative error = 3.5160079976161225251531634654697e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.95
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 2.8495544154093009253020354325275
y[1] (numeric) = 2.8495544154093009253020354325265
absolute error = 1.0e-30
relative error = 3.5093205962040320724291903089954e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.96
Order of pole (three term test) = 5.224e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 2.8549735269911140070466539352201
y[1] (numeric) = 2.8549735269911140070466539352192
absolute error = 9e-31
relative error = 3.1523935037972813211521300922117e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.97
Order of pole (three term test) = 5.643e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 2.8603919371306214194146804017308
y[1] (numeric) = 2.8603919371306214194146804017298
absolute error = 1.0e-30
relative error = 3.4960243979821232207686864020322e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.98
Order of pole (three term test) = 6.094e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 2.8658096481718258225478620962427
y[1] (numeric) = 2.8658096481718258225478620962418
absolute error = 9e-31
relative error = 3.1404737595678530261798730436438e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 5.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.99
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 2.8712266624470000775574273699597
y[1] (numeric) = 2.8712266624470000775574273699588
absolute error = 9e-31
relative error = 3.1345487688978754883111040069227e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 2.8766429822767653801635824296672
y[1] (numeric) = 2.8766429822767653801635824296662
absolute error = 1.0e-30
relative error = 3.4762742758176195632261655188814e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.01
Order of pole (three term test) = 3.836e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 2.8820586099701687448441691475842
y[1] (numeric) = 2.8820586099701687448441691475832
absolute error = 1.0e-30
relative error = 3.4697420674951182762172789222332e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.02
Order of pole (three term test) = 4.141e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 2.8874735478247598459604529205746
y[1] (numeric) = 2.8874735478247598459604529205736
absolute error = 1.0e-30
relative error = 3.4632351896464534705094463947067e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.03
Order of pole (three term test) = 4.469e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 2.8928877981266672222529874386226
y[1] (numeric) = 2.8928877981266672222529874386216
absolute error = 1.0e-30
relative error = 3.4567534926434580775515927966141e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.04
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 2.8983013631506738510264739253115
y[1] (numeric) = 2.8983013631506738510264739253105
absolute error = 1.0e-30
relative error = 3.4502968280459420567625390185681e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.05
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 2.9037142451602920982694812093458
y[1] (numeric) = 2.9037142451602920982694812093448
absolute error = 1.0e-30
relative error = 3.4438650485898538012663857956739e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.06
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 2.909126446407838050882805361734
y[1] (numeric) = 2.909126446407838050882805361733
absolute error = 1.0e-30
relative error = 3.4374580081755833812780854475840e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.07
Order of pole (three term test) = 6.058e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 2.914537969134505237119109312817
y[1] (numeric) = 2.914537969134505237119109312816
absolute error = 1.0e-30
relative error = 3.4310755618564056414867460410250e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.08
Order of pole (three term test) = 1.960e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 2.9199488155704377412662798062043
y[1] (numeric) = 2.9199488155704377412662798062032
absolute error = 1.1e-30
relative error = 3.7671893224097673205282282356159e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.09
Order of pole (three term test) = 5.638e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 2.9253589879348027185376574425498
y[1] (numeric) = 2.9253589879348027185376574425488
absolute error = 1.0e-30
relative error = 3.4183838774124734313811317188809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.1
Order of pole (three term test) = 5.320e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 2.9307684884358623160639218308567
y[1] (numeric) = 2.9307684884358623160639218308556
absolute error = 1.1e-30
relative error = 3.7532817905622594867769678278752e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.11
Order of pole (three term test) = 8.195e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 2.936177319271045005813934636681
y[1] (numeric) = 2.9361773192710450058139346366798
absolute error = 1.2e-30
relative error = 4.0869466299736966011614160399648e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.12
Order of pole (three term test) = 2.651e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 2.9415854826270163352052454514164
y[1] (numeric) = 2.9415854826270163352052454514152
absolute error = 1.2e-30
relative error = 4.0794326973912257907877805259048e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.13
Order of pole (three term test) = 1.905e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 2.9469929806797491010992359752075
y[1] (numeric) = 2.9469929806797491010992359752064
absolute error = 1.1e-30
relative error = 3.7326183238694908766301766744746e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.14
Order of pole (three term test) = 6.160e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 2.9523998155945929528110042888189
y[1] (numeric) = 2.9523998155945929528110042888178
absolute error = 1.1e-30
relative error = 3.7257826470174995233082499217130e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.15
Order of pole (three term test) = 3.319e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 2.9578059895263434297000604744681
y[1] (numeric) = 2.957805989526343429700060474467
absolute error = 1.1e-30
relative error = 3.7189727923167522890328388906794e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.16
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=313.9MB, alloc=44.3MB, time=3.53
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 2.9632115046193104388447052226749
y[1] (numeric) = 2.9632115046193104388447052226739
absolute error = 1.0e-30
relative error = 3.3747169192651739191389267417069e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.17
Order of pole (three term test) = 5.138e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 2.9686163630073861782405822213809
y[1] (numeric) = 2.9686163630073861782405822213798
absolute error = 1.1e-30
relative error = 3.7054299562158113166357283334705e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.18
Order of pole (three term test) = 4.152e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 2.9740205668141125109023211505598
y[1] (numeric) = 2.9740205668141125109023211505587
absolute error = 1.1e-30
relative error = 3.6986966811005047898122659580951e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.19
Order of pole (three term test) = 2.982e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 2.9794241181527477951864092781936
y[1] (numeric) = 2.9794241181527477951864092781925
absolute error = 1.1e-30
relative error = 3.6919886406840373423070495083695e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.2
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 2.9848270191263331765934344386668
y[1] (numeric) = 2.9848270191263331765934344386657
absolute error = 1.1e-30
relative error = 3.6853056909206515144280568495437e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.21
Order of pole (three term test) = 5.188e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 2.9902292718277583462486192247451
y[1] (numeric) = 2.990229271827758346248619224744
absolute error = 1.1e-30
relative error = 3.6786476888697972593118367192786e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.22
Order of pole (three term test) = 5.586e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 2.9956308783398267712011043740506
y[1] (numeric) = 2.9956308783398267712011043740496
absolute error = 1.0e-30
relative error = 3.3381949933504430827842557847882e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.23
Order of pole (three term test) = 2.005e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 3.0010318407353204016247275941025
y[1] (numeric) = 3.0010318407353204016247275941014
absolute error = 1.1e-30
relative error = 3.6654059616057763039909532304163e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.24
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 3.0064321610770638599460716362486
y[1] (numeric) = 3.0064321610770638599460716362474
absolute error = 1.2e-30
relative error = 3.9914421337553021414812599407903e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.25
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 3.0118318414179881168693116607012
y[1] (numeric) = 3.0118318414179881168693116607
absolute error = 1.2e-30
relative error = 3.9842861858948703903052304939501e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.26
Order of pole (three term test) = 2.501e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 3.0172308838011936592118663647162
y[1] (numeric) = 3.0172308838011936592118663647151
absolute error = 1.1e-30
relative error = 3.6457269674178483047454321762885e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.27
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 3.0226292902600131544100396728523
y[1] (numeric) = 3.0226292902600131544100396728512
absolute error = 1.1e-30
relative error = 3.6392157104564271735571154912211e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.28
Order of pole (three term test) = 2.896e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 3.0280270628180736164997198752485
y[1] (numeric) = 3.0280270628180736164997198752474
absolute error = 1.1e-30
relative error = 3.6327284306906768044411638917206e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.29
Order of pole (three term test) = 3.116e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 3.0334242034893580783237709710155
y[1] (numeric) = 3.0334242034893580783237709710144
absolute error = 1.1e-30
relative error = 3.6262649936486505745781889277613e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.3
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 3.0388207142782667746649968114388
y[1] (numeric) = 3.0388207142782667746649968114376
absolute error = 1.2e-30
relative error = 3.9489002900423010124368457467887e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 7.212e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 3.0442165971796778409514727794864
y[1] (numeric) = 3.0442165971796778409514727794852
absolute error = 1.2e-30
relative error = 3.9419008526257396807548636477827e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.32
Order of pole (three term test) = 7.757e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 3.0496118541790075321296126786166
y[1] (numeric) = 3.0496118541790075321296126786154
absolute error = 1.2e-30
relative error = 3.9349269919566683419835751076441e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.33
Order of pole (three term test) = 8.342e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 3.0550064872522699662495608757116
y[1] (numeric) = 3.0550064872522699662495608757104
absolute error = 1.2e-30
relative error = 3.9279785656995526307050932690882e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.34
Order of pole (three term test) = 4.485e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 3.060400498366136397257362338258
y[1] (numeric) = 3.0604004983661363972573623382568
absolute error = 1.2e-30
relative error = 3.9210554325835686393446155367928e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.35
Order of pole (three term test) = 4.822e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 3.0657938894779940214388569577394
y[1] (numeric) = 3.0657938894779940214388569577382
absolute error = 1.2e-30
relative error = 3.9141574523926047719987439581913e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.36
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 3.0711866625360043219113605351353
y[1] (numeric) = 3.0711866625360043219113605351342
absolute error = 1.1e-30
relative error = 3.5816774454590951233889813343224e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.37
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 3.0765788194791609555109242359687
y[1] (numeric) = 3.0765788194791609555109242359675
absolute error = 1.2e-30
relative error = 3.9004363951356525184467298705614e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.38
Order of pole (three term test) = 5.391e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 3.0819703622373471863752985546119
y[1] (numeric) = 3.0819703622373471863752985546107
absolute error = 1.2e-30
relative error = 3.8936130428225908745620485014593e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.39
Order of pole (three term test) = 3.862e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 3.0873612927313928704756583488807
y[1] (numeric) = 3.0873612927313928704756583488796
absolute error = 1.1e-30
relative error = 3.5629131018444182655078384872363e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.4
Order of pole (three term test) = 4.150e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 3.0927516128731309953036639375228
y[1] (numeric) = 3.0927516128731309953036639375216
absolute error = 1.2e-30
relative error = 3.8800400103428082228904664258459e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.41
Order of pole (three term test) = 1.486e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 3.0981413245654537788745313468734
y[1] (numeric) = 3.0981413245654537788745313468722
absolute error = 1.2e-30
relative error = 3.8732900609958855118814174924246e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.42
Order of pole (three term test) = 5.589e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 3.1035304297023683321614544289094
y[1] (numeric) = 3.1035304297023683321614544289082
absolute error = 1.2e-30
relative error = 3.8665643117766407674369346210179e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.43
Order of pole (three term test) = 3.431e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 3.1089189301690518890319547575648
y[1] (numeric) = 3.1089189301690518890319547575636
absolute error = 1.2e-30
relative error = 3.8598626305599686161324210545011e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.44
Order of pole (three term test) = 2.764e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 3.114306827841906607712524073896
y[1] (numeric) = 3.1143068278419066077125240738948
absolute error = 1.2e-30
relative error = 3.8531848861903991785387024356409e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.45
Order of pole (three term test) = 9.895e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 3.1196941245886139477642608458272
y[1] (numeric) = 3.1196941245886139477642608458259
absolute error = 1.3e-30
relative error = 4.1670751941792616010080419637179e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.46
Order of pole (three term test) = 1.063e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 3.1250808222681886265090796069368
y[1] (numeric) = 3.1250808222681886265090796069355
absolute error = 1.3e-30
relative error = 4.1598924121791446479114878830900e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.47
Order of pole (three term test) = 2.282e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 3.1304669227310321588034816310385
y[1] (numeric) = 3.1304669227310321588034816310373
absolute error = 1.2e-30
relative error = 3.8332939769672285419821035013038e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.48
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 3.1358524278189859840148107909436
y[1] (numeric) = 3.1358524278189859840148107909423
absolute error = 1.3e-30
relative error = 4.1456032448062674880514543004472e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 6.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.49
Order of pole (three term test) = 2.630e-29
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ;
Iterations = 980
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Time to Timeout = 2 Minutes 56 Seconds
Percent Done = 100.1 %
> quit
memory used=336.5MB, alloc=44.3MB, time=3.78