|\^/| 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(1.0) + exp(c(x)));
> end;
exact_soln_y := proc(x) return c(1.0) + exp(c(x)) end proc
> exact_soln_yp := proc(x)
> return(exp(c(x)));
> end;
exact_soln_yp := proc(x) return exp(c(x)) end proc
> exact_soln_ypp := proc(x)
> return(exp(c(x)));
> end;
exact_soln_ypp := proc(x) return exp(c(x)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_1,
#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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
#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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
#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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
#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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
#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_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)*21*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_2, array_const_0D0, array_const_1,
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_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)*21*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_2,
> array_const_0D0,
> array_const_1,
#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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
#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_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 - 2 - 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 - 2 - 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 - 2 - 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_2, array_const_0D0, array_const_1,
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_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 - 12;
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 - 12;
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 - 12;
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_2,
> array_const_0D0,
> array_const_1,
#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_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 diff $eq_no = 1 i = 1 order_d = 1
> array_tmp1[1] := array_y_higher[2,1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2));
> 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);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[3,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2 order_d = 1
> array_tmp1[2] := array_y_higher[2,2];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3));
> 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);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[3,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3 order_d = 1
> array_tmp1[3] := array_y_higher[2,3];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4));
> 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);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[3,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4 order_d = 1
> array_tmp1[4] := array_y_higher[2,4];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5));
> 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);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[3,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5 order_d = 1
> array_tmp1[5] := array_y_higher[2,5];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,7]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[3,5] := 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 diff $eq_no = 1
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp1[kkk] := array_y_higher[2,kkk];
> fi;# end if 1;
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_2, array_const_0D0, array_const_1,
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_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_y_higher[2, 1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 3] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(2))*c(factorial_3(0, 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);
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[3, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_y_higher[2, 2];
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 4] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(2))*c(factorial_3(1, 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);
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[3, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_y_higher[2, 3];
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 5] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(2))*c(factorial_3(2, 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);
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[3, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_y_higher[2, 4];
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 6] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(2))*c(factorial_3(3, 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);
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[3, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_y_higher[2, 5];
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 7] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(2))*c(factorial_3(4, 6));
if 7 <= ATS_MAX_TERMS then
array_y[7] := temporary; array_y_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_y_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[3, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
if kkk <= ATS_MAX_TERMS then
array_tmp1[kkk] := array_y_higher[2, kkk]
end if;
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 2;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_1,
> #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_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_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(3) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(3) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(3) ,(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_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) 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 <=3) 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 <=3) 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_m1);
> zero_ats_ar(array_const_2);
> array_const_2[1] := c(2);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> 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] := true;
> 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/diffpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; ");
> 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(-5.0);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
> 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,"return(c(1.0) + exp(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"return(exp(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_ypp := proc(x)");
> omniout_str(ALWAYS,"return(exp(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(-5.0);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.005);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 2;
> #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 := 2;
> #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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> 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 := 2;
> calc_term := 2;
> #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 := 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 := 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 := 3;
> #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 := 3;
> #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 , 2 ) = diff ( y , x , 1 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-02T21:26:24-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"diff")
> ;
> logitem_str(html_log_file,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"diff diffeq.mxt")
> ;
> logitem_str(html_log_file,"diff 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_2, array_const_0D0, array_const_1,
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_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_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 3, 0 .. 31, []);
array_y_higher_work := Array(0 .. 3, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 3, 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_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 3 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 <= 3 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 <= 3 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_m1);
zero_ats_ar(array_const_2);
array_const_2[1] := c(2);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
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] := true;
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/diffpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; ");
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(-5.0);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
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, "return(c(1.0) + exp(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "return(exp(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_ypp := proc(x)");
omniout_str(ALWAYS, "return(exp(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(-5.0);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.005);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 2;
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 := 2;
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 := 3;
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, 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 := 3;
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 := 2;
calc_term := 2;
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 := 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 := 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 := 3;
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 := 3;
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 , 2 ) = diff ( y , x , 1 ) ; ")
;
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-05-02T21:26:24-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "diff")
;
logitem_str(html_log_file, "diff ( y , x , 2 ) = di\
ff ( y , x , 1 ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file,
"diff diffeq.mxt");
logitem_str(html_log_file,
"diff 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/diffpostode.ode#################
diff ( y , x , 2 ) = diff ( y , x , 1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-5.0);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.005);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(1.0) + exp(c(x)));
end;
exact_soln_yp := proc(x)
return(exp(c(x)));
end;
exact_soln_ypp := proc(x)
return(exp(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (closed_form) = 1.0067379469990854670966360484231
y[1] (numeric) = 1.0067379469990854670966360484231
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.99
y[1] (closed_form) = 1.0068056644922305447989653325038
y[1] (numeric) = 1.0068056644922305447989653325038
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4.2MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = -4.98
y[1] (closed_form) = 1.0068740625574962515372906482734
y[1] (numeric) = 1.0068740625574962515372906482734
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.97
y[1] (closed_form) = 1.0069431480347461124600022155601
y[1] (numeric) = 1.0069431480347461124600022155601
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.96
y[1] (closed_form) = 1.0070129278325854239761383024475
y[1] (numeric) = 1.0070129278325854239761383024475
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.95
y[1] (closed_form) = 1.0070834089290521200422164000473
y[1] (numeric) = 1.0070834089290521200422164000474
absolute error = 1e-31
relative error = 9.9296641284500483897916979247656e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.94
y[1] (closed_form) = 1.0071545983723145817706798693521
y[1] (numeric) = 1.0071545983723145817706798693521
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.93
y[1] (closed_form) = 1.0072265032813764601415024147785
y[1] (numeric) = 1.0072265032813764601415024147785
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.92
y[1] (closed_form) = 1.0072991308467885822998088990669
y[1] (numeric) = 1.0072991308467885822998088990669
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.91
y[1] (closed_form) = 1.0073724883313680126307355188432
y[1] (numeric) = 1.0073724883313680126307355188431
absolute error = 1e-31
relative error = 9.9268146746435377630739400126755e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.9
y[1] (closed_form) = 1.0074465830709243405182360464201
y[1] (numeric) = 1.0074465830709243405182360464201
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.89
y[1] (closed_form) = 1.0075214224749932674172152602805
y[1] (numeric) = 1.0075214224749932674172152602805
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.88
y[1] (closed_form) = 1.0075970140275775665983081021806
y[1] (numeric) = 1.0075970140275775665983081021806
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.87
y[1] (closed_form) = 1.0076733652878954896618965073037
y[1] (numeric) = 1.0076733652878954896618965073037
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.86
y[1] (closed_form) = 1.00775048389113669466263898332
y[1] (numeric) = 1.00775048389113669466263898332
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.85
y[1] (closed_form) = 1.0078283775492257714379553335143
y[1] (numeric) = 1.0078283775492257714379553335143
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.84
y[1] (closed_form) = 1.0079070540515934404936356456817
y[1] (numeric) = 1.0079070540515934404936356456817
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.83
y[1] (closed_form) = 1.0079865212659555025671047755709
y[1] (numeric) = 1.0079865212659555025671047755709
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.82
y[1] (closed_form) = 1.0080667871390996167639477781226
y[1] (numeric) = 1.0080667871390996167639477781227
absolute error = 1e-31
relative error = 9.9199776518578375802789425893765e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.81
y[1] (closed_form) = 1.0081478596976799859461655896795
y[1] (numeric) = 1.0081478596976799859461655896796
absolute error = 1e-31
relative error = 9.9191799137467460486663417203571e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.8
y[1] (closed_form) = 1.0082297470490200288413620267661
y[1] (numeric) = 1.0082297470490200288413620267662
absolute error = 1e-31
relative error = 9.9183742884684010481986457496691e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.79
y[1] (closed_form) = 1.0083124573819231191407419157932
y[1] (numeric) = 1.0083124573819231191407419157934
absolute error = 2e-31
relative error = 1.9835121398707968721316885436590e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.78
y[1] (closed_form) = 1.0083959989674914726605057716668
y[1] (numeric) = 1.008395998967491472660505771667
absolute error = 2e-31
relative error = 1.9833478138031324305450216674911e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.77
y[1] (closed_form) = 1.0084803801599532644560395730107
y[1] (numeric) = 1.008480380159953264456039573011
absolute error = 3e-31
relative error = 2.9747727958021110735901800291715e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.76
y[1] (closed_form) = 1.0085656093974980586013003195423
y[1] (numeric) = 1.0085656093974980586013003195426
absolute error = 3e-31
relative error = 2.9745214114450669452507439606693e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.75
y[1] (closed_form) = 1.0086516952031206341770715039573
y[1] (numeric) = 1.0086516952031206341770715039575
absolute error = 2e-31
relative error = 1.9828450291725760300235380162015e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.74
y[1] (closed_form) = 1.008738646185473291851390514541
y[1] (numeric) = 1.0087386461854732918513905145413
absolute error = 3e-31
relative error = 2.9740111686455605058165948182804e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.73
y[1] (closed_form) = 1.0088264710397267262835162690968
y[1] (numeric) = 1.008826471039726726283516269097
absolute error = 2e-31
relative error = 1.9825015078547058716511393177356e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.72
y[1] (closed_form) = 1.0089151785484395504393948730148
y[1] (numeric) = 1.008915178548439550439394873015
absolute error = 2e-31
relative error = 1.9823271990787845617220425764169e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.71
y[1] (closed_form) = 1.009004777582436558771779454061
y[1] (numeric) = 1.0090047775824365587717794540612
absolute error = 2e-31
relative error = 1.9821511695831373589448721056825e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.7
y[1] (closed_form) = 1.0090952771016958170920540742914
y[1] (numeric) = 1.0090952771016958170920540742916
absolute error = 2e-31
relative error = 1.9819734026943043509639615436698e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.69
y[1] (closed_form) = 1.0091866861562446678434881455062
y[1] (numeric) = 1.0091866861562446678434881455064
absolute error = 2e-31
relative error = 1.9817938815835262349445272653774e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.68
y[1] (closed_form) = 1.0092790138870647403771953472374
y[1] (numeric) = 1.0092790138870647403771953472376
absolute error = 2e-31
relative error = 1.9816125892654238149456942922754e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.67
y[1] (closed_form) = 1.0093722695270060567325788209032
y[1] (numeric) = 1.0093722695270060567325788209034
absolute error = 2e-31
relative error = 1.9814295085966688549682140701793e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.66
y[1] (closed_form) = 1.0094664624017103243336024420067
y[1] (numeric) = 1.0094664624017103243336024420068
absolute error = 1e-31
relative error = 9.9062231113732314377862222560719e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.65
y[1] (closed_form) = 1.0095616019305435079309272106497
y[1] (numeric) = 1.0095616019305435079309272106498
absolute error = 1e-31
relative error = 9.9052895641805388969779528777819e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.64
y[1] (closed_form) = 1.0096576976275377740478841198775
y[1] (numeric) = 1.0096576976275377740478841198775
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.63
y[1] (closed_form) = 1.0097547591023429021255130554615
y[1] (numeric) = 1.0097547591023429021255130554615
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.62
y[1] (closed_form) = 1.0098527960611872575085750762749
y[1] (numeric) = 1.0098527960611872575085750762749
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.61
y[1] (closed_form) = 1.0099518183078484223706374899795
y[1] (numeric) = 1.0099518183078484223706374899794
absolute error = 1e-31
relative error = 9.9014624447676873306209070173920e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.6
y[1] (closed_form) = 1.0100518357446335816421330943316
y[1] (numeric) = 1.0100518357446335816421330943315
absolute error = 1e-31
relative error = 9.9004819813309567842705096155051e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.59
y[1] (closed_form) = 1.0101528583733697619808033810288
y[1] (numeric) = 1.0101528583733697619808033810287
absolute error = 1e-31
relative error = 9.8994918611652624558191624573620e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.58
y[1] (closed_form) = 1.0102548962964040228092479483096
y[1] (numeric) = 1.0102548962964040228092479483096
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.57
y[1] (closed_form) = 1.0103579597176136994395173725574
y[1] (numeric) = 1.0103579597176136994395173725574
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.56
y[1] (closed_form) = 1.0104620589434267993099038702723
y[1] (numeric) = 1.0104620589434267993099038702723
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.55
y[1] (closed_form) = 1.0105672043838526533744037625093
y[1] (numeric) = 1.0105672043838526533744037625093
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=46.7MB, alloc=40.3MB, time=0.56
TOP MAIN SOLVE Loop
x[1] = -4.54
y[1] (closed_form) = 1.0106734065535229257108495670498
y[1] (numeric) = 1.0106734065535229257108495670497
absolute error = 1e-31
relative error = 9.8943931196337687867162661912279e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.53
y[1] (closed_form) = 1.0107806760727430854495400424133
y[1] (numeric) = 1.0107806760727430854495400424132
absolute error = 1e-31
relative error = 9.8933430730529000531222045416999e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.52
y[1] (closed_form) = 1.0108890236685544461704372762439
y[1] (numeric) = 1.0108890236685544461704372762438
absolute error = 1e-31
relative error = 9.8922826995485837998281423503751e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.51
y[1] (closed_form) = 1.0109984601758068789737555735586
y[1] (numeric) = 1.0109984601758068789737555735584
absolute error = 2e-31
relative error = 1.9782423799658521550315608222319e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.5
y[1] (closed_form) = 1.0111089965382423064961431342869
y[1] (numeric) = 1.0111089965382423064961431342867
absolute error = 2e-31
relative error = 1.9780261147388136399227292430062e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.49
y[1] (closed_form) = 1.0112206438095890862227610529593
y[1] (numeric) = 1.0112206438095890862227610529591
absolute error = 2e-31
relative error = 1.9778077240050848645486013421971e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.48
y[1] (closed_form) = 1.0113334131546673925345028375762
y[1] (numeric) = 1.011333413154667392534502837576
absolute error = 2e-31
relative error = 1.9775871873563142585717748215029e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.47
y[1] (closed_form) = 1.0114473158505057080294803243879
y[1] (numeric) = 1.0114473158505057080294803243877
absolute error = 2e-31
relative error = 1.9773644841978153052242656211409e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.46
y[1] (closed_form) = 1.0115623632874685357688385497119
y[1] (numeric) = 1.0115623632874685357688385497116
absolute error = 3e-31
relative error = 2.9657093906205878321734328586270e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.45
y[1] (closed_form) = 1.0116785669703954452190639236115
y[1] (numeric) = 1.0116785669703954452190639236112
absolute error = 3e-31
relative error = 2.9653687425482331300436106759527e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.44
y[1] (closed_form) = 1.0117959385197515657963291443707
y[1] (numeric) = 1.0117959385197515657963291443704
absolute error = 3e-31
relative error = 2.9650247503355006979562054880537e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.43
y[1] (closed_form) = 1.0119144896727896430631880360715
y[1] (numeric) = 1.0119144896727896430631880360713
absolute error = 2e-31
relative error = 1.9764515879664055700663169437906e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.42
y[1] (closed_form) = 1.01203423228472377378420836215
y[1] (numeric) = 1.0120342322847237737842083621498
absolute error = 2e-31
relative error = 1.9762177367112260172878150650777e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.41
y[1] (closed_form) = 1.0121551783299149372150262940186
y[1] (numeric) = 1.0121551783299149372150262940184
absolute error = 2e-31
relative error = 1.9759815913801452264484405432958e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.4
y[1] (closed_form) = 1.0122773399030684411789393862365
y[1] (numeric) = 1.0122773399030684411789393862364
absolute error = 1e-31
relative error = 9.8787156501572576020715333401510e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.39
y[1] (closed_form) = 1.0124007292204434026766435925812
y[1] (numeric) = 1.0124007292204434026766435925811
absolute error = 1e-31
relative error = 9.8775116526240349253219083208513e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.38
y[1] (closed_form) = 1.0125253586210743839781832005917
y[1] (numeric) = 1.0125253586210743839781832005915
absolute error = 2e-31
relative error = 1.9752591705196751501726198044801e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.37
y[1] (closed_form) = 1.0126512405680053063617409130458
y[1] (numeric) = 1.0126512405680053063617409130457
absolute error = 1e-31
relative error = 9.8750681373687044488197366255369e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.36
y[1] (closed_form) = 1.0127783876495357648916702202577
y[1] (numeric) = 1.0127783876495357648916702202576
absolute error = 1e-31
relative error = 9.8738283932066130497011202952860e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.35
y[1] (closed_form) = 1.0129068125804798688682864655417
y[1] (numeric) = 1.0129068125804798688682864655415
absolute error = 2e-31
relative error = 1.9745153010717767953518608929871e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.34
y[1] (closed_form) = 1.0130365282034377338345106201543
y[1] (numeric) = 1.0130365282034377338345106201542
absolute error = 1e-31
relative error = 9.8713123580394749436990192078239e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.33
y[1] (closed_form) = 1.0131675474900797522896260122973
y[1] (numeric) = 1.0131675474900797522896260122972
absolute error = 1e-31
relative error = 9.8700358344214664064609992488146e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.32
y[1] (closed_form) = 1.013299883542443771538289615015
y[1] (numeric) = 1.0132998835424437715382896150148
absolute error = 2e-31
relative error = 1.9737493633257943949513494633564e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.31
y[1] (closed_form) = 1.0134335495942453083936637792599
y[1] (numeric) = 1.0134335495942453083936637792598
absolute error = 1e-31
relative error = 9.8674451857290122063532457355483e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.3
y[1] (closed_form) = 1.0135685590122009317572305745258
y[1] (numeric) = 1.0135685590122009317572305745257
absolute error = 1e-31
relative error = 9.8661308217233522247963141168592e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.29
y[1] (closed_form) = 1.0137049252973649454146495409732
y[1] (numeric) = 1.0137049252973649454146495409732
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.28
y[1] (closed_form) = 1.0138426620864795047170523448676
y[1] (numeric) = 1.0138426620864795047170523448676
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.27
y[1] (closed_form) = 1.0139817831533383021605675677785
y[1] (numeric) = 1.0139817831533383021605675677785
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.26
y[1] (closed_form) = 1.0141223024101639582337699904576
y[1] (numeric) = 1.0141223024101639582337699904577
absolute error = 1e-31
relative error = 9.8607435969349960860567282939688e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.25
y[1] (closed_form) = 1.014264233908999255273286945856
y[1] (numeric) = 1.014264233908999255273286945856
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.24
y[1] (closed_form) = 1.0144075918431123534521066673262
y[1] (numeric) = 1.0144075918431123534521066673262
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.23
y[1] (closed_form) = 1.0145523905484161294233584800719
y[1] (numeric) = 1.0145523905484161294233584800719
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.22
y[1] (closed_form) = 1.0146986445049017795546120000092
y[1] (numeric) = 1.0146986445049017795546120000092
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.21
y[1] (closed_form) = 1.0148463683380868311142134433043
y[1] (numeric) = 1.0148463683380868311142134433043
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.2
y[1] (closed_form) = 1.0149955768204777062119843602287
y[1] (numeric) = 1.0149955768204777062119843602287
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.19
y[1] (closed_form) = 1.0151462848730469847518956705525
y[1] (numeric) = 1.0151462848730469847518956705524
absolute error = 1e-31
relative error = 9.8507970220770579725361743914860e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.18
y[1] (closed_form) = 1.015298507566725514124243324443
y[1] (numeric) = 1.0152985075667255141242433244429
absolute error = 1e-31
relative error = 9.8493201018940718303251060482880e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.17
y[1] (closed_form) = 1.0154522601239095148495382353233
y[1] (numeric) = 1.0154522601239095148495382353232
absolute error = 1e-31
relative error = 9.8478287879134370261466844869404e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.16
y[1] (closed_form) = 1.0156075579199828328859307992401
y[1] (numeric) = 1.01560755791998283288593079924
absolute error = 1e-31
relative error = 9.8463229443472444781638060201248e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.15
y[1] (closed_form) = 1.0157644164848544908266692910111
y[1] (numeric) = 1.015764416484854490826669291011
absolute error = 1e-31
relative error = 9.8448024342159110725031443104013e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.14
y[1] (closed_form) = 1.0159228515045116917439931799265
y[1] (numeric) = 1.0159228515045116917439931799264
absolute error = 1e-31
relative error = 9.8432671193395143479590845508101e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.13
y[1] (closed_form) = 1.0160828788225884309811399285206
y[1] (numeric) = 1.0160828788225884309811399285205
absolute error = 1e-31
relative error = 9.8417168603291015889958276255238e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.12
y[1] (closed_form) = 1.0162445144419498727549516559441
y[1] (numeric) = 1.016244514441949872754951655944
absolute error = 1e-31
relative error = 9.8401515165779741560886987100783e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=89.0MB, alloc=40.3MB, time=1.02
TOP MAIN SOLVE Loop
x[1] = -4.11
y[1] (closed_form) = 1.0164077745262926500080622448391
y[1] (numeric) = 1.016407774526292650008062244839
absolute error = 1e-31
relative error = 9.8385709462529479082911928880996e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.1
y[1] (closed_form) = 1.0165726754017612475419836980835
y[1] (numeric) = 1.0165726754017612475419836980834
absolute error = 1e-31
relative error = 9.8369750062855905992509470027333e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.09
y[1] (closed_form) = 1.0167392335585806300707520444753
y[1] (numeric) = 1.0167392335585806300707520444752
absolute error = 1e-31
relative error = 9.8353635523634371547320051194059e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.08
y[1] (closed_form) = 1.0169074656527052784592986858592
y[1] (numeric) = 1.0169074656527052784592986858591
absolute error = 1e-31
relative error = 9.8337364389211837670388195112361e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.07
y[1] (closed_form) = 1.0170773885074847990515452242772
y[1] (numeric) = 1.0170773885074847990515452242771
absolute error = 1e-31
relative error = 9.8320935191318617695857839775393e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.06
y[1] (closed_form) = 1.0172490191153462726505425910253
y[1] (numeric) = 1.0172490191153462726505425910252
absolute error = 1e-31
relative error = 9.8304346448979922832211218333442e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.05
y[1] (closed_form) = 1.0174223746394935113869544536867
y[1] (numeric) = 1.0174223746394935113869544536866
absolute error = 1e-31
relative error = 9.8287596668427226548020406295689e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.04
y[1] (closed_form) = 1.017597472415623393402987801592
y[1] (numeric) = 1.0175974724156233934029878015919
absolute error = 1e-31
relative error = 9.8270684343009457379356133511083e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.03
y[1] (closed_form) = 1.017774329953659446986669386436
y[1] (numeric) = 1.0177743299536594469866693864359
absolute error = 1e-31
relative error = 9.8253607953104030957532422477184e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.02
y[1] (closed_form) = 1.0179529649395028575163261039565
y[1] (numeric) = 1.0179529649395028575163261039564
absolute error = 1e-31
relative error = 9.8236365966027732360821909645417e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.01
y[1] (closed_form) = 1.01813339523680107231742294203
y[1] (numeric) = 1.0181333952368010723174229420299
absolute error = 1e-31
relative error = 9.8218956835947460204219077840954e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4
y[1] (closed_form) = 1.0183156388887341802937180212732
y[1] (numeric) = 1.0183156388887341802937180212732
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.99
y[1] (closed_form) = 1.0184997141198192449721864983093
y[1] (numeric) = 1.0184997141198192449721864983093
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.98
y[1] (closed_form) = 1.0186856393377327713965214399713
y[1] (numeric) = 1.0186856393377327713965214399713
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.97
y[1] (closed_form) = 1.0188734331351514891174197460049
y[1] (numeric) = 1.0188734331351514891174197460049
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.96
y[1] (closed_form) = 1.0190631142916116353594861398
y[1] (numeric) = 1.0190631142916116353594861398
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.95
y[1] (closed_form) = 1.0192547017753869242946213253559
y[1] (numeric) = 1.0192547017753869242946213253558
absolute error = 1e-31
relative error = 9.8110903806296094834367229160213e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.94
y[1] (closed_form) = 1.0194482147453853902203866289042
y[1] (numeric) = 1.019448214745385390220386628904
absolute error = 2e-31
relative error = 1.9618456053694836802073369207277e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.93
y[1] (closed_form) = 1.0196436725530652943292436695736
y[1] (numeric) = 1.0196436725530652943292436695734
absolute error = 2e-31
relative error = 1.9614695347368166420130912790948e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.92
y[1] (closed_form) = 1.0198410947443702866609425773594
y[1] (numeric) = 1.0198410947443702866609425773591
absolute error = 3e-31
relative error = 2.9416347462954209027473141332988e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.91
y[1] (closed_form) = 1.0200405010616840167558666375535
y[1] (numeric) = 1.0200405010616840167558666375533
absolute error = 2e-31
relative error = 1.9607064601046226005310062669817e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.9
y[1] (closed_form) = 1.0202419114458043884720275437437
y[1] (numeric) = 1.0202419114458043884720275437434
absolute error = 3e-31
relative error = 2.9404790827977674803427604159429e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.89
y[1] (closed_form) = 1.0204453460379376563928381767342
y[1] (numeric) = 1.020445346037937656392838176734
absolute error = 2e-31
relative error = 1.9599285819327406711541149981636e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.88
y[1] (closed_form) = 1.0206508251817125632369654392163
y[1] (numeric) = 1.020650825181712563236965439216
absolute error = 3e-31
relative error = 2.9393010087126437972377354523565e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.87
y[1] (closed_form) = 1.0208583694252147196856825849039
y[1] (numeric) = 1.0208583694252147196856825849035
absolute error = 4e-31
relative error = 3.9182712507437879352512917612687e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.86
y[1] (closed_form) = 1.0210679995230414300673990995446
y[1] (numeric) = 1.0210679995230414300673990995442
absolute error = 4e-31
relative error = 3.9174668110923752071135768441719e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.85
y[1] (closed_form) = 1.0212797364383771693836489472373
y[1] (numeric) = 1.021279736438377169383648947237
absolute error = 3e-31
relative error = 2.9374909664439587245861677024088e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.84
y[1] (closed_form) = 1.0214936013450899192259693508355
y[1] (numeric) = 1.0214936013450899192259693508352
absolute error = 3e-31
relative error = 2.9368759589385951645850681298138e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.83
y[1] (closed_form) = 1.0217096156298485722190087467336
y[1] (numeric) = 1.0217096156298485722190087467333
absolute error = 3e-31
relative error = 2.9362550318669595377231675622079e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.82
y[1] (closed_form) = 1.0219278008942616167320727344178
y[1] (numeric) = 1.0219278008942616167320727344175
absolute error = 3e-31
relative error = 2.9356281308471894409609363875658e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.81
y[1] (closed_form) = 1.0221481789570373157293614185755
y[1] (numeric) = 1.0221481789570373157293614185753
absolute error = 2e-31
relative error = 1.9566634673660789398836680674127e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.8
y[1] (closed_form) = 1.0223707718561655957785833225408
y[1] (numeric) = 1.0223707718561655957785833225406
absolute error = 2e-31
relative error = 1.9562374581277390520954974060287e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.79
y[1] (closed_form) = 1.0225956018511218644086649813674
y[1] (numeric) = 1.0225956018511218644086649813672
absolute error = 2e-31
relative error = 1.9558073556932596241416570301597e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.78
y[1] (closed_form) = 1.0228226914250929762001285060763
y[1] (numeric) = 1.0228226914250929762001285060761
absolute error = 2e-31
relative error = 1.9553731226019355291477440059123e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.77
y[1] (closed_form) = 1.0230520632872255702066011347591
y[1] (numeric) = 1.023052063287225570206601134759
absolute error = 1e-31
relative error = 9.7746736054355268917485844818480e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.76
y[1] (closed_form) = 1.0232837403748970035430725422555
y[1] (numeric) = 1.0232837403748970035430725422554
absolute error = 1e-31
relative error = 9.7724605653719600946646641496976e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.75
y[1] (closed_form) = 1.0235177458560091082361511851004
y[1] (numeric) = 1.0235177458560091082361511851002
absolute error = 2e-31
relative error = 1.9540452601799487700921922266197e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.74
y[1] (closed_form) = 1.0237541031313050007139161777898
y[1] (numeric) = 1.0237541031313050007139161777896
absolute error = 2e-31
relative error = 1.9535941237087118391668366697696e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.73
y[1] (closed_form) = 1.0239928358367091756182443665626
y[1] (numeric) = 1.0239928358367091756182443665624
absolute error = 2e-31
relative error = 1.9531386646526593694675165777695e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.72
y[1] (closed_form) = 1.024233967845691117950943918083
y[1] (numeric) = 1.0242339678456911179509439180828
absolute error = 2e-31
relative error = 1.9526788436890775813153905187585e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.71
y[1] (closed_form) = 1.0244775232716526699168787197371
y[1] (numeric) = 1.0244775232716526699168787197369
absolute error = 2e-31
relative error = 1.9522146211788344778609668386657e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.7
y[1] (closed_form) = 1.0247235264703393912027573829834
y[1] (numeric) = 1.0247235264703393912027573829832
absolute error = 2e-31
relative error = 1.9517459571646615974392395037256e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.69
y[1] (closed_form) = 1.024972002042276153829624202256
y[1] (numeric) = 1.0249720020422761538296242022558
absolute error = 2e-31
relative error = 1.9512728113694443045508496568081e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.68
y[1] (closed_form) = 1.0252229748352272151405669876582
y[1] (numeric) = 1.025222974835227215140566987658
absolute error = 2e-31
relative error = 1.9507951431945211220363235082614e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=131.5MB, alloc=40.3MB, time=1.47
TOP MAIN SOLVE Loop
x[1] = -3.67
y[1] (closed_form) = 1.0254764699466810149329906098868
y[1] (numeric) = 1.0254764699466810149329906098865
absolute error = 3e-31
relative error = 2.9254693675769889264488251759016e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.66
y[1] (closed_form) = 1.0257325127263599452172401559202
y[1] (numeric) = 1.0257325127263599452172401559199
absolute error = 3e-31
relative error = 2.9247391135395605533021120228741e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.65
y[1] (closed_form) = 1.0259911287787553435806410395574
y[1] (numeric) = 1.0259911287787553435806410395571
absolute error = 3e-31
relative error = 2.9240018903193848117504224696507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.64
y[1] (closed_form) = 1.0262523439656879636584049723293
y[1] (numeric) = 1.026252343965687963658404972329
absolute error = 3e-31
relative error = 2.9232576350639769376352920775649e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.63
y[1] (closed_form) = 1.0265161844088941787605826178852
y[1] (numeric) = 1.0265161844088941787605826178849
absolute error = 3e-31
relative error = 2.9225062844260078347746593773952e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.62
y[1] (closed_form) = 1.0267826764926381772775808019925
y[1] (numeric) = 1.0267826764926381772775808019922
absolute error = 3e-31
relative error = 2.9217477745608511823737803377827e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.61
y[1] (closed_form) = 1.0270518468663504110859616666317
y[1] (numeric) = 1.0270518468663504110859616666314
absolute error = 3e-31
relative error = 2.9209820411241498395567670300630e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.6
y[1] (closed_form) = 1.0273237224472925608015630624356
y[1] (numeric) = 1.0273237224472925608015630624353
absolute error = 3e-31
relative error = 2.9202090192694024344695974721960e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.59
y[1] (closed_form) = 1.0275983304232492843786863032922
y[1] (numeric) = 1.027598330423249284378686303292
absolute error = 2e-31
relative error = 1.9462857624303806953977002962826e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.58
y[1] (closed_form) = 1.0278756982552470182324543331974
y[1] (numeric) = 1.0278756982552470182324543331972
absolute error = 2e-31
relative error = 1.9457605655964739205627236899846e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.57
y[1] (closed_form) = 1.0281558536803001027667182163266
y[1] (numeric) = 1.0281558536803001027667182163265
absolute error = 1e-31
relative error = 9.7261518904987431602638499671080e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.56
y[1] (closed_form) = 1.0284388247141845069223531865445
y[1] (numeric) = 1.0284388247141845069223531865443
absolute error = 2e-31
relative error = 1.9446951553543537261084202863303e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.55
y[1] (closed_form) = 1.0287246396542394291207105307843
y[1] (numeric) = 1.0287246396542394291207105307841
absolute error = 2e-31
relative error = 1.9441548524318539620617803033737e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.54
y[1] (closed_form) = 1.0290133270821970547646543267218
y[1] (numeric) = 1.0290133270821970547646543267215
absolute error = 3e-31
relative error = 2.9154141360895722826670427028375e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.53
y[1] (closed_form) = 1.029304915867040753275291277527
y[1] (numeric) = 1.0293049158670407532752912775268
absolute error = 2e-31
relative error = 1.9430588246198055053914143116204e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.52
y[1] (closed_form) = 1.0295994351678920004864791554834
y[1] (numeric) = 1.0295994351678920004864791554831
absolute error = 3e-31
relative error = 2.9137545122203800801588582002194e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.51
y[1] (closed_form) = 1.0298969144369263150917590819967
y[1] (numeric) = 1.0298969144369263150917590819964
absolute error = 3e-31
relative error = 2.9129128924909776976966839720493e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.5
y[1] (closed_form) = 1.0301973834223185007397862923636
y[1] (numeric) = 1.0301973834223185007397862923634
absolute error = 2e-31
relative error = 1.9413755384972873622694208837717e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.49
y[1] (closed_form) = 1.030500872171217488304923304969
y[1] (numeric) = 1.0305008721712174883049233049688
absolute error = 2e-31
relative error = 1.9408037916417216282592652870365e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.48
y[1] (closed_form) = 1.0308074110327510758197015977179
y[1] (numeric) = 1.0308074110327510758197015977176
absolute error = 3e-31
relative error = 2.9103399605890912975689105820121e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.47
y[1] (closed_form) = 1.0311170306610608665456489961601
y[1] (numeric) = 1.0311170306610608665456489961598
absolute error = 3e-31
relative error = 2.9094660555423721865383293204886e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.46
y[1] (closed_form) = 1.0314297620183677086788189795365
y[1] (numeric) = 1.0314297620183677086788189795363
absolute error = 2e-31
relative error = 1.9390559334707116833245641511998e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.45
y[1] (closed_form) = 1.0317456363780679432365469992797
y[1] (numeric) = 1.0317456363780679432365469992795
absolute error = 2e-31
relative error = 1.9384622812857039816669397228148e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.44
y[1] (closed_form) = 1.0320646853278607697528027007736
y[1] (numeric) = 1.0320646853278607697528027007734
absolute error = 2e-31
relative error = 1.9378630316806651850098690529583e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.43
y[1] (closed_form) = 1.0323869407729070425213137303623
y[1] (numeric) = 1.0323869407729070425213137303621
absolute error = 2e-31
relative error = 1.9372581355036121862288849368170e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.42
y[1] (closed_form) = 1.0327124349390198132687177789643
y[1] (numeric) = 1.0327124349390198132687177789641
absolute error = 2e-31
relative error = 1.9366475432418872043693065838785e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.41
y[1] (closed_form) = 1.0330412003758869393146689719212
y[1] (numeric) = 1.033041200375886939314668971921
absolute error = 2e-31
relative error = 1.9360312050209334883516658689408e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.4
y[1] (closed_form) = 1.0333732699603260794824001314709
y[1] (numeric) = 1.0333732699603260794824001314707
absolute error = 2e-31
relative error = 1.9354090706030989805224487577461e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.39
y[1] (closed_form) = 1.0337086768995724032620444737059
y[1] (numeric) = 1.0337086768995724032620444737056
absolute error = 3e-31
relative error = 2.9021716340797032146143916540427e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.38
y[1] (closed_form) = 1.0340474547345993420003728389543
y[1] (numeric) = 1.034047454734599342000372838954
absolute error = 3e-31
relative error = 2.9012208156055912477091671750074e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.37
y[1] (closed_form) = 1.0343896373434727141948327311903
y[1] (numeric) = 1.0343896373434727141948327311899
absolute error = 4e-31
relative error = 3.8670147646421035663922495399417e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.36
y[1] (closed_form) = 1.0347352589447385603072136841051
y[1] (numeric) = 1.0347352589447385603072136841047
absolute error = 4e-31
relative error = 3.8657231068740699251068354338635e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.35
y[1] (closed_form) = 1.0350843541008450258832435254655
y[1] (numeric) = 1.0350843541008450258832435254651
absolute error = 4e-31
relative error = 3.8644193433632874053613821051099e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.34
y[1] (closed_form) = 1.0354369577215986351692790781561
y[1] (numeric) = 1.0354369577215986351692790781556
absolute error = 5e-31
relative error = 4.8288792115380206112894808088595e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.33
y[1] (closed_form) = 1.0357931050676553008563332045916
y[1] (numeric) = 1.0357931050676553008563332045911
absolute error = 5e-31
relative error = 4.8272188485686174330159572080993e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.32
y[1] (closed_form) = 1.0361528317540464190553217816872
y[1] (numeric) = 1.0361528317540464190553217816867
absolute error = 5e-31
relative error = 4.8255429573413158131101544192644e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.31
y[1] (closed_form) = 1.0365161737537404021159665533578
y[1] (numeric) = 1.0365161737537404021159665533573
absolute error = 5e-31
relative error = 4.8238514039703925613746178309396e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.3
y[1] (closed_form) = 1.0368831674012400054456037047415
y[1] (numeric) = 1.036883167401240005445603704741
absolute error = 5e-31
relative error = 4.8221440536368191361132176297969e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.29
y[1] (closed_form) = 1.0372538493962158080635778213451
y[1] (numeric) = 1.0372538493962158080635778213446
absolute error = 5e-31
relative error = 4.8204207705861914706433040792272e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.28
y[1] (closed_form) = 1.0376282568071762102423045830638
y[1] (numeric) = 1.0376282568071762102423045830633
absolute error = 5e-31
relative error = 4.8186814181267582930504056642546e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.27
y[1] (closed_form) = 1.0380064270751743152378246409055
y[1] (numeric) = 1.038006427075174315237824640905
absolute error = 5e-31
relative error = 4.8169258586275505758754838448936e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.26
y[1] (closed_form) = 1.0383883980175520658011108102137
y[1] (numeric) = 1.0383883980175520658011108102131
absolute error = 6e-31
relative error = 5.7781847442199377512290704699187e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.25
y[1] (closed_form) = 1.0387742078317220098868998352676
y[1] (numeric) = 1.038774207831722009886899835267
absolute error = 6e-31
relative error = 5.7760386759352232388137150037690e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.24
y[1] (closed_form) = 1.0391638950989870737397710903658
y[1] (numeric) = 1.0391638950989870737397710903652
memory used=173.9MB, alloc=40.3MB, time=1.92
absolute error = 6e-31
relative error = 5.7738726569483644748286835133312e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.23
y[1] (closed_form) = 1.0395574987883987243379639801109
y[1] (numeric) = 1.0395574987883987243379639801104
absolute error = 5e-31
relative error = 4.8097387646450394738579396112322e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.22
y[1] (closed_form) = 1.0399550582606539070143935667244
y[1] (numeric) = 1.0399550582606539070143935667238
absolute error = 6e-31
relative error = 5.7694800869906076978608770174865e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.21
y[1] (closed_form) = 1.040356613272031147951873984794
y[1] (numeric) = 1.0403566132720311479518739847935
absolute error = 5e-31
relative error = 4.8060443276988197934668173400015e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.2
y[1] (closed_form) = 1.0407622039783662151660792621444
y[1] (numeric) = 1.0407622039783662151660792621439
absolute error = 5e-31
relative error = 4.8041713860161782067081605577222e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.19
y[1] (closed_form) = 1.0411718709390677355456529047735
y[1] (numeric) = 1.0411718709390677355456529047729
absolute error = 6e-31
relative error = 5.7627373226942822723716708649250e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.18
y[1] (closed_form) = 1.041585655121173169514516615502
y[1] (numeric) = 1.0415856551211731695145166155014
absolute error = 6e-31
relative error = 5.7604479962831172616973380392596e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.17
y[1] (closed_form) = 1.04200359790344554891722436736
y[1] (numeric) = 1.0420035979034455489172243673594
absolute error = 6e-31
relative error = 5.7581375074637446753732838305835e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.16
y[1] (closed_form) = 1.042425741080511387804564326735
y[1] (numeric) = 1.0424257410805113878045643267344
absolute error = 6e-31
relative error = 5.7558056785712010702207328771091e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.15
y[1] (closed_form) = 1.0428521268670401799139354569562
y[1] (numeric) = 1.0428521268670401799139354569555
absolute error = 7e-31
relative error = 6.7123610525967449246099778290991e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.14
y[1] (closed_form) = 1.0432827979019659007977297661522
y[1] (numeric) = 1.0432827979019659007977297661515
absolute error = 7e-31
relative error = 6.7095901648881290457462517641073e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.13
y[1] (closed_form) = 1.0437177972527509367534509677739
y[1] (numeric) = 1.0437177972527509367534509677731
absolute error = 8e-31
relative error = 7.6649071435376583305905234080238e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.12
y[1] (closed_form) = 1.0441571684196928669520158516001
y[1] (numeric) = 1.0441571684196928669520158515993
absolute error = 8e-31
relative error = 7.6616818252637296352697274745492e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.11
y[1] (closed_form) = 1.0446009553402745294460401924352
y[1] (numeric) = 1.0446009553402745294460401924345
absolute error = 7e-31
relative error = 6.7011234904718025626540816095557e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.1
y[1] (closed_form) = 1.0450492023935578060683350921783
y[1] (numeric) = 1.0450492023935578060683350921776
absolute error = 7e-31
relative error = 6.6982492154123971421236012943022e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.09
y[1] (closed_form) = 1.0455019544046215656027651045195
y[1] (numeric) = 1.0455019544046215656027651045188
absolute error = 7e-31
relative error = 6.6953485553130946948885416313849e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.08
y[1] (closed_form) = 1.0459592566490442090254835263785
y[1] (numeric) = 1.0459592566490442090254835263778
absolute error = 7e-31
relative error = 6.6924212922270107201204551357672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.07
y[1] (closed_form) = 1.0464211548574312650748044464352
y[1] (numeric) = 1.0464211548574312650748044464345
absolute error = 7e-31
relative error = 6.6894672068759054063732869051271e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.06
y[1] (closed_form) = 1.0468876952199884889130415468398
y[1] (numeric) = 1.0468876952199884889130415468392
absolute error = 6e-31
relative error = 5.7312737817012795639140666010620e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.05
y[1] (closed_form) = 1.0473589243911409211939907702397
y[1] (numeric) = 1.0473589243911409211939907702391
absolute error = 6e-31
relative error = 5.7286951591002750631358184656757e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.04
y[1] (closed_form) = 1.0478348894941983694458128291081
y[1] (numeric) = 1.0478348894941983694458128291075
absolute error = 6e-31
relative error = 5.7260929752933376398721053969003e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.03
y[1] (closed_form) = 1.0483156381260677783213417597388
y[1] (numeric) = 1.0483156381260677783213417597381
absolute error = 7e-31
relative error = 6.6773782107390424752595293371136e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.02
y[1] (closed_form) = 1.04880121836201295995677154006
y[1] (numeric) = 1.0488012183620129599567715400594
absolute error = 6e-31
relative error = 5.7208171529116111773079549707887e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.01
y[1] (closed_form) = 1.0492916787604621604157230951175
y[1] (numeric) = 1.0492916787604621604157230951169
absolute error = 6e-31
relative error = 5.7181431259302987866532272417581e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3
y[1] (closed_form) = 1.0497870683678639429793424156501
y[1] (numeric) = 1.0497870683678639429793424156494
absolute error = 7e-31
relative error = 6.6680188877570325338480629375975e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.99
y[1] (closed_form) = 1.050287436723591873874805382468
y[1] (numeric) = 1.0502874367235918738748053824674
absolute error = 6e-31
relative error = 5.7127218609004867537475250639729e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.98
y[1] (closed_form) = 1.050792833864898500914889398847
y[1] (numeric) = 1.0507928338648985009148893988464
absolute error = 6e-31
relative error = 5.7099742276805687446256332860160e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.97
y[1] (closed_form) = 1.0513033103319191204506041173959
y[1] (numeric) = 1.0513033103319191204506041173953
absolute error = 6e-31
relative error = 5.7072016620072000383146745366087e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.96
y[1] (closed_form) = 1.0518189171727258330177463441629
y[1] (numeric) = 1.0518189171727258330177463441622
absolute error = 7e-31
relative error = 6.6551379574118134561540897140010e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.95
y[1] (closed_form) = 1.0523397059484323930871555025493
y[1] (numeric) = 1.0523397059484323930871555025486
absolute error = 7e-31
relative error = 6.6518444190901029237121999100298e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.94
y[1] (closed_form) = 1.0528657287383503634078987382166
y[1] (numeric) = 1.0528657287383503634078987382159
absolute error = 7e-31
relative error = 6.6485210876681342967934035134284e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.93
y[1] (closed_form) = 1.053397038145197089563116793104
y[1] (numeric) = 1.0533970381451970895631167931033
absolute error = 7e-31
relative error = 6.6451677254812453598349367206461e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.92
y[1] (closed_form) = 1.053933687300356015540326226409
y[1] (numeric) = 1.0539336873003560155403262264083
absolute error = 7e-31
relative error = 6.6417840935803584325254481812834e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.91
y[1] (closed_form) = 1.0544757298691898663521186236729
y[1] (numeric) = 1.0544757298691898663521186236722
absolute error = 7e-31
relative error = 6.6383699517374060952458810344494e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.9
y[1] (closed_form) = 1.0550232200564072290299465308342
y[1] (numeric) = 1.0550232200564072290299465308335
absolute error = 7e-31
relative error = 6.6349250584510758565403127250775e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.89
y[1] (closed_form) = 1.0555762126114830686535676575805
y[1] (numeric) = 1.0555762126114830686535676575798
absolute error = 7e-31
relative error = 6.6314491709528796309456583119844e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.88
y[1] (closed_form) = 1.0561347628341337214722674061654
y[1] (numeric) = 1.0561347628341337214722674061647
absolute error = 7e-31
relative error = 6.6279420452135539461805036290725e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.87
y[1] (closed_form) = 1.0566989265798469126217343574206
y[1] (numeric) = 1.0566989265798469126217343574199
absolute error = 7e-31
relative error = 6.6244034359497968484768776010266e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.86
y[1] (closed_form) = 1.0572687602654673514429687649702
y[1] (numeric) = 1.0572687602654673514429687649695
absolute error = 7e-31
relative error = 6.6208330966313475236810429255844e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.85
y[1] (closed_form) = 1.0578443208748384629674106267774
y[1] (numeric) = 1.0578443208748384629674106267767
absolute error = 7e-31
relative error = 6.6172307794884146995956028401911e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.84
y[1] (closed_form) = 1.0584256659645008197461373054073
y[1] (numeric) = 1.0584256659645008197461373054065
absolute error = 8e-31
relative error = 7.5583956977365256478048872401128e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.83
y[1] (closed_form) = 1.059012853669447843871062325787
y[1] (numeric) = 1.0590128536694478438710623257862
absolute error = 8e-31
relative error = 7.5542048165706765726915749665293e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.82
y[1] (closed_form) = 1.0596059427089393547631339046828
y[1] (numeric) = 1.0596059427089393547631339046821
absolute error = 7e-31
relative error = 6.6062294649878284144940418040040e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.81
y[1] (closed_form) = 1.0602049923923735440871566710524
y[1] (numeric) = 1.0602049923923735440871566710517
absolute error = 7e-31
relative error = 6.6024967343384806063276225669014e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=216.3MB, alloc=40.3MB, time=2.38
TOP MAIN SOLVE Loop
x[1] = -2.8
y[1] (closed_form) = 1.0608100626252179649956213881839
y[1] (numeric) = 1.0608100626252179649956213881832
absolute error = 7e-31
relative error = 6.5987307687079187765419617820898e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.79
y[1] (closed_form) = 1.0614212139150001288054095681066
y[1] (numeric) = 1.0614212139150001288054095681059
absolute error = 7e-31
relative error = 6.5949313130654729048478734701291e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.78
y[1] (closed_form) = 1.0620385073773583081720328292716
y[1] (numeric) = 1.0620385073773583081720328292708
absolute error = 8e-31
relative error = 7.5326835556608299866857242966809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.77
y[1] (closed_form) = 1.0626620047421531518467667742247
y[1] (numeric) = 1.0626620047421531518467667742239
absolute error = 8e-31
relative error = 7.5282638922816659062639764210082e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.76
y[1] (closed_form) = 1.0632917683596407221832481299345
y[1] (numeric) = 1.0632917683596407221832481299338
absolute error = 7e-31
relative error = 6.5833294381644894353101827610851e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.75
y[1] (closed_form) = 1.063927861206707572702430025558
y[1] (numeric) = 1.0639278612067075727024300255572
absolute error = 8e-31
relative error = 7.5193067986079390238422124352404e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.74
y[1] (closed_form) = 1.0645703468931684892288478184621
y[1] (numeric) = 1.0645703468931684892288478184614
absolute error = 7e-31
relative error = 6.5754226767904350979639071957104e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.73
y[1] (closed_form) = 1.065219289668127524377557230193
y[1] (numeric) = 1.0652192896681275243775572301923
absolute error = 7e-31
relative error = 6.5714168602606439672734052446327e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.72
y[1] (closed_form) = 1.0658747544264029615004943659454
y[1] (numeric) = 1.0658747544264029615004943659447
absolute error = 7e-31
relative error = 6.5673757361548799164231540604120e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.71
y[1] (closed_form) = 1.0665368067150168505940064080062
y[1] (numeric) = 1.0665368067150168505940064080055
absolute error = 7e-31
relative error = 6.5632990403400392266156828118747e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.7
y[1] (closed_form) = 1.067205512739749765126551700856
y[1] (numeric) = 1.0672055127397497651265517008553
absolute error = 7e-31
relative error = 6.5591865076010245734009057004372e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.69
y[1] (closed_form) = 1.0678809393717614352677143135015
y[1] (numeric) = 1.0678809393717614352677143135008
absolute error = 7e-31
relative error = 6.5550378716546130922180059144973e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.68
y[1] (closed_form) = 1.068563154154277919587373193244
y[1] (numeric) = 1.0685631541542779195873731932433
absolute error = 7e-31
relative error = 6.5508528651637824004921179335371e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.67
y[1] (closed_form) = 1.0692522253093459839477684894559
y[1] (numeric) = 1.0692522253093459839477684894552
absolute error = 7e-31
relative error = 6.5466312197525012620689030581226e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.66
y[1] (closed_form) = 1.0699482217446553630319829218383
y[1] (numeric) = 1.0699482217446553630319829218375
absolute error = 8e-31
relative error = 7.4769973325954189673885072382663e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.65
y[1] (closed_form) = 1.0706512130604295867406762781867
y[1] (numeric) = 1.0706512130604295867406762781859
absolute error = 8e-31
relative error = 7.4720879240702497711161114591020e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.64
y[1] (closed_form) = 1.0713612695563860605454550895863
y[1] (numeric) = 1.0713612695563860605454550895856
absolute error = 7e-31
relative error = 6.5337437509743653555408562336301e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.63
y[1] (closed_form) = 1.0720784622387660958127129062998
y[1] (numeric) = 1.0720784622387660958127129062992
absolute error = 6e-31
relative error = 5.5966052964728997638947205098680e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.62
y[1] (closed_form) = 1.0728028628274355931068319365058
y[1] (numeric) = 1.0728028628274355931068319365051
absolute error = 7e-31
relative error = 6.5249639449610385064394703373356e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.61
y[1] (closed_form) = 1.0735345437630570885469936238617
y[1] (numeric) = 1.073534543763057088546993623861
absolute error = 7e-31
relative error = 6.5205167739297173734849763886012e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.6
y[1] (closed_form) = 1.07427357821433388042821057017
y[1] (numeric) = 1.0742735782143338804282105701692
absolute error = 8e-31
relative error = 7.4468926372532254571798148637468e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.59
y[1] (closed_form) = 1.0750200400853269605252786986446
y[1] (numeric) = 1.0750200400853269605252786986439
absolute error = 7e-31
relative error = 6.5115065198639394110452813190918e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.58
y[1] (closed_form) = 1.0757740040228454817788775160744
y[1] (numeric) = 1.0757740040228454817788775160737
absolute error = 7e-31
relative error = 6.5069428837502804677487691441705e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.57
y[1] (closed_form) = 1.0765355454239115014167458275085
y[1] (numeric) = 1.0765355454239115014167458275078
absolute error = 7e-31
relative error = 6.5023398714099898507193473166132e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.56
y[1] (closed_form) = 1.0773047404432997459904656610398
y[1] (numeric) = 1.0773047404432997459904656610391
absolute error = 7e-31
relative error = 6.4976972041537406396965150984835e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.55
y[1] (closed_form) = 1.0780816660011531523106412395528
y[1] (numeric) = 1.0780816660011531523106412395521
absolute error = 7e-31
relative error = 6.4930146024693759750925354569661e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.54
y[1] (closed_form) = 1.0788663997906749458409128226
y[1] (numeric) = 1.0788663997906749458409128225993
absolute error = 7e-31
relative error = 6.4882917860433525685047613394323e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.53
y[1] (closed_form) = 1.0796590202858980257650549064864
y[1] (numeric) = 1.0796590202858980257650549064857
absolute error = 7e-31
relative error = 6.4835284737827430083935150420046e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.52
y[1] (closed_form) = 1.0804596067495324336721400015193
y[1] (numeric) = 1.0804596067495324336721400015185
absolute error = 8e-31
relative error = 7.4042564386717754370076209349116e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.51
y[1] (closed_form) = 1.0812682392408916906131760818382
y[1] (numeric) = 1.0812682392408916906131760818374
absolute error = 8e-31
relative error = 7.3987191241429870962973494253921e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.5
y[1] (closed_form) = 1.0820849986238987951695286744672
y[1] (numeric) = 1.0820849986238987951695286744664
absolute error = 8e-31
relative error = 7.3931345598300515904535505868297e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.49
y[1] (closed_form) = 1.0829099665751726831396061170947
y[1] (numeric) = 1.0829099665751726831396061170939
absolute error = 8e-31
relative error = 7.3875024211855027019913840576313e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.48
y[1] (closed_form) = 1.0837432255921959574965153919751
y[1] (numeric) = 1.0837432255921959574965153919743
absolute error = 8e-31
relative error = 7.3818223829067209401796680363643e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.47
y[1] (closed_form) = 1.084584859001564705396490765854
y[1] (numeric) = 1.0845848590015647053964907658532
absolute error = 8e-31
relative error = 7.3760941189650689985586748408342e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.46
y[1] (closed_form) = 1.0854349509673212272266709492054
y[1] (numeric) = 1.0854349509673212272266709492046
absolute error = 8e-31
relative error = 7.3703173026357181715628835660066e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.45
y[1] (closed_form) = 1.0862935864993705109720735165162
y[1] (numeric) = 1.0862935864993705109720735165153
absolute error = 9e-31
relative error = 8.2850530573441946303853897761202e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.44
y[1] (closed_form) = 1.0871608514619812935562170370773
y[1] (numeric) = 1.0871608514619812935562170370764
absolute error = 9e-31
relative error = 8.2784437904446890619849316349501e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.43
y[1] (closed_form) = 1.088036832582372559268609219894
y[1] (numeric) = 1.0880368325823725592686092198932
absolute error = 8e-31
relative error = 7.3526922622762772333277632369184e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.42
y[1] (closed_form) = 1.0889216174593863339360992607368
y[1] (numeric) = 1.088921617459386333936099260736
absolute error = 8e-31
relative error = 7.3467179563072427935733635674336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.41
y[1] (closed_form) = 1.0898152945722476421247388791339
y[1] (numeric) = 1.0898152945722476421247388791332
absolute error = 7e-31
relative error = 6.4231067731046104166486826072288e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.4
y[1] (closed_form) = 1.0907179532894125033751722200797
y[1] (numeric) = 1.090717953289412503375172220079
absolute error = 7e-31
relative error = 6.4177911245425434053593329263431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.39
y[1] (closed_form) = 1.0916296838775048522785515142203
y[1] (numeric) = 1.0916296838775048522785515142196
absolute error = 7e-31
relative error = 6.4124309767170930831398612947129e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.38
y[1] (closed_form) = 1.092550577510343276092433546306
y[1] (numeric) = 1.0925505775103432760924335463053
absolute error = 7e-31
relative error = 6.4070260398848495055031535647188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.37
y[1] (closed_form) = 1.093480726278058472577940827977
y[1] (numeric) = 1.0934807262780584725779408279763
absolute error = 7e-31
relative error = 6.4015760239563541686853002816636e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.36
y[1] (closed_form) = 1.0944202231963023398115690978577
y[1] (numeric) = 1.094420223196302339811569097857
absolute error = 7e-31
relative error = 6.3960806385285831885010445463099e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
memory used=258.8MB, alloc=40.3MB, time=2.86
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.35
y[1] (closed_form) = 1.0953691622155496188882965967998
y[1] (numeric) = 1.0953691622155496188882965967991
absolute error = 7e-31
relative error = 6.3905395929181011819063180937453e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.34
y[1] (closed_form) = 1.0963276382304930196880168239591
y[1] (numeric) = 1.0963276382304930196880168239584
absolute error = 7e-31
relative error = 6.3849525961948913263994506534896e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.33
y[1] (closed_form) = 1.0972957470895327692257007145515
y[1] (numeric) = 1.0972957470895327692257007145508
absolute error = 7e-31
relative error = 6.3793193572168669602737983001278e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.32
y[1] (closed_form) = 1.0982735856043615315480312388239
y[1] (numeric) = 1.0982735856043615315480312388231
absolute error = 8e-31
relative error = 7.2841595253315085359450480184483e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.31
y[1] (closed_form) = 1.0992612515596456576764875455719
y[1] (numeric) = 1.0992612515596456576764875455711
absolute error = 8e-31
relative error = 7.2776148423766412332330609670849e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.3
y[1] (closed_form) = 1.100258843722803733729940693798
y[1] (numeric) = 1.1002588437228037337299406937972
absolute error = 8e-31
relative error = 7.2710163118811509172855620241886e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.29
y[1] (closed_form) = 1.1012664618538834050897220493467
y[1] (numeric) = 1.1012664618538834050897220493459
absolute error = 8e-31
relative error = 7.2643636005519653003859657180856e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.28
y[1] (closed_form) = 1.1022842067155374642978115675971
y[1] (numeric) = 1.1022842067155374642978115675963
absolute error = 8e-31
relative error = 7.2576563750627439913103112188093e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.27
y[1] (closed_form) = 1.1033121800831002003052492153345
y[1] (numeric) = 1.1033121800831002003052492153337
absolute error = 8e-31
relative error = 7.2508943020981144530675411134665e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.26
y[1] (closed_form) = 1.1043504847547650167140913586396
y[1] (numeric) = 1.1043504847547650167140913586388
absolute error = 8e-31
relative error = 7.2440770483987256218626063100945e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.25
y[1] (closed_form) = 1.1053992245618643367832176892407
y[1] (numeric) = 1.1053992245618643367832176892399
absolute error = 8e-31
relative error = 7.2372042808071240482430818941733e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.24
y[1] (closed_form) = 1.1064585043792528231970558860814
y[1] (numeric) = 1.1064585043792528231970558860805
absolute error = 9e-31
relative error = 8.1340601246037643845425460035528e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.23
y[1] (closed_form) = 1.107528430135794950927853596553
y[1] (numeric) = 1.1075284301357949509278535965521
absolute error = 9e-31
relative error = 8.1262022311215096905413436485647e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.22
y[1] (closed_form) = 1.1086091088249579819575236377746
y[1] (numeric) = 1.1086091088249579819575236377737
absolute error = 9e-31
relative error = 8.1182807613220145816943822481894e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.21
y[1] (closed_form) = 1.1097006485155114011653621107986
y[1] (numeric) = 1.1097006485155114011653621107977
absolute error = 9e-31
relative error = 8.1102953413964756779089435748129e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.2
y[1] (closed_form) = 1.1108031583623338833341444258499
y[1] (numeric) = 1.1108031583623338833341444258491
absolute error = 8e-31
relative error = 7.2019960870425188240458453224030e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.19
y[1] (closed_form) = 1.1119167486173288719803056840571
y[1] (numeric) = 1.1119167486173288719803056840563
absolute error = 8e-31
relative error = 7.1947832514871451250203173591971e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.18
y[1] (closed_form) = 1.1130415306404498615751847797268
y[1] (numeric) = 1.1130415306404498615751847797259
absolute error = 9e-31
relative error = 8.0859516489212701575876826532818e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.17
y[1] (closed_form) = 1.1141776169108364856947421133822
y[1] (numeric) = 1.1141776169108364856947421133814
absolute error = 8e-31
relative error = 7.1801837324472211282471291711687e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.16
y[1] (closed_form) = 1.1153251210380625247158459917298
y[1] (numeric) = 1.115325121038062524715845991729
absolute error = 8e-31
relative error = 7.1727963883340033369402661682618e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.15
y[1] (closed_form) = 1.1164841577734969578692707141828
y[1] (numeric) = 1.116484157773496957869270714182
absolute error = 8e-31
relative error = 7.1653502150479896210407715802032e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.14
y[1] (closed_form) = 1.1176548430217791957640792206891
y[1] (numeric) = 1.1176548430217791957640792206883
absolute error = 8e-31
relative error = 7.1578448838199217600727320773217e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.13
y[1] (closed_form) = 1.1188372938524096409162054647724
y[1] (numeric) = 1.1188372938524096409162054647716
absolute error = 8e-31
relative error = 7.1502800665985955260613479492354e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.12
y[1] (closed_form) = 1.1200316285114567353469482026623
y[1] (numeric) = 1.1200316285114567353469482026614
absolute error = 9e-31
relative error = 8.0354873656212464252462236340483e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.11
y[1] (closed_form) = 1.1212379664333816659658919534078
y[1] (numeric) = 1.1212379664333816659658919534069
absolute error = 9e-31
relative error = 8.0268419991419679076108481315696e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.1
y[1] (closed_form) = 1.1224564282529819102186473760726
y[1] (numeric) = 1.1224564282529819102186473760717
absolute error = 9e-31
relative error = 8.0181286092394835553080453483240e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.09
y[1] (closed_form) = 1.12368713581745481636392882593
y[1] (numeric) = 1.1236871358174548163639288259291
absolute error = 9e-31
relative error = 8.0093468307374728974577819294222e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.08
y[1] (closed_form) = 1.1249302121985824247480498144888
y[1] (numeric) = 1.1249302121985824247480498144879
absolute error = 9e-31
relative error = 8.0004962995973318615414356408721e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.07
y[1] (closed_form) = 1.1261857817050387485691178744718
y[1] (numeric) = 1.1261857817050387485691178744709
absolute error = 9e-31
relative error = 7.9915766529870872144174269695862e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.06
y[1] (closed_form) = 1.1274539698948207448692613507224
y[1] (numeric) = 1.1274539698948207448692613507215
absolute error = 9e-31
relative error = 7.9825875293512892684683987142061e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.05
y[1] (closed_form) = 1.1287349035878042188623465167449
y[1] (numeric) = 1.1287349035878042188623465167439
absolute error = 1.0e-30
relative error = 8.8594761872020914376314937116111e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.04
y[1] (closed_form) = 1.1300287108784259171980810770711
y[1] (numeric) = 1.1300287108784259171980810770701
absolute error = 1.0e-30
relative error = 8.8493326795445018599396191118451e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.03
y[1] (closed_form) = 1.1313355211484930783823989120881
y[1] (numeric) = 1.1313355211484930783823989120871
absolute error = 1.0e-30
relative error = 8.8391107793100515847917104142628e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.02
y[1] (closed_form) = 1.1326554650801217213198427647316
y[1] (numeric) = 1.1326554650801217213198427647307
absolute error = 9e-31
relative error = 7.9459290821179752877944305587407e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.01
y[1] (closed_form) = 1.1339886746688049658175810503738
y[1] (numeric) = 1.1339886746688049658175810503728
absolute error = 1.0e-30
relative error = 8.8184302219073045846598653775771e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2
y[1] (closed_form) = 1.1353352832366126918939994949725
y[1] (numeric) = 1.1353352832366126918939994949715
absolute error = 1.0e-30
relative error = 8.8079707797788244405972914130238e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (closed_form) = 1.1366954254455238578687982134042
y[1] (numeric) = 1.1366954254455238578687982134032
absolute error = 1.0e-30
relative error = 8.7974313753224918929627222979012e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (closed_form) = 1.1380692373108928104775135397954
y[1] (numeric) = 1.1380692373108928104775135397944
absolute error = 1.0e-30
relative error = 8.7868116210826314075873258656603e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (closed_form) = 1.1394568562150509336526980245391
y[1] (numeric) = 1.1394568562150509336526980245381
absolute error = 1.0e-30
relative error = 8.7761111317695113392455907489836e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (closed_form) = 1.140858420921044996147971461096
y[1] (numeric) = 1.1408584209210449961479714610949
absolute error = 1.1e-30
relative error = 9.6418624767825360943670455372698e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (closed_form) = 1.1422740715865135718511540088638
y[1] (numeric) = 1.1422740715865135718511540088627
absolute error = 1.1e-30
relative error = 9.6299130599384193625799648511686e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (closed_form) = 1.1437039497777029204400764475696
y[1] (numeric) = 1.1437039497777029204400764475685
absolute error = 1.1e-30
relative error = 9.6178735783311976915351012665520e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (closed_form) = 1.1451481984836237299808130836871
y[1] (numeric) = 1.145148198483623729980813083686
absolute error = 1.1e-30
relative error = 9.6057436186564513477110444787957e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=301.2MB, alloc=40.3MB, time=3.30
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (closed_form) = 1.146606962130350137154394456995
y[1] (numeric) = 1.1466069621303501371543944569939
absolute error = 1.1e-30
relative error = 9.5935227704901053889404244403918e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (closed_form) = 1.1480803865954624550259384084542
y[1] (numeric) = 1.1480803865954624550259384084531
absolute error = 1.1e-30
relative error = 9.5812106263914074029728815541384e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (closed_form) = 1.1495686192226350526410120691037
y[1] (numeric) = 1.1495686192226350526410120691026
absolute error = 1.1e-30
relative error = 9.5688067820070236262914140981849e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (closed_form) = 1.1510718088363708452493410130273
y[1] (numeric) = 1.1510718088363708452493410130262
absolute error = 1.1e-30
relative error = 9.5563108361762433403996969090640e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (closed_form) = 1.1525901057568838686171667280872
y[1] (numeric) = 1.1525901057568838686171667280861
absolute error = 1.1e-30
relative error = 9.5437223910372807474895218658754e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (closed_form) = 1.154123661815131425698085826774
y[1] (numeric) = 1.1541236618151314256980858267729
absolute error = 1.1e-30
relative error = 9.5310410521346628199718438410609e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (closed_form) = 1.1556726303679973088895649117416
y[1] (numeric) = 1.1556726303679973088895649117405
absolute error = 1.1e-30
relative error = 9.5182664285276908989424795067672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (closed_form) = 1.1572371663136276162100094749031
y[1] (numeric) = 1.1572371663136276162100094749021
absolute error = 1.0e-30
relative error = 8.6412710299090573503625348089727e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (closed_form) = 1.158817426106920694990784426392
y[1] (numeric) = 1.1588174261069206949907844263909
absolute error = 1.1e-30
relative error = 9.4924357816699437250855249021498e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (closed_form) = 1.160413567775172762090463784878
y[1] (numeric) = 1.160413567775172762090463784877
absolute error = 1.0e-30
relative error = 8.6176172682750595758182348260844e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (closed_form) = 1.1620257509338807652063690145142
y[1] (numeric) = 1.1620257509338807652063690145132
absolute error = 1.0e-30
relative error = 8.6056612703834992191071876593709e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (closed_form) = 1.1636541368027040655826962573359
y[1] (numeric) = 1.1636541368027040655826962573349
absolute error = 1.0e-30
relative error = 8.5936187426586582400118213862284e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (closed_form) = 1.1652988882215865382968047204322
y[1] (numeric) = 1.1652988882215865382968047204311
absolute error = 1.1e-30
relative error = 9.4396382860946343144629408068196e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (closed_form) = 1.1669601696670407023471299750829
y[1] (numeric) = 1.1669601696670407023471299750819
absolute error = 1.0e-30
relative error = 8.5692727651991918809847557328352e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (closed_form) = 1.1686381472685955089693011128318
y[1] (numeric) = 1.1686381472685955089693011128308
absolute error = 1.0e-30
relative error = 8.5569686590948127314348833339153e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (closed_form) = 1.1703329888254094329729999061631
y[1] (numeric) = 1.1703329888254094329729999061621
absolute error = 1.0e-30
relative error = 8.5445767106303473539996501328438e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (closed_form) = 1.172044863823050528422539948626
y[1] (numeric) = 1.172044863823050528422539948625
absolute error = 1.0e-30
relative error = 8.5320966019861761752230129354753e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (closed_form) = 1.1737739434504451266807172586664
y[1] (numeric) = 1.1737739434504451266807172586654
absolute error = 1.0e-30
relative error = 8.5195280196831053029381513481566e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (closed_form) = 1.1755204006169968716998606943422
y[1] (numeric) = 1.1755204006169968716998606943413
absolute error = 9e-31
relative error = 7.6561835892224062434730729147037e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (closed_form) = 1.1772844099698778044778771942594
y[1] (numeric) = 1.1772844099698778044778771942585
absolute error = 9e-31
relative error = 7.6447117822874045389052056761806e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (closed_form) = 1.1790661479114932258021467343306
y[1] (numeric) = 1.1790661479114932258021467343297
absolute error = 9e-31
relative error = 7.6331595270900664740994268040663e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (closed_form) = 1.1808657926171220837820954906518
y[1] (numeric) = 1.1808657926171220837820954906509
absolute error = 9e-31
relative error = 7.6215265581142244222584506196131e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (closed_form) = 1.1826835240527346502239008377589
y[1] (numeric) = 1.182683524052734650223900837758
absolute error = 9e-31
relative error = 7.6098126142481876609944161114776e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (closed_form) = 1.1845195239929892676298137659024
y[1] (numeric) = 1.1845195239929892676298137659015
absolute error = 9e-31
relative error = 7.5980174388862734075188105583712e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (closed_form) = 1.1863739760394099665117959887401
y[1] (numeric) = 1.1863739760394099665117959887391
absolute error = 1.0e-30
relative error = 8.4290453111454727379837147735861e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (closed_form) = 1.1882470656387467707963511700788
y[1] (numeric) = 1.1882470656387467707963511700778
absolute error = 1.0e-30
relative error = 8.4157582115504418423026188432352e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (closed_form) = 1.1901389801015205273663910582943
y[1] (numeric) = 1.1901389801015205273663910582933
absolute error = 1.0e-30
relative error = 8.4023800305633094616936080902046e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (closed_form) = 1.1920499086207541142385447911733
y[1] (numeric) = 1.1920499086207541142385447911723
absolute error = 1.0e-30
relative error = 8.3889105042341476280854740321649e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (closed_form) = 1.1939800422908919005123384942873
y[1] (numeric) = 1.1939800422908919005123384942863
absolute error = 1.0e-30
relative error = 8.3753493741930392359826077916689e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (closed_form) = 1.1959295741269093500530063600373
y[1] (numeric) = 1.1959295741269093500530063600363
absolute error = 1.0e-30
relative error = 8.3616963877664108556345423708252e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (closed_form) = 1.1978986990836146798842262112941
y[1] (numeric) = 1.1978986990836146798842262112931
absolute error = 1.0e-30
relative error = 8.3479512980938538647839133756685e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (closed_form) = 1.1998876140751445034727035921351
y[1] (numeric) = 1.1998876140751445034727035921341
absolute error = 1.0e-30
relative error = 8.3341138642454035297561660810929e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (closed_form) = 1.2018965179946554084851792676434
y[1] (numeric) = 1.2018965179946554084851792676424
absolute error = 1.0e-30
relative error = 8.3201838513392448184242232820009e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (closed_form) = 1.2039256117342134381920455363505
y[1] (numeric) = 1.2039256117342134381920455363496
absolute error = 9e-31
relative error = 7.4755449275938315896099221747244e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (closed_form) = 1.2059750982048834654822863400384
y[1] (numeric) = 1.2059750982048834654822863400375
absolute error = 9e-31
relative error = 7.4628406617986297283134925062462e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (closed_form) = 1.2080451823570204684438838657276
y[1] (numeric) = 1.2080451823570204684438838657267
absolute error = 9e-31
relative error = 7.4500524743950998810075510332758e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (closed_form) = 1.2101360712007647366541591331939
y[1] (numeric) = 1.210136071200764736654159133193
absolute error = 9e-31
relative error = 7.4371801768289547005407809668609e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (closed_form) = 1.2122479738267430577177549975797
y[1] (numeric) = 1.2122479738267430577177549975788
absolute error = 9e-31
relative error = 7.4242235865236416368890615814372e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (closed_form) = 1.2143811014269779541881664116833
y[1] (numeric) = 1.2143811014269779541881664116824
absolute error = 9e-31
relative error = 7.4111825269879495979669399314636e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (closed_form) = 1.2165356673160070618139345231369
y[1] (numeric) = 1.2165356673160070618139345231359
absolute error = 1.0e-30
relative error = 8.2200631421375350423886085040853e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (closed_form) = 1.2187118869522147610649287664188
y[1] (numeric) = 1.2187118869522147610649287664178
absolute error = 1.0e-30
relative error = 8.2053848059267319458790279191577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (closed_form) = 1.2209099779593781951196459967695
y[1] (numeric) = 1.2209099779593781951196459967685
absolute error = 1.0e-30
relative error = 8.1906120684785798722470671569546e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (closed_form) = 1.223130160148429828933280470764
y[1] (numeric) = 1.2231301601484298289332804707631
absolute error = 9e-31
relative error = 7.3581702857427929364649546079063e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.49
y[1] (closed_form) = 1.2253726555394387256606070068809
y[1] (numeric) = 1.2253726555394387256606070068799
absolute error = 1.0e-30
relative error = 8.1607827258049574853607932724094e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=343.6MB, alloc=40.3MB, time=3.77
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (closed_form) = 1.2276376883838127385796374057948
y[1] (numeric) = 1.2276376883838127385796374057937
absolute error = 1.1e-30
relative error = 8.9602983877771951697336004849874e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (closed_form) = 1.2299254851867238387537443843114
y[1] (numeric) = 1.2299254851867238387537443843104
absolute error = 1.0e-30
relative error = 8.1305738603195363803119226139481e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (closed_form) = 1.2322362747297588209837070706824
y[1] (numeric) = 1.2322362747297588209837070706814
absolute error = 1.0e-30
relative error = 8.1153267478618055359915715045860e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.45
y[1] (closed_form) = 1.234570288093797653139148917061
y[1] (numeric) = 1.2345702880937976531391489170599
absolute error = 1.1e-30
relative error = 8.9099827738315572732334828848763e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.44
y[1] (closed_form) = 1.2369277586821217567233665275514
y[1] (numeric) = 1.2369277586821217567233665275504
absolute error = 1.0e-30
relative error = 8.0845465143853251042456696491424e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.43
y[1] (closed_form) = 1.2393089222437545295188628493952
y[1] (numeric) = 1.2393089222437545295188628493942
absolute error = 1.0e-30
relative error = 8.0690131576678356988953903552802e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.42
y[1] (closed_form) = 1.2417140168970364443852997809855
y[1] (numeric) = 1.2417140168970364443852997809845
absolute error = 1.0e-30
relative error = 8.0533841640842209066125342075611e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (closed_form) = 1.2441432831534370817393959731224
y[1] (numeric) = 1.2441432831534370817393959731213
absolute error = 1.1e-30
relative error = 8.8414253799764295245403711931912e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.4
y[1] (closed_form) = 1.2465969639416064769398612398338
y[1] (numeric) = 1.2465969639416064769398612398327
absolute error = 1.1e-30
relative error = 8.8240227741443992296977795070708e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.39
y[1] (closed_form) = 1.2490753046316681877321489284998
y[1] (numeric) = 1.2490753046316681877321489284988
absolute error = 1.0e-30
relative error = 8.0059224315133152985320930891865e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (closed_form) = 1.2515785530597565110800150148691
y[1] (numeric) = 1.2515785530597565110800150148681
absolute error = 1.0e-30
relative error = 7.9899100024947062626820214377067e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (closed_form) = 1.2541069595528003031260148277283
y[1] (numeric) = 1.2541069595528003031260148277273
absolute error = 1.0e-30
relative error = 7.9738015356886956673083946220074e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.36
y[1] (closed_form) = 1.2566607769535558806835867050428
y[1] (numeric) = 1.2566607769535558806835867050417
absolute error = 1.1e-30
relative error = 8.7533566748749905017740653143828e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.35
y[1] (closed_form) = 1.2592402606458915075717326107116
y[1] (numeric) = 1.2592402606458915075717326107105
absolute error = 1.1e-30
relative error = 8.7354259101895793814490000949536e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.34
y[1] (closed_form) = 1.2618456685803259942619996555144
y[1] (numeric) = 1.2618456685803259942619996555133
absolute error = 1.1e-30
relative error = 8.7173893558440082980899476902200e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (closed_form) = 1.2644772612998239647190094577137
y[1] (numeric) = 1.2644772612998239647190094577126
absolute error = 1.1e-30
relative error = 8.6992469826563035992705818612281e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (closed_form) = 1.2671353019658503699827155236038
y[1] (numeric) = 1.2671353019658503699827155236026
absolute error = 1.2e-30
relative error = 9.4701804782670344697962880835950e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (closed_form) = 1.2698200563846868539654590407689
y[1] (numeric) = 1.2698200563846868539654590407676
absolute error = 1.3e-30
relative error = 1.0237671026406990803520717711621e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.3
y[1] (closed_form) = 1.2725317930340126031223331675634
y[1] (numeric) = 1.272531793034012603122333167562
absolute error = 1.4e-30
relative error = 1.1001689762595820576429238611618e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.29
y[1] (closed_form) = 1.2752707830897523381019736371362
y[1] (numeric) = 1.2752707830897523381019736371348
absolute error = 1.4e-30
relative error = 1.0978060648484795867054080106257e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (closed_form) = 1.2780373004531941321993141560141
y[1] (numeric) = 1.2780373004531941321993141560127
absolute error = 1.4e-30
relative error = 1.0954296869923574950575638213830e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.27
y[1] (closed_form) = 1.2808316217783797684147501301548
y[1] (numeric) = 1.2808316217783797684147501301534
absolute error = 1.4e-30
relative error = 1.0930398470769796032105665194790e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.26
y[1] (closed_form) = 1.2836540264997703741782420084759
y[1] (numeric) = 1.2836540264997703741782420084745
absolute error = 1.4e-30
relative error = 1.0906365508917370566236741490603e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.25
y[1] (closed_form) = 1.2865047968601901003248854266478
y[1] (numeric) = 1.2865047968601901003248854266464
absolute error = 1.4e-30
relative error = 1.0882198056445676057993273667262e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.24
y[1] (closed_form) = 1.2893842179390506387131321849311
y[1] (numeric) = 1.2893842179390506387131321849296
absolute error = 1.5e-30
relative error = 1.1633460214036101975618945383769e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.23
y[1] (closed_form) = 1.2922925776808594009609443919072
y[1] (numeric) = 1.2922925776808594009609443919057
absolute error = 1.5e-30
relative error = 1.1607278614041807063677588839266e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (closed_form) = 1.2952301669240142091415122843203
y[1] (numeric) = 1.2952301669240142091415122843188
absolute error = 1.5e-30
relative error = 1.1580953241401756118102427766899e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (closed_form) = 1.298197279429887377931600950376
y[1] (numeric) = 1.2981972794298873779316009503745
absolute error = 1.5e-30
relative error = 1.1554484235699028197210792730194e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (closed_form) = 1.3011942119122020966449776070832
y[1] (numeric) = 1.3011942119122020966449776070817
absolute error = 1.5e-30
relative error = 1.1527871752485264643963689786952e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (closed_form) = 1.3042212640667040488136031743295
y[1] (numeric) = 1.304221264066704048813603174328
absolute error = 1.5e-30
relative error = 1.1501115963428141897987471029386e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (closed_form) = 1.3072787386011312365032726969182
y[1] (numeric) = 1.3072787386011312365032726969167
absolute error = 1.5e-30
relative error = 1.1474217056456470657404189993404e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (closed_form) = 1.3103669412654850063711111154575
y[1] (numeric) = 1.310366941265485006371111115456
absolute error = 1.5e-30
relative error = 1.1447175235902831441750415320220e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.16
y[1] (closed_form) = 1.313486180882605304592756074811
y[1] (numeric) = 1.3134861808826053045927560748095
absolute error = 1.5e-30
relative error = 1.1419990722643656296250218008266e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.15
y[1] (closed_form) = 1.3166367693790532182101999524295
y[1] (numeric) = 1.316636769379053218210199952428
absolute error = 1.5e-30
relative error = 1.1392663754236666118785790338882e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (closed_form) = 1.3198190218163038911801614276738
y[1] (numeric) = 1.3198190218163038911801614276723
absolute error = 1.5e-30
relative error = 1.1365194585055572885397471264495e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (closed_form) = 1.3230332564222529344405856126403
y[1] (numeric) = 1.3230332564222529344405856126388
absolute error = 1.5e-30
relative error = 1.1337583486421955899340752318367e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (closed_form) = 1.3262797946230394806625348237426
y[1] (numeric) = 1.326279794623039480662534823741
absolute error = 1.6e-30
relative error = 1.2063819463183169166831006275470e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (closed_form) = 1.3295589610751890660194644838161
y[1] (numeric) = 1.3295589610751890660194644838145
absolute error = 1.6e-30
relative error = 1.2034065783033122540367688131772e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (closed_form) = 1.3328710836980795532888469064313
y[1] (numeric) = 1.3328710836980795532888469064297
absolute error = 1.6e-30
relative error = 1.2004161689521881667359629478593e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.09
y[1] (closed_form) = 1.336216493706733342905508150893
y[1] (numeric) = 1.3362164937067333429055081508914
absolute error = 1.6e-30
relative error = 1.1974107545713027616332649351199e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (closed_form) = 1.3395955256449391512151102152476
y[1] (numeric) = 1.339595525644939151215110215246
absolute error = 1.6e-30
relative error = 1.1943903733402594685425173049452e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (closed_form) = 1.3430085174187066681332054893988
y[1] (numeric) = 1.3430085174187066681332054893971
absolute error = 1.7e-30
relative error = 1.2658147569067091185556110393173e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (closed_form) = 1.3464558103300574397035083480901
y[1] (numeric) = 1.3464558103300574397035083480885
absolute error = 1.6e-30
relative error = 1.1883048724842972278463627346176e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (closed_form) = 1.3499377491111553546717988735768
y[1] (numeric) = 1.3499377491111553546717988735752
absolute error = 1.6e-30
relative error = 1.1852398386914463900654330033029e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=386.0MB, alloc=40.3MB, time=4.20
TOP MAIN SOLVE Loop
x[1] = -1.04
y[1] (closed_form) = 1.353454681958780148152558265309
y[1] (numeric) = 1.3534546819587801481525582653073
absolute error = 1.7e-30
relative error = 1.2560450103432232903089296678066e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (closed_form) = 1.3570069605691473697674306156514
y[1] (numeric) = 1.3570069605691473697674306156497
absolute error = 1.7e-30
relative error = 1.2527570229168143952992092890190e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (closed_form) = 1.360594940173078298281341634654
y[1] (numeric) = 1.3605949401730782982813416346524
absolute error = 1.6e-30
relative error = 1.1759561591464300970584774612858e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.01
y[1] (closed_form) = 1.3642189795715233197570462956374
y[1] (numeric) = 1.3642189795715233197570462956357
absolute error = 1.7e-30
relative error = 1.2461342537060578560232333808373e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (closed_form) = 1.3678794411714423215955237701615
y[1] (numeric) = 1.3678794411714423215955237701598
absolute error = 1.7e-30
relative error = 1.2427995836710082947269707110971e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (closed_form) = 1.3715766910220456905315241199082
y[1] (numeric) = 1.3715766910220456905315241199065
absolute error = 1.7e-30
relative error = 1.2394494679938210473709092885336e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (closed_form) = 1.3753110988513995387142672324775
y[1] (numeric) = 1.3753110988513995387142672324758
absolute error = 1.7e-30
relative error = 1.2360839677799202053847418140173e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (closed_form) = 1.3790830381033988184264065277403
y[1] (numeric) = 1.3790830381033988184264065277386
absolute error = 1.7e-30
relative error = 1.2327031462426992385414221078118e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (closed_form) = 1.3828928859751120227835403627544
y[1] (numeric) = 1.3828928859751120227835403627527
absolute error = 1.7e-30
relative error = 1.2293070687114627085572581835407e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (closed_form) = 1.386741023454501206915461774036
y[1] (numeric) = 1.3867410234545012069154617740342
absolute error = 1.8e-30
relative error = 1.2980073204411535651775343551749e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (closed_form) = 1.3906278353585211016626981379217
y[1] (numeric) = 1.3906278353585211016626981379199
absolute error = 1.8e-30
relative error = 1.2943793833494909711138182575907e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (closed_form) = 1.3945537103716011297314597702349
y[1] (numeric) = 1.3945537103716011297314597702331
absolute error = 1.8e-30
relative error = 1.2907355138873505451826192167022e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (closed_form) = 1.3985190410845141725406814138044
y[1] (numeric) = 1.3985190410845141725406814138026
absolute error = 1.8e-30
relative error = 1.2870757902617815373661987289113e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (closed_form) = 1.4025242240336359746702320649927
y[1] (numeric) = 1.4025242240336359746702320649909
absolute error = 1.8e-30
relative error = 1.2834002929541069946285842157237e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (closed_form) = 1.4065696597405991118834542396456
y[1] (numeric) = 1.4065696597405991118834542396438
absolute error = 1.8e-30
relative error = 1.2797091047250071342335768262406e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (closed_form) = 1.4106557527523454881538800158902
y[1] (numeric) = 1.4106557527523454881538800158884
absolute error = 1.8e-30
relative error = 1.2760023106190158708060601781495e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (closed_form) = 1.4147829116815813669792037174992
y[1] (numeric) = 1.4147829116815813669792037174974
absolute error = 1.8e-30
relative error = 1.2722799979684216441630348807605e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (closed_form) = 1.4189515492476389825193552735605
y[1] (numeric) = 1.4189515492476389825193552735587
absolute error = 1.8e-30
relative error = 1.2685422563965638874278066135897e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (closed_form) = 1.4231620823177488167538395179062
y[1] (numeric) = 1.4231620823177488167538395179044
absolute error = 1.8e-30
relative error = 1.2647891778205166762618042415975e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (closed_form) = 1.4274149319487266699204508411764
y[1] (numeric) = 1.4274149319487266699204508411746
absolute error = 1.8e-30
relative error = 1.2610208564531513101826779860649e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (closed_form) = 1.4317105234290796929771464081439
y[1] (numeric) = 1.4317105234290796929771464081421
absolute error = 1.8e-30
relative error = 1.2572373888045697958541483355066e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (closed_form) = 1.4360492863215355927254126049699
y[1] (numeric) = 1.4360492863215355927254126049681
absolute error = 1.8e-30
relative error = 1.2534388736829014298923544814416e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (closed_form) = 1.4404316545059992625510781754405
y[1] (numeric) = 1.4404316545059992625510781754387
absolute error = 1.8e-30
relative error = 1.2496254121944549150851406659926e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (closed_form) = 1.4448580662229411344814454391058
y[1] (numeric) = 1.444858066222941134481445439104
absolute error = 1.8e-30
relative error = 1.2457971077432186889047849971385e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (closed_form) = 1.4493289641172215914301023850156
y[1] (numeric) = 1.4493289641172215914301023850138
absolute error = 1.8e-30
relative error = 1.2419540660297023967409733115072e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (closed_form) = 1.4538447952823558221071605875315
y[1] (numeric) = 1.4538447952823558221071605875297
absolute error = 1.8e-30
relative error = 1.2380963950491127043089877519492e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (closed_form) = 1.4584060113052235451172974700586
y[1] (numeric) = 1.4584060113052235451172974700568
absolute error = 1.8e-30
relative error = 1.2342242050888569141074396435249e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (closed_form) = 1.4630130683112280732552709485309
y[1] (numeric) = 1.4630130683112280732552709485291
absolute error = 1.8e-30
relative error = 1.2303376087253681295093573575958e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (closed_form) = 1.4676664270099092339429686851366
y[1] (numeric) = 1.4676664270099092339429686851348
absolute error = 1.8e-30
relative error = 1.2264367208202459969585069818210e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (closed_form) = 1.4723665527410147071380465509433
y[1] (numeric) = 1.4723665527410147071380465509414
absolute error = 1.9e-30
relative error = 1.2904395284332466490033922199755e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (closed_form) = 1.4771139155210343878863400708347
y[1] (numeric) = 1.4771139155210343878863400708328
absolute error = 1.9e-30
relative error = 1.2862921268531936949778363771732e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (closed_form) = 1.4819089900902024269930828566272
y[1] (numeric) = 1.4819089900902024269930828566252
absolute error = 2.0e-30
relative error = 1.3496105451646270486088980236931e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (closed_form) = 1.4867522559599716500561676479956
y[1] (numeric) = 1.4867522559599716500561676479937
absolute error = 1.9e-30
relative error = 1.2779533324287448488003804420915e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (closed_form) = 1.4916441974609651023429154350493
y[1] (numeric) = 1.4916441974609651023429154350474
absolute error = 1.9e-30
relative error = 1.2737622036368503201705559284889e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (closed_form) = 1.4965853037914095147048000933975
y[1] (numeric) = 1.4965853037914095147048000933956
absolute error = 1.9e-30
relative error = 1.2695567671195156024084978262968e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (closed_form) = 1.5015760690660555339170813603031
y[1] (numeric) = 1.5015760690660555339170813603012
absolute error = 1.9e-30
relative error = 1.2653371608284584870114577780857e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (closed_form) = 1.5066169923655896095071471097274
y[1] (numeric) = 1.5066169923655896095071471097255
absolute error = 1.9e-30
relative error = 1.2611035250682700747889908553786e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (closed_form) = 1.511708577786542478301424470106
y[1] (numeric) = 1.5117085777865424783014244701041
absolute error = 1.9e-30
relative error = 1.2568560024856096089590072520175e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (closed_form) = 1.5168513344916992375809050183918
y[1] (numeric) = 1.5168513344916992375809050183899
absolute error = 1.9e-30
relative error = 1.2525947380576322994480148355699e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (closed_form) = 1.5220457767610160478946081372088
y[1] (numeric) = 1.5220457767610160478946081372069
absolute error = 1.9e-30
relative error = 1.2483198790796476932731433122472e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (closed_form) = 1.5272924240430485572436946085663
y[1] (numeric) = 1.5272924240430485572436946085643
absolute error = 2.0e-30
relative error = 1.3095069212126384621817278440586e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (closed_form) = 1.532591801006897189521506018502
y[1] (numeric) = 1.5325918010068971895215060185
absolute error = 2.0e-30
relative error = 1.3049789243854889401414344450334e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (closed_form) = 1.5379444375946744917816618612558
y[1] (numeric) = 1.5379444375946744917816618612539
absolute error = 1.9e-30
relative error = 1.2354152422902714193774961401401e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (closed_form) = 1.5433508690744997871126640878166
y[1] (numeric) = 1.5433508690744997871126640878146
absolute error = 2.0e-30
relative error = 1.2958816041613004698847682979465e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=428.5MB, alloc=44.3MB, time=4.67
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (closed_form) = 1.5488116360940264326284589172326
y[1] (numeric) = 1.5488116360940264326284589172306
absolute error = 2.0e-30
relative error = 1.2913126124515909058182212728237e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (closed_form) = 1.5543272847345070353453611638809
y[1] (numeric) = 1.5543272847345070353453611638789
absolute error = 2.0e-30
relative error = 1.2867302913888035104342524237119e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (closed_form) = 1.5598983665654020325119832698729
y[1] (numeric) = 1.5598983665654020325119832698709
absolute error = 2.0e-30
relative error = 1.2821348126696341259980638678710e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (closed_form) = 1.5655254386995370972957093374648
y[1] (numeric) = 1.5655254386995370972957093374628
absolute error = 2.0e-30
relative error = 1.2775263502976838407616961951719e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (closed_form) = 1.5712090638488148856122474668313
y[1] (numeric) = 1.5712090638488148856122474668293
absolute error = 2.0e-30
relative error = 1.2729050805631326858293178537671e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (closed_form) = 1.5769498103804866953193699648816
y[1] (numeric) = 1.5769498103804866953193699648796
absolute error = 2.0e-30
relative error = 1.2682711820216013654764381847890e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (closed_form) = 1.5827482523739896649876540047778
y[1] (numeric) = 1.5827482523739896649876540047758
absolute error = 2.0e-30
relative error = 1.2636248354722033021785142849033e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.53
y[1] (closed_form) = 1.5886049696783551960154643004118
y[1] (numeric) = 1.5886049696783551960154643004098
absolute error = 2.0e-30
relative error = 1.2589662239347897446906870273212e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (closed_form) = 1.5945205479701943389782298053389
y[1] (numeric) = 1.5945205479701943389782298053369
absolute error = 2.0e-30
relative error = 1.2542955326263911573415376973850e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (closed_form) = 1.6004955788122659427989706801995
y[1] (numeric) = 1.6004955788122659427989706801975
absolute error = 2.0e-30
relative error = 1.2496129489368585808726305387446e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (closed_form) = 1.6065306597126334236037995349912
y[1] (numeric) = 1.6065306597126334236037995349892
absolute error = 2.0e-30
relative error = 1.2449186624037091292778011314910e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (closed_form) = 1.612626394184416068988579968019
y[1] (numeric) = 1.612626394184416068988579968017
absolute error = 2.0e-30
relative error = 1.2402128646861802627704659706149e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (closed_form) = 1.6187833918061408528769619869106
y[1] (numeric) = 1.6187833918061408528769619869086
absolute error = 2.0e-30
relative error = 1.2354957495384979538260989270105e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (closed_form) = 1.6250022682827007962015734619291
y[1] (numeric) = 1.6250022682827007962015734619272
absolute error = 1.9e-30
relative error = 1.1692291371432461237571180976515e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (closed_form) = 1.6312836455069259692952345339618
y[1] (numeric) = 1.6312836455069259692952345339598
absolute error = 2.0e-30
relative error = 1.2260283522786709414583111729537e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (closed_form) = 1.6376281516217732931437434383122
y[1] (numeric) = 1.6376281516217732931437434383103
absolute error = 1.9e-30
relative error = 1.1602145445035217777657615427341e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (closed_form) = 1.644036421083141358532184030009
y[1] (numeric) = 1.644036421083141358532184030007
absolute error = 2.0e-30
relative error = 1.2165180614930288309522375179287e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (closed_form) = 1.6505090947233165446190154984879
y[1] (numeric) = 1.650509094723316544619015498486
absolute error = 1.9e-30
relative error = 1.1511599700203450973419201965462e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (closed_form) = 1.65704681981505678160267362234
y[1] (numeric) = 1.6570468198150567816026736223381
absolute error = 1.9e-30
relative error = 1.1466181747429799572650787755870e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (closed_form) = 1.6636502501363193659103535378148
y[1] (numeric) = 1.6636502501363193659103535378128
absolute error = 2.0e-30
relative error = 1.2021757576967395418586218160873e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (closed_form) = 1.6703200460356393007444329251478
y[1] (numeric) = 1.6703200460356393007444329251458
absolute error = 2.0e-30
relative error = 1.1973753202249040007381573188110e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (closed_form) = 1.6770568744981646998750723870924
y[1] (numeric) = 1.6770568744981646998750723870904
absolute error = 2.0e-30
relative error = 1.1925653985935756738851274646600e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (closed_form) = 1.6838614092123558582744019662858
y[1] (numeric) = 1.6838614092123558582744019662837
absolute error = 2.1e-30
relative error = 1.2471335161616996780954848220909e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (closed_form) = 1.6907343306373546595549399642394
y[1] (numeric) = 1.6907343306373546595549399642373
absolute error = 2.1e-30
relative error = 1.2420638547088381500697108607601e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (closed_form) = 1.6976763260710310572091292638382
y[1] (numeric) = 1.697676326071031057209129263836
absolute error = 2.2e-30
relative error = 1.2958889549290632197375384595673e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (closed_form) = 1.7046880897187134343548206990309
y[1] (numeric) = 1.7046880897187134343548206990287
absolute error = 2.2e-30
relative error = 1.2905586736181261271471900545434e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.34
y[1] (closed_form) = 1.711770322762609715079953510757
y[1] (numeric) = 1.7117703227626097150799535107548
absolute error = 2.2e-30
relative error = 1.2852191504578961790494250035399e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (closed_form) = 1.7189237334319261695554184761104
y[1] (numeric) = 1.7189237334319261695554184761082
absolute error = 2.2e-30
relative error = 1.2798706290520397286684438278995e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (closed_form) = 1.7261490370736909248550475294236
y[1] (numeric) = 1.7261490370736909248550475294214
absolute error = 2.2e-30
relative error = 1.2745133547272488106425539036401e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.31
y[1] (closed_form) = 1.7334469562242892638928316633154
y[1] (numeric) = 1.7334469562242892638928316633133
absolute error = 2.1e-30
relative error = 1.2114590483772972986218942864260e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (closed_form) = 1.7408182206817178660668737793178
y[1] (numeric) = 1.7408182206817178660668737793157
absolute error = 2.1e-30
relative error = 1.2063292853044838730193496569928e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (closed_form) = 1.7482635675785652150943529512748
y[1] (numeric) = 1.7482635675785652150943529512727
absolute error = 2.1e-30
relative error = 1.2011918791561891320168484740884e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (closed_form) = 1.7557837414557254721391008071943
y[1] (numeric) = 1.7557837414557254721391008071922
absolute error = 2.1e-30
relative error = 1.1960470702723809333871322810313e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (closed_form) = 1.7633794943368531856805312195579
y[1] (numeric) = 1.7633794943368531856805312195558
absolute error = 2.1e-30
relative error = 1.1908951004274540983233617723350e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (closed_form) = 1.7710515858035662836569559954336
y[1] (numeric) = 1.7710515858035662836569559954315
absolute error = 2.1e-30
relative error = 1.1857362127863612499428073425063e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (closed_form) = 1.7788007830714048682451702669783
y[1] (numeric) = 1.7788007830714048682451702669762
absolute error = 2.1e-30
relative error = 1.1805706518601760184573796395962e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (closed_form) = 1.7866278610665534092190847475156
y[1] (numeric) = 1.7866278610665534092190847475135
absolute error = 2.1e-30
relative error = 1.1753986634611051840946903221254e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (closed_form) = 1.7945336025033340081706760906637
y[1] (numeric) = 1.7945336025033340081706760906615
absolute error = 2.2e-30
relative error = 1.2259452801168222696567136172310e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (closed_form) = 1.8025187979624784829842553829934
y[1] (numeric) = 1.8025187979624784829842553829912
absolute error = 2.2e-30
relative error = 1.2205143172358724819923490821863e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (closed_form) = 1.8105842459701870998377291515507
y[1] (numeric) = 1.8105842459701870998377291515485
absolute error = 2.2e-30
relative error = 1.2150774010635155947597580747299e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (closed_form) = 1.818730753077981858669935508619
y[1] (numeric) = 1.8187307530779818586699355086168
absolute error = 2.2e-30
relative error = 1.2096347940874513988301355920462e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (closed_form) = 1.8269591339433623175091467937083
y[1] (numeric) = 1.8269591339433623175091467937061
absolute error = 2.2e-30
relative error = 1.2041867599147964014436151683281e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (closed_form) = 1.8352702114112720213123849740188
y[1] (numeric) = 1.8352702114112720213123849740166
absolute error = 2.2e-30
relative error = 1.1987335632218761188396695358287e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (closed_form) = 1.8436648165963836820263226519154
y[1] (numeric) = 1.8436648165963836820263226519132
absolute error = 2.2e-30
relative error = 1.1932754697035721821284102644834e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
memory used=470.9MB, alloc=44.3MB, time=5.13
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (closed_form) = 1.8521437889662113384563469814686
y[1] (numeric) = 1.8521437889662113384563469814664
absolute error = 2.2e-30
relative error = 1.1878127460222444980229246675555e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (closed_form) = 1.8607079764250578072290337645433
y[1] (numeric) = 1.8607079764250578072290337645412
absolute error = 2.1e-30
relative error = 1.1286026752218740538345329567541e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (closed_form) = 1.8693582353988058196630844161712
y[1] (numeric) = 1.8693582353988058196630844161691
absolute error = 2.1e-30
relative error = 1.1233801848322504351846221136878e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (closed_form) = 1.8780954309205613237330724091574
y[1] (numeric) = 1.8780954309205613237330724091553
absolute error = 2.1e-30
relative error = 1.1181540434133693800947598116237e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (closed_form) = 1.8869204367171575155275652287698
y[1] (numeric) = 1.8869204367171575155275652287678
absolute error = 2.0e-30
relative error = 1.0599281035291435015414690775749e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (closed_form) = 1.8958341352965282506768545828765
y[1] (numeric) = 1.8958341352965282506768545828745
absolute error = 2.0e-30
relative error = 1.0549446086891874223081315954198e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (closed_form) = 1.9048374180359595731642490594464
y[1] (numeric) = 1.9048374180359595731642490594444
absolute error = 2.0e-30
relative error = 1.0499583749578799721983863652083e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.09
y[1] (closed_form) = 1.9139311852712281867473535464995
y[1] (numeric) = 1.9139311852712281867473535464975
absolute error = 2.0e-30
relative error = 1.0449696495836002467024030835973e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.08
y[1] (closed_form) = 1.9231163463866357829107598495724
y[1] (numeric) = 1.9231163463866357829107598495704
absolute error = 2.0e-30
relative error = 1.0399786803111635705099427422512e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (closed_form) = 1.932393819905948228857972632485
y[1] (numeric) = 1.9323938199059482288579726324829
absolute error = 2.1e-30
relative error = 1.0867350010994184154529294450113e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.06
y[1] (closed_form) = 1.9417645335842487095371527832712
y[1] (numeric) = 1.9417645335842487095371527832691
absolute error = 2.1e-30
relative error = 1.0814905534007611518152000753399e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (closed_form) = 1.9512294245007140090914253197796
y[1] (numeric) = 1.9512294245007140090914253197776
absolute error = 2.0e-30
relative error = 1.0249947929684206873230026642589e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.04
y[1] (closed_form) = 1.9607894391523232094392106913232
y[1] (numeric) = 1.9607894391523232094392106913212
absolute error = 2.0e-30
relative error = 1.0199973337599309318302838690150e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (closed_form) = 1.9704455335485081769325283519592
y[1] (numeric) = 1.9704455335485081769325283519572
absolute error = 2.0e-30
relative error = 1.0149988751012407798585170921669e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (closed_form) = 1.9801986733067553022208141042253
y[1] (numeric) = 1.9801986733067553022208141042233
absolute error = 2.0e-30
relative error = 1.0099996666799994603393289197088e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (closed_form) = 1.99004983374916805357390597718
y[1] (numeric) = 1.990049833749168053573905977178
absolute error = 2.0e-30
relative error = 1.0049999583337499957837728721422e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (closed_form) = 2
y[1] (numeric) = 1.999999999999999999999999999998
absolute error = 2.0e-30
relative error = 1.0000000000000000000000000000000e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (closed_form) = 2.0100501670841680575421654569029
y[1] (numeric) = 2.0100501670841680575421654569009
absolute error = 2.0e-30
relative error = 9.9500004166625000421622712785780e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (closed_form) = 2.0202013400267558101601439204832
y[1] (numeric) = 2.0202013400267558101601439204812
absolute error = 2.0e-30
relative error = 9.9000033332000053966067108029114e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (closed_form) = 2.0304545339535168556124399538312
y[1] (numeric) = 2.0304545339535168556124399538293
absolute error = 1.9e-30
relative error = 9.3575106865382125913440876244146e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (closed_form) = 2.0408107741923882267570447579169
y[1] (numeric) = 2.0408107741923882267570447579149
absolute error = 2.0e-30
relative error = 9.8000266624006906816971613098497e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (closed_form) = 2.0512710963760240396975176363356
y[1] (numeric) = 2.0512710963760240396975176363336
absolute error = 2.0e-30
relative error = 9.7500520703157931267699733574113e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (closed_form) = 2.0618365465453596222246848771684
y[1] (numeric) = 2.0618365465453596222246848771663
absolute error = 2.1e-30
relative error = 1.0185094465992388481847999246601e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (closed_form) = 2.0725081812542164790531039498891
y[1] (numeric) = 2.072508181254216479053103949887
absolute error = 2.1e-30
relative error = 1.0132649989005815845470705549887e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (closed_form) = 2.0832870676749585544359877586749
y[1] (numeric) = 2.0832870676749585544359877586727
absolute error = 2.2e-30
relative error = 1.0560234516577200724390629835237e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (closed_form) = 2.0941742837052103578728976235449
y[1] (numeric) = 2.0941742837052103578728976235427
absolute error = 2.2e-30
relative error = 1.0505333854580397286273566080429e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 2.1051709180756476248117078264902
y[1] (numeric) = 2.1051709180756476248117078264881
absolute error = 2.1e-30
relative error = 9.9754370629422602919169431653132e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 2.116278070458871291500737769053
y[1] (numeric) = 2.1162780704588712915007377690509
absolute error = 2.1e-30
relative error = 9.9230816087635320657646182480923e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 2.1274968515793756714792655693748
y[1] (numeric) = 2.1274968515793756714792655693728
absolute error = 2.0e-30
relative error = 9.4007189647085649845853092242510e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 2.138828383324621830615712602619
y[1] (numeric) = 2.1388283833246218306157126026169
absolute error = 2.1e-30
relative error = 9.8184595658663061990524018837627e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 2.1502737988572272681235642576211
y[1] (numeric) = 2.1502737988572272681235642576191
absolute error = 2.0e-30
relative error = 9.3011410968357101410988370124977e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 2.1618342427282831226166202143317
y[1] (numeric) = 2.1618342427282831226166202143297
absolute error = 2.0e-30
relative error = 9.2514030931250090110996861261514e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 2.173510870991810235018611086892
y[1] (numeric) = 2.17351087099181023501861108689
absolute error = 2.0e-30
relative error = 9.2017023088886863816097757494948e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 2.1853048513203655140288527643693
y[1] (numeric) = 2.1853048513203655140288527643673
absolute error = 2.0e-30
relative error = 9.1520411845129801624689975956055e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 2.1972173631218101648768239736005
y[1] (numeric) = 2.1972173631218101648768239735985
absolute error = 2.0e-30
relative error = 9.1024221525283989196393678561023e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 2.2092495976572514582858497035543
y[1] (numeric) = 2.2092495976572514582858497035523
absolute error = 2.0e-30
relative error = 9.0528476371382145323307711970177e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 2.2214027581601698339210719946397
y[1] (numeric) = 2.2214027581601698339210719946377
absolute error = 2.0e-30
relative error = 9.0033200537504418288169491632164e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 2.2336780599567432511313258071563
y[1] (numeric) = 2.2336780599567432511313258071543
absolute error = 2.0e-30
relative error = 8.9538418085134945930931084115467e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 2.2460767305873808195202647829927
y[1] (numeric) = 2.2460767305873808195202647829907
absolute error = 2.0e-30
relative error = 8.9044152978557047091604628892155e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 2.258600009929477862811072376219
y[1] (numeric) = 2.258600009929477862811072376217
absolute error = 2.0e-30
relative error = 8.8550429080288884576662398433541e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 2.2712491503214046916134410512278
y[1] (numeric) = 2.2712491503214046916134410512258
absolute error = 2.0e-30
relative error = 8.8057270146561411038600921702341e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 2.2840254166877414840734205680624
y[1] (numeric) = 2.2840254166877414840734205680604
absolute error = 2.0e-30
relative error = 8.7564699822840379194535272419412e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 2.2969300866657717979985630881788
y[1] (numeric) = 2.2969300866657717979985630881768
absolute error = 2.0e-30
relative error = 8.7072741639394166672113586427968e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=513.1MB, alloc=44.3MB, time=5.58
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 2.3099644507332473639149892266262
y[1] (numeric) = 2.3099644507332473639149892266241
absolute error = 2.1e-30
relative error = 9.0910489957254590167663822766501e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 2.3231298123374369356421517730364
y[1] (numeric) = 2.3231298123374369356421517730342
absolute error = 2.2e-30
relative error = 9.4699830733369616502300427701480e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 2.3364274880254721033778956250755
y[1] (numeric) = 2.3364274880254721033778956250733
absolute error = 2.2e-30
relative error = 9.4160850755065900455377778905025e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 2.349858807576003103983744313328
y[1] (numeric) = 2.3498588075760031039837443133257
absolute error = 2.3e-30
relative error = 9.7878221133318432955023608996030e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 2.3634251141321777941611551872143
y[1] (numeric) = 2.363425114132177794161155187212
absolute error = 2.3e-30
relative error = 9.7316389939629343484268721010485e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 2.3771277643359570845268770678281
y[1] (numeric) = 2.3771277643359570845268770678258
absolute error = 2.3e-30
relative error = 9.6755422005787624341914819164900e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 2.3909681284637802662427478049531
y[1] (numeric) = 2.3909681284637802662427478049507
absolute error = 2.4e-30
relative error = 1.0037774955795930232707885513823e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 2.4049475905635937968456495337223
y[1] (numeric) = 2.4049475905635937968456495337199
absolute error = 2.4e-30
relative error = 9.9794274495502235012789999613830e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 2.4190675485932572482703956619399
y[1] (numeric) = 2.4190675485932572482703956619375
absolute error = 2.4e-30
relative error = 9.9211781059840786129397448595266e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 2.4333294145603402577756905512456
y[1] (numeric) = 2.4333294145603402577756905512433
absolute error = 2.3e-30
relative error = 9.4520700166507027027439161045238e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 2.4477346146633244615847523355192
y[1] (numeric) = 2.4477346146633244615847523355169
absolute error = 2.3e-30
relative error = 9.3964434960460583563793572392946e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 2.46228458943422453155163160907
y[1] (numeric) = 2.4622845894342245315516316090677
absolute error = 2.3e-30
relative error = 9.3409186325147178113351662342430e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 2.4769807938826425770757438765387
y[1] (numeric) = 2.4769807938826425770757438765364
absolute error = 2.3e-30
relative error = 9.2854979161738797503210341564104e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 2.4918246976412703178248529528372
y[1] (numeric) = 2.4918246976412703178248529528349
absolute error = 2.3e-30
relative error = 9.2301838174136039915111908336734e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 2.5068177851128535776050298262424
y[1] (numeric) = 2.5068177851128535776050298262401
absolute error = 2.3e-30
relative error = 9.1749787864874952686258491149961e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 2.5219615556186337959494448003237
y[1] (numeric) = 2.5219615556186337959494448003214
absolute error = 2.3e-30
relative error = 9.1198852531112952541595727165787e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 2.5372575235482814017008534659144
y[1] (numeric) = 2.5372575235482814017008534659121
absolute error = 2.3e-30
relative error = 9.0649056260695067163872818312824e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 2.5527072185113360420500796461917
y[1] (numeric) = 2.5527072185113360420500796461894
absolute error = 2.3e-30
relative error = 9.0100422928301684440492685438199e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 2.5683121854901688111795997746932
y[1] (numeric) = 2.5683121854901688111795997746909
absolute error = 2.3e-30
relative error = 8.9552976191678942691513076405870e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 2.5840739849944817748625620134736
y[1] (numeric) = 2.5840739849944817748625620134713
absolute error = 2.3e-30
relative error = 8.9006739487952841732294215110320e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 2.5999941932173602410984500463115
y[1] (numeric) = 2.5999941932173602410984500463091
absolute error = 2.4e-30
relative error = 9.2307898466116279104364029770333e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 2.616074402192893382142499105688
y[1] (numeric) = 2.6160744021928933821424991056856
absolute error = 2.4e-30
relative error = 9.1740510055380245540868128758740e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 2.6323162199553789701224181313345
y[1] (numeric) = 2.6323162199553789701224181313321
absolute error = 2.4e-30
relative error = 9.1174456237658368467544083526214e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 2.6487212707001281468486507878142
y[1] (numeric) = 2.6487212707001281468486507878118
absolute error = 2.4e-30
relative error = 9.0609760511554904486663864221077e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 2.6652911949458863084291607887622
y[1] (numeric) = 2.6652911949458863084291607887598
absolute error = 2.4e-30
relative error = 9.0046446127576970295284335350648e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 2.6820276496988863469125541946667
y[1] (numeric) = 2.6820276496988863469125541946643
absolute error = 2.4e-30
relative error = 8.9484536084833061119015476313801e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 2.6989323086185506544204144868253
y[1] (numeric) = 2.6989323086185506544204144868229
absolute error = 2.4e-30
relative error = 8.8924053127825230637117556721452e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 2.716006862184858460107349114715
y[1] (numeric) = 2.7160068621848584601073491147126
absolute error = 2.4e-30
relative error = 8.8365019743335603738578285811597e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 2.7332530178673952368219167671373
y[1] (numeric) = 2.7332530178673952368219167671349
absolute error = 2.4e-30
relative error = 8.7807458157407836142827417825315e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 2.7506725002961010825499764350019
y[1] (numeric) = 2.7506725002961010825499764349994
absolute error = 2.5e-30
relative error = 9.0886864929608414271335268279109e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 2.7682670514337351516208933928238
y[1] (numeric) = 2.7682670514337351516208933928213
absolute error = 2.5e-30
relative error = 9.0309206212789519904787975603513e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 2.7860384307500733822634435579423
y[1] (numeric) = 2.7860384307500733822634435579397
absolute error = 2.6e-30
relative error = 9.3322474352947563620251697176761e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 2.8039884153978569404293370747409
y[1] (numeric) = 2.8039884153978569404293370747383
absolute error = 2.6e-30
relative error = 9.2725062119455543643547184917455e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 2.8221188003905089748753676681629
y[1] (numeric) = 2.8221188003905089748753676681603
absolute error = 2.6e-30
relative error = 9.2129360381293182243631234532909e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 2.8404313987816374553277937710156
y[1] (numeric) = 2.840431398781637455327793771013
absolute error = 2.6e-30
relative error = 9.1535391459030938914980121266949e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 2.8589280418463420441623540602681
y[1] (numeric) = 2.8589280418463420441623540602654
absolute error = 2.7e-30
relative error = 9.4440991885066693035829495874831e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 2.8776105792643431324381749672586
y[1] (numeric) = 2.8776105792643431324381749672559
absolute error = 2.7e-30
relative error = 9.3827845207958993080906349920492e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 2.8964808793049513533417815912859
y[1] (numeric) = 2.8964808793049513533417815912832
absolute error = 2.7e-30
relative error = 9.3216565636293807605466741052086e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 2.9155408290138960701466981926821
y[1] (numeric) = 2.9155408290138960701466981926793
absolute error = 2.8e-30
relative error = 9.6037070451420339938694669774107e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 2.9347923344020315216931251510197
y[1] (numeric) = 2.9347923344020315216931251510169
absolute error = 2.8e-30
relative error = 9.5407091233612082186608340021272e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 2.9542373206359394961594960015662
y[1] (numeric) = 2.9542373206359394961594960015634
absolute error = 2.8e-30
relative error = 9.4779115423173320784988404965844e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 2.9738777322304475935521277966183
y[1] (numeric) = 2.9738777322304475935521277966155
absolute error = 2.8e-30
relative error = 9.4153164726781252136359242365251e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 2.9937155332430823288996461769344
y[1] (numeric) = 2.9937155332430823288996461769315
absolute error = 2.9e-30
relative error = 9.6869591241972125666672233871126e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 3.0137527074704765216245493885831
y[1] (numeric) = 3.0137527074704765216245493885802
absolute error = 2.9e-30
relative error = 9.6225546071231829106071384407336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=555.6MB, alloc=44.3MB, time=6.03
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 3.0339912586467506119945217716624
y[1] (numeric) = 3.0339912586467506119945217716596
absolute error = 2.8e-30
relative error = 9.2287675253516794922233863170067e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 3.0544332106438877429504601670086
y[1] (numeric) = 3.0544332106438877429504601670057
absolute error = 2.9e-30
relative error = 9.4943965050349470446257721996563e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 3.0750806076741226449863758349892
y[1] (numeric) = 3.0750806076741226449863758349864
absolute error = 2.8e-30
relative error = 9.1054523676952213194754276682967e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 3.0959355144943645631383178428338
y[1] (numeric) = 3.0959355144943645631383178428309
absolute error = 2.9e-30
relative error = 9.3671201690828330766540763484085e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 3.1170000166126746685453698198371
y[1] (numeric) = 3.1170000166126746685453698198342
absolute error = 2.9e-30
relative error = 9.3038177239136037783692766424792e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 3.138276220496818602495941263298
y[1] (numeric) = 3.1382762204968186024959412632951
absolute error = 2.9e-30
relative error = 9.2407417201182589378907208484399e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 3.15976625378491500838755239034
y[1] (numeric) = 3.1597662537849150083875523903371
absolute error = 2.9e-30
relative error = 9.1778940816468468023492425720675e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 3.181472265498201116628849542537
y[1] (numeric) = 3.181472265498201116628849542534
absolute error = 3.0e-30
relative error = 9.4295965818523847648760059412528e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 3.203396426255936659219646589984
y[1] (numeric) = 3.203396426255936659219646589981
absolute error = 3.0e-30
relative error = 9.3650600825147882615168708008465e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 3.2255409284924676045795375313951
y[1] (numeric) = 3.2255409284924676045795375313921
absolute error = 3.0e-30
relative error = 9.3007655661716267209837781415468e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 3.2479079866764714191794502001334
y[1] (numeric) = 3.2479079866764714191794502001304
absolute error = 3.0e-30
relative error = 9.2367148709463551849202500476910e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 3.2704998375324057806850092252533
y[1] (numeric) = 3.2704998375324057806850092252503
absolute error = 3.0e-30
relative error = 9.1729097967590847485809889001225e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 3.2933187402641828876675637932731
y[1] (numeric) = 3.2933187402641828876675637932701
absolute error = 3.0e-30
relative error = 9.1093521052849761684607586426407e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 3.3163669767810917335002471928655
y[1] (numeric) = 3.3163669767810917335002471928625
absolute error = 3.0e-30
relative error = 9.0460435199238367357641944082222e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 3.3396468519259909368547269375638
y[1] (numeric) = 3.3396468519259909368547269375607
absolute error = 3.1e-30
relative error = 9.2824185833068385468538791288812e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 3.3631606937057949482718564674462
y[1] (numeric) = 3.3631606937057949482718564674431
absolute error = 3.1e-30
relative error = 9.2175197153133239088244825058210e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 3.3869108535242766816189579740184
y[1] (numeric) = 3.3869108535242766816189579740153
absolute error = 3.1e-30
relative error = 9.1528833620591774942988860992888e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 3.4108997064172098508908849161329
y[1] (numeric) = 3.4108997064172098508908849161298
absolute error = 3.1e-30
relative error = 9.0885111460994050171921770535701e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 3.4351296512898745267844969337052
y[1] (numeric) = 3.4351296512898745267844969337021
absolute error = 3.1e-30
relative error = 9.0244046504502822250067413763146e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 3.4596031111569496638001265636025
y[1] (numeric) = 3.4596031111569496638001265635994
absolute error = 3.1e-30
relative error = 8.9605654186248771326439546591896e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 3.4843225333848165873226590099968
y[1] (numeric) = 3.4843225333848165873226590099936
absolute error = 3.2e-30
relative error = 9.1839947919269867621585028315784e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 3.5092903899362976712328533227943
y[1] (numeric) = 3.509290389936297671232853322791
absolute error = 3.3e-30
relative error = 9.4036105118673384816196899699596e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 3.5345091776178546801206156940979
y[1] (numeric) = 3.5345091776178546801206156940946
absolute error = 3.3e-30
relative error = 9.3365155787319066716519810271275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 3.5599814183292714961404455052082
y[1] (numeric) = 3.5599814183292714961404455052049
absolute error = 3.3e-30
relative error = 9.2697113052593321962466652775039e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 3.5857096593158461989898093013769
y[1] (numeric) = 3.5857096593158461989898093013736
absolute error = 3.3e-30
relative error = 9.2031991252455179717452034884601e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 3.6116964734231177184286012988948
y[1] (numeric) = 3.6116964734231177184286012988915
absolute error = 3.3e-30
relative error = 9.1369804308951356574179293783293e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 3.6379444593541525322172152885726
y[1] (numeric) = 3.6379444593541525322172152885692
absolute error = 3.4e-30
relative error = 9.3459370751460152291715578437640e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 3.6644562419294171383574280391061
y[1] (numeric) = 3.6644562419294171383574280391027
absolute error = 3.4e-30
relative error = 9.2783206444015958923051637196546e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 3.691234472349262289099879404071
y[1] (numeric) = 3.6912344723492622890998794040676
absolute error = 3.4e-30
relative error = 9.2110106401235790525818142293280e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 3.7182818284590452353602874713527
y[1] (numeric) = 3.7182818284590452353602874713493
absolute error = 3.4e-30
relative error = 9.1440083265798341054605857780575e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 3.7456010150169164939897763166604
y[1] (numeric) = 3.745601015016916493989776316657
absolute error = 3.4e-30
relative error = 9.0773149258788428795353323832537e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = 3.7731947639642979167991997771454
y[1] (numeric) = 3.773194763964297916799199777142
absolute error = 3.4e-30
relative error = 9.0109316181383604375073539476780e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 3.8010658346990791093697628196836
y[1] (numeric) = 3.8010658346990791093697628196801
absolute error = 3.5e-30
relative error = 9.2079436458302918614868675790191e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 3.8292170143515595195194860071813
y[1] (numeric) = 3.8292170143515595195194860071779
absolute error = 3.4e-30
relative error = 8.8790997931355341938214066438680e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 3.8576511180631637898643122162488
y[1] (numeric) = 3.8576511180631637898643122162453
absolute error = 3.5e-30
relative error = 9.0728785286246102173186530527498e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = 3.8863709892679582462413752849215
y[1] (numeric) = 3.8863709892679582462413752849181
absolute error = 3.4e-30
relative error = 8.7485214597086839082647918893761e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 3.9153794999769966738778707729755
y[1] (numeric) = 3.9153794999769966738778707729721
absolute error = 3.4e-30
relative error = 8.6837048618658176288877792136528e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 3.9446795510655238161201013252344
y[1] (numeric) = 3.9446795510655238161201013252309
absolute error = 3.5e-30
relative error = 8.8727105831818241256324339543256e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = 3.9742740725630653163119065891359
y[1] (numeric) = 3.9742740725630653163119065891324
absolute error = 3.5e-30
relative error = 8.8066397437527520892723295442523e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 4.0041660239464331120584079535887
y[1] (numeric) = 4.0041660239464331120584079535851
absolute error = 3.6e-30
relative error = 8.9906361985757662484408336731657e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 4.0343583944356755826586664593838
y[1] (numeric) = 4.0343583944356755826586664593802
absolute error = 3.6e-30
relative error = 8.9233519881754742841727017035141e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 4.0648542032930020449686230918988
y[1] (numeric) = 4.0648542032930020449686230918952
absolute error = 3.6e-30
relative error = 8.8564062078378693746302358801922e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 4.0956565001247114903930123270235
y[1] (numeric) = 4.0956565001247114903930123270199
absolute error = 3.6e-30
relative error = 8.7897996325873058415821944359194e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 4.1267683651861557561315562411795
y[1] (numeric) = 4.1267683651861557561315562411759
absolute error = 3.6e-30
relative error = 8.7235329958666250750460689652119e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=598.0MB, alloc=44.3MB, time=6.50
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 4.1581929096897676272507006280068
y[1] (numeric) = 4.1581929096897676272507006280032
absolute error = 3.6e-30
relative error = 8.6576069898320013149141031866840e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 4.1899332761161846726477912360218
y[1] (numeric) = 4.1899332761161846726477912360182
absolute error = 3.6e-30
relative error = 8.5920222656552248889994767801619e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = 4.2219926385284999275505572724101
y[1] (numeric) = 4.2219926385284999275505572724065
absolute error = 3.6e-30
relative error = 8.5267794338332045397990032314704e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 4.2543742028896708478820285629729
y[1] (numeric) = 4.2543742028896708478820285629693
absolute error = 3.6e-30
relative error = 8.4618790645044704222299440158303e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (closed_form) = 4.2870812073831182776508312036078
y[1] (numeric) = 4.2870812073831182776508312036042
absolute error = 3.6e-30
relative error = 8.3973216877724594448300695294736e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 4.3201169227365474895307674296016
y[1] (numeric) = 4.320116922736547489530767429598
absolute error = 3.6e-30
relative error = 8.3331077940353648544871445113159e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = 4.3534846525490236810035894273757
y[1] (numeric) = 4.353484652549023681003589427372
absolute error = 3.7e-30
relative error = 8.4989388852757304468800445988550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 4.3871877336213346338871451880633
y[1] (numeric) = 4.3871877336213346338871451880595
absolute error = 3.8e-30
relative error = 8.6615851217822178341405163238563e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 4.4212295362896735737901523514522
y[1] (numeric) = 4.4212295362896735737901523514484
absolute error = 3.8e-30
relative error = 8.5948941777607554386834416071939e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 4.455613464762675598057615494122
y[1] (numeric) = 4.4556134647626755980576154941181
absolute error = 3.9e-30
relative error = 8.7530034435061348633907420021984e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 4.4903429574618413761305460296723
y[1] (numeric) = 4.4903429574618413761305460296683
absolute error = 4.0e-30
relative error = 8.9080055530123541200192180935383e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 4.5254214873653821649737080556228
y[1] (numeric) = 4.5254214873653821649737080556187
absolute error = 4.1e-30
relative error = 9.0599295810277004845923999203776e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 4.5608525623555205243594713895519
y[1] (numeric) = 4.5608525623555205243594713895479
absolute error = 4.0e-30
relative error = 8.7702900835148684796980994434550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = 4.5966397255692814623687184072408
y[1] (numeric) = 4.5966397255692814623687184072367
absolute error = 4.1e-30
relative error = 8.9195591666523876447427738023545e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 4.6327865557528090905156817025115
y[1] (numeric) = 4.6327865557528090905156817025073
absolute error = 4.2e-30
relative error = 9.0658180545456123988377596812272e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = 4.6692966676192442204574899160115
y[1] (numeric) = 4.6692966676192442204574899160073
absolute error = 4.2e-30
relative error = 8.9949307122125382707122841651460e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 4.7061737122101986903463250122245
y[1] (numeric) = 4.7061737122101986903463250122203
absolute error = 4.2e-30
relative error = 8.9244474531466450963176812393769e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 4.7434213772608625685580558298259
y[1] (numeric) = 4.7434213772608625685580558298216
absolute error = 4.3e-30
relative error = 9.0651866195431264832299677004513e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 4.7810433875687807458219777860331
y[1] (numeric) = 4.7810433875687807458219777860287
absolute error = 4.4e-30
relative error = 9.2030120693747856029176725550884e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 4.8190435053663357937181865600786
y[1] (numeric) = 4.8190435053663357937181865600742
absolute error = 4.4e-30
relative error = 9.1304425766239668076402092391188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 4.8574255306969743381388389099302
y[1] (numeric) = 4.8574255306969743381388389099257
absolute error = 4.5e-30
relative error = 9.2641667310426298031631814297340e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 4.8961933017952145706641697713002
y[1] (numeric) = 4.8961933017952145706641697712957
absolute error = 4.5e-30
relative error = 9.1908136027841297654697328047964e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 4.9353506954704728989210772223787
y[1] (numeric) = 4.9353506954704728989210772223742
absolute error = 4.5e-30
relative error = 9.1178930894008694971122242009679e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 4.9749016274947481189091677809396
y[1] (numeric) = 4.9749016274947481189091677809351
absolute error = 4.5e-30
relative error = 9.0454049887738218179309035303198e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 5.0148500529942018780345658588566
y[1] (numeric) = 5.0148500529942018780345658588521
absolute error = 4.5e-30
relative error = 8.9733490581900811566055810986617e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 5.0551999668446745872241088952286
y[1] (numeric) = 5.0551999668446745872241088952241
absolute error = 4.5e-30
relative error = 8.9017250148638213330545383801639e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (closed_form) = 5.0959554040711763340407372797126
y[1] (numeric) = 5.095955404071176334040737279708
absolute error = 4.6e-30
relative error = 9.0267665928258401701039022830173e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 5.1371204402513927462243008090194
y[1] (numeric) = 5.1371204402513927462243008090147
absolute error = 4.7e-30
relative error = 9.1490944288041617389210892244623e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 5.1786991919232461565803917643529
y[1] (numeric) = 5.1786991919232461565803917643482
absolute error = 4.7e-30
relative error = 9.0756381589611722151916653301832e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 5.2206958169965528256733289292909
y[1] (numeric) = 5.2206958169965528256733289292861
absolute error = 4.8e-30
relative error = 9.1941767309504394996207856841164e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 5.2631145151688173883886106755809
y[1] (numeric) = 5.2631145151688173883886106755761
absolute error = 4.8e-30
relative error = 9.1200751687350228077084383205391e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 5.3059595283452061041559898892827
y[1] (numeric) = 5.3059595283452061041559898892779
absolute error = 4.8e-30
relative error = 9.0464316102633334272404567779886e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 5.3492351410627409085081719198621
y[1] (numeric) = 5.3492351410627409085081719198573
absolute error = 4.8e-30
relative error = 8.9732454704662253745027714530507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 5.3929456809187566857337876433172
y[1] (numeric) = 5.3929456809187566857337876433124
absolute error = 4.8e-30
relative error = 8.9005161260631483502533797018715e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 5.4370955190036646087089558540139
y[1] (numeric) = 5.437095519003664608708955854009
absolute error = 4.9e-30
relative error = 9.0121646435557083217321129651930e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 5.4816890703380648226020554601193
y[1] (numeric) = 5.4816890703380648226020554601144
absolute error = 4.9e-30
relative error = 8.9388506665114606792463582458438e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 5.5267307943142521840843397438116
y[1] (numeric) = 5.5267307943142521840843397438066
absolute error = 5.0e-30
relative error = 9.0469396576071006387646642152259e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 5.5722251951421592069882364234397
y[1] (numeric) = 5.5722251951421592069882364234347
absolute error = 5.0e-30
relative error = 8.9730759703663402706048604042101e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 5.6181768222997808090795197077546
y[1] (numeric) = 5.6181768222997808090795197077496
absolute error = 5.0e-30
relative error = 8.8996842893123247880569574795720e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 5.6645902709881259027933867662438
y[1] (numeric) = 5.6645902709881259027933867662388
absolute error = 5.0e-30
relative error = 8.8267637389558355668503337140912e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 5.7114701825907413254726398125845
y[1] (numeric) = 5.7114701825907413254726398125795
absolute error = 5.0e-30
relative error = 8.7543134082019909061718801031274e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 5.758821245137854061883935504415
y[1] (numeric) = 5.7588212451378540618839355044099
absolute error = 5.1e-30
relative error = 8.8559789979692566969355745211219e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 5.8066481937751781736211397590791
y[1] (numeric) = 5.806648193775178173621139759074
absolute error = 5.1e-30
relative error = 8.7830359784277673409572108114358e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 5.8549558112374333164794020642401
y[1] (numeric) = 5.854955811237433316479402064235
memory used=640.4MB, alloc=44.3MB, time=6.95
absolute error = 5.1e-30
relative error = 8.7105695831410982062235424646059e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 5.9037489283266221980462867706038
y[1] (numeric) = 5.9037489283266221980462867705986
absolute error = 5.2e-30
relative error = 8.8079626405689730378093385460374e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 5.953032424395114803654286356424
y[1] (numeric) = 5.9530324243951148036542863564188
absolute error = 5.2e-30
relative error = 8.7350439730359269441940389335936e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 6.0028112278335876995198834453142
y[1] (numeric) = 6.002811227833587699519883445309
absolute error = 5.2e-30
relative error = 8.6626079059239016452679363783167e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 6.053090316563867207406092924905
y[1] (numeric) = 6.0530903165638672074060929248997
absolute error = 5.3e-30
relative error = 8.7558581201025745166452591089580e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 6.1038747185367257355366544351225
y[1] (numeric) = 6.1038747185367257355366544351171
absolute error = 5.4e-30
relative error = 8.8468395060613813795734711975437e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 6.1551695122346810458097983038692
y[1] (numeric) = 6.1551695122346810458097983038638
absolute error = 5.4e-30
relative error = 8.7731133793575881256939179249896e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 6.2069798271798487376573070927123
y[1] (numeric) = 6.2069798271798487376573070927069
absolute error = 5.4e-30
relative error = 8.6998832771356028083384402263108e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 6.2593108444468987342204704726538
y[1] (numeric) = 6.2593108444468987342204704726484
absolute error = 5.4e-30
relative error = 8.6271478349581289068545163128969e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 6.3121677971811670669190161888314
y[1] (numeric) = 6.3121677971811670669190161888259
absolute error = 5.5e-30
relative error = 8.7133298364725698673355963622063e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 6.3655559711219747700232352669232
y[1] (numeric) = 6.3655559711219747700232352669176
absolute error = 5.6e-30
relative error = 8.7973462575853526672911972679169e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 6.4194807051312062175548592062532
y[1] (numeric) = 6.4194807051312062175548592062475
absolute error = 5.7e-30
relative error = 8.8792228870536017523808664636511e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 6.4739473917271997607908626630091
y[1] (numeric) = 6.4739473917271997607908626630034
absolute error = 5.7e-30
relative error = 8.8045201097614781470353646273100e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 6.528961477624004055878852351461
y[1] (numeric) = 6.5289614776240040558788523514553
absolute error = 5.7e-30
relative error = 8.7303317986099119923631460757858e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 6.5845284642760540076461854730193
y[1] (numeric) = 6.5845284642760540076461854730135
absolute error = 5.8e-30
relative error = 8.8085274920862382780259161515741e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 6.640653908428320797651096717808
y[1] (numeric) = 6.6406539084283207976510967178022
absolute error = 5.8e-30
relative error = 8.7340796252589485270553411979485e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 6.6973434226719910119370988363601
y[1] (numeric) = 6.6973434226719910119370988363542
absolute error = 5.9e-30
relative error = 8.8094631373197812927876331147203e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 6.7546026760057304368664997048427
y[1] (numeric) = 6.7546026760057304368664997048367
absolute error = 6.0e-30
relative error = 8.8828318819013681823710919110594e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 6.8124373944025886498803406244497
y[1] (numeric) = 6.8124373944025886498803406244436
absolute error = 6.1e-30
relative error = 8.9542107278843253311396210935983e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 6.8708533613826010961162539158285
y[1] (numeric) = 6.8708533613826010961162539158224
absolute error = 6.1e-30
relative error = 8.8780820651548811406021341896507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 6.9298564185911459115690715820469
y[1] (numeric) = 6.9298564185911459115690715820406
absolute error = 6.3e-30
relative error = 9.0910974477026797919602349963340e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 6.9894524663831133289584667268155
y[1] (numeric) = 6.9894524663831133289584667268091
absolute error = 6.4e-30
relative error = 9.1566543027251719616975633098565e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 7.0496474644129460837310239530277
y[1] (numeric) = 7.0496474644129460837310239530213
absolute error = 6.4e-30
relative error = 9.0784681536312185340337989421410e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 7.1104474322306098247290409259947
y[1] (numeric) = 7.1104474322306098247290409259883
absolute error = 6.4e-30
relative error = 9.0008400469845872639243431281400e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 7.1718584498835531270637716458996
y[1] (numeric) = 7.1718584498835531270637716458931
absolute error = 6.5e-30
relative error = 9.0632017425072550758032802140916e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 7.2338866585247173036960337699729
y[1] (numeric) = 7.2338866585247173036960337699663
absolute error = 6.6e-30
relative error = 9.1237260293846067995996501478453e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 7.2965382610266568172120145770248
y[1] (numeric) = 7.2965382610266568172120145770182
absolute error = 6.6e-30
relative error = 9.0453853099803376494868505870989e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 7.3598195226018317043472218706367
y[1] (numeric) = 7.3598195226018317043472218706301
absolute error = 6.6e-30
relative error = 8.9676112026002214876072702607811e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 7.4237367714291340430179442929097
y[1] (numeric) = 7.423736771429134043017944292903
absolute error = 6.7e-30
relative error = 9.0251044807858827064412611860531e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 7.4882963992867111150290313243491
y[1] (numeric) = 7.4882963992867111150290313243423
absolute error = 6.8e-30
relative error = 9.0808371322584480219922380734408e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 7.5535048621911485473016181413198
y[1] (numeric) = 7.5535048621911485473016181413129
absolute error = 6.9e-30
relative error = 9.1348322744025116748384537504162e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 7.6193686810430773504675724967601
y[1] (numeric) = 7.6193686810430773504675724967531
absolute error = 7.0e-30
relative error = 9.1871128606966332883655651241380e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 7.6858944422792694160725307276929
y[1] (numeric) = 7.6858944422792694160725307276859
absolute error = 7.0e-30
relative error = 9.1075932054098496508728193751888e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 7.7530887985312866824806579188518
y[1] (numeric) = 7.7530887985312866824806579188447
absolute error = 7.1e-30
relative error = 9.1576405023827340353568554232878e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 7.8209584692907498349465988329418
y[1] (numeric) = 7.8209584692907498349465988329347
absolute error = 7.1e-30
relative error = 9.0781712086547743077481695211079e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 7.8895102415812930672790192339938
y[1] (numeric) = 7.8895102415812930672790192339867
absolute error = 7.1e-30
relative error = 8.9992911886719958465923492732269e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 7.958750970637272101131868125876
y[1] (numeric) = 7.9587509706372721011318681258688
absolute error = 7.2e-30
relative error = 9.0466456691048878372247917098420e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 8.0286875805892933342908819335644
y[1] (numeric) = 8.0286875805892933342908819335572
absolute error = 7.2e-30
relative error = 8.9678417894939823540220482468983e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 8.099327065156632671441435472082
y[1] (numeric) = 8.0993270651566326714414354720748
absolute error = 7.2e-30
relative error = 8.8896274246961273823247928469594e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 8.1706764883466132798778341038975
y[1] (numeric) = 8.1706764883466132798778341038903
absolute error = 7.2e-30
relative error = 8.8119998512595183574317466073189e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 8.2427429851610122085124347531447
y[1] (numeric) = 8.2427429851610122085124347531374
absolute error = 7.3e-30
relative error = 8.8562751660967907246125211806778e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 8.315533762309566511435170833514
y[1] (numeric) = 8.3155337623095665114351708335066
absolute error = 7.4e-30
relative error = 8.8990078226135599920758549955304e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 8.389056098930650227230427460575
y[1] (numeric) = 8.3890560989306502272304274605676
absolute error = 7.4e-30
relative error = 8.8210162296366991395800435436226e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 8.4633173473191942823497647873654
y[1] (numeric) = 8.4633173473191942823497647873579
absolute error = 7.5e-30
relative error = 8.8617733356952156150510096681689e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 8.5383249336619221111374286770603
y[1] (numeric) = 8.5383249336619221111374286770528
absolute error = 7.5e-30
relative error = 8.7839243156835392683797453438307e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=682.8MB, alloc=44.3MB, time=7.41
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 8.6140863587799745166833496561362
y[1] (numeric) = 8.6140863587799745166833496561286
absolute error = 7.6e-30
relative error = 8.8227580772436079555830008516027e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 8.6906091988789980356085715614843
y[1] (numeric) = 8.6906091988789980356085715614766
absolute error = 7.7e-30
relative error = 8.8601383675073356784649328387926e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 8.7679011063067718162446641452442
y[1] (numeric) = 8.7679011063067718162446641452365
absolute error = 7.7e-30
relative error = 8.7820333585438959302374984205931e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 8.8459698103184487735262954149556
y[1] (numeric) = 8.8459698103184487735262954149478
absolute error = 7.8e-30
relative error = 8.8175747456221596732738778102145e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 8.9248231178494875453501560543463
y[1] (numeric) = 8.9248231178494875453501560543385
absolute error = 7.8e-30
relative error = 8.7396690074452441417156329302508e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 9.0044689142963525442399839278696
y[1] (numeric) = 9.0044689142963525442399839278617
absolute error = 7.9e-30
relative error = 8.7734213702011981042473982634577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 9.0849151643050601749734407164419
y[1] (numeric) = 9.084915164305060174973440716434
absolute error = 7.9e-30
relative error = 8.6957333746377379000928030639600e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 9.1661699125676500734497274104786
y[1] (numeric) = 9.1661699125676500734497274104707
absolute error = 7.9e-30
relative error = 8.6186488744534221256293797202692e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 9.2482412846266610145855536665902
y[1] (numeric) = 9.2482412846266610145855536665822
absolute error = 8.0e-30
relative error = 8.6502933409602852656813499416046e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 9.3311374876876919375006494494469
y[1] (numeric) = 9.3311374876876919375006494494388
absolute error = 8.1e-30
relative error = 8.6806137094087821727839872935644e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 9.414866811440129344772473954749
y[1] (numeric) = 9.4148668114401293447724739547409
absolute error = 8.1e-30
relative error = 8.6034143256892202986288520139941e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 9.4994376288861231491839890633767
y[1] (numeric) = 9.4994376288861231491839890633686
absolute error = 8.1e-30
relative error = 8.5268205513232921792635877171154e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 9.5848583971778938662399876124018
y[1] (numeric) = 9.5848583971778938662399876123936
absolute error = 8.2e-30
relative error = 8.5551602957581063843320913029195e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 9.6711376584634548838689864354103
y[1] (numeric) = 9.671137658463454883868986435402
absolute error = 8.3e-30
relative error = 8.5822374710347153792447385042872e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 9.7582840407408343822424252687577
y[1] (numeric) = 9.7582840407408343822424252687494
absolute error = 8.3e-30
relative error = 8.5055937758600807944360348491278e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 9.8463062587208823266150074163392
y[1] (numeric) = 9.8463062587208823266150074163308
absolute error = 8.4e-30
relative error = 8.5311179434014785291816285693668e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 9.9352131146987488146044744309985
y[1] (numeric) = 9.9352131146987488146044744309901
absolute error = 8.4e-30
relative error = 8.4547758593849761872866677284336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 10.025013499434120926471777166889
y[1] (numeric) = 10.02501349943412092647177716688
absolute error = 9e-30
relative error = 8.9775440207716632294842401229684e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 10.115716393040306102820204373562
y[1] (numeric) = 10.115716393040306102820204373553
absolute error = 9e-30
relative error = 8.8970465860352432209105642518671e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 10.20733086588225095879214402908
y[1] (numeric) = 10.20733086588225095879214402907
absolute error = 1.0e-29
relative error = 9.7968804297553935367290861312266e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 10.299866079483585337393248594605
y[1] (numeric) = 10.299866079483585337393248594595
absolute error = 1.0e-29
relative error = 9.7088640986498923273184039048393e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 10.393331287442782307105209171014
y[1] (numeric) = 10.393331287442782307105209171004
absolute error = 1.0e-29
relative error = 9.6215541710692846161939332938534e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 10.487735836358525720550369044512
y[1] (numeric) = 10.487735836358525720550369044502
absolute error = 1.0e-29
relative error = 9.5349464899109493969614763228334e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 10.583089166764377871735185285297
y[1] (numeric) = 10.583089166764377871735185285287
absolute error = 1.0e-29
relative error = 9.4490368950159297267174211238203e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 10.679400814072840719417155056108
y[1] (numeric) = 10.679400814072840719417155056098
absolute error = 1.0e-29
relative error = 9.3638212237735693366557360816679e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 10.776680409528905083504263631818
y[1] (numeric) = 10.776680409528905083504263631808
absolute error = 1.0e-29
relative error = 9.2792953117157001086211097648826e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 10.874937681173183170201221053971
y[1] (numeric) = 10.874937681173183170201221053961
absolute error = 1.0e-29
relative error = 9.1954549931004337451754285239275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 10.974182454814720739957615156909
y[1] (numeric) = 10.974182454814720739957615156899
absolute error = 1.0e-29
relative error = 9.1122961014856135339304746976410e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 11.074424655013586200245455289684
y[1] (numeric) = 11.074424655013586200245455289675
absolute error = 9e-30
relative error = 8.1268330232627861261280641202931e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 11.175674306073334882894211461532
y[1] (numeric) = 11.175674306073334882894211461523
absolute error = 9e-30
relative error = 8.0532053400205289706182097924539e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 11.277941533043447753238138736105
y[1] (numeric) = 11.277941533043447753238138736095
absolute error = 1.0e-29
relative error = 8.8668663254733291389457385696063e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 11.381236562731844795782169982426
y[1] (numeric) = 11.381236562731844795782169982417
absolute error = 9e-30
relative error = 7.9077523346371115177213487408495e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 11.485569724727574328568707539109
y[1] (numeric) = 11.485569724727574328568707539099
absolute error = 1.0e-29
relative error = 8.7065772440271259727668843750671e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 11.590951452433780516028994407103
y[1] (numeric) = 11.590951452433780516028994407093
absolute error = 1.0e-29
relative error = 8.6274194495916687356993636241448e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 11.69739228411105237793115923818
y[1] (numeric) = 11.69739228411105237793115923817
absolute error = 1.0e-29
relative error = 8.5489139434806547330671388333768e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 11.804902863931258630195290329287
y[1] (numeric) = 11.804902863931258630195290329277
absolute error = 1.0e-29
relative error = 8.4710565730735784928120919325876e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 11.913493943041973741937818758192
y[1] (numeric) = 11.913493943041973741937818758182
absolute error = 1.0e-29
relative error = 8.3938431897558130980019815041010e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 12.023176380641601652237939769668
y[1] (numeric) = 12.023176380641601652237939769657
absolute error = 1.1e-29
relative error = 9.1489966143314607729247683003226e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 12.133961145065304659893688471457
y[1] (numeric) = 12.133961145065304659893688471446
absolute error = 1.1e-29
relative error = 9.0654649940704077383778447435482e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 12.245859314881846079961589205531
y[1] (numeric) = 12.24585931488184607996158920552
absolute error = 1.1e-29
relative error = 8.9826281007754115883662509477841e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 12.358882080001456352259571153473
y[1] (numeric) = 12.358882080001456352259571153462
absolute error = 1.1e-29
relative error = 8.9004813937011880417432554923742e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 12.473040742794833389367225302064
y[1] (numeric) = 12.473040742794833389367225302053
absolute error = 1.1e-29
relative error = 8.8190203390093559090730577950503e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 12.58834671922338906509070619308
y[1] (numeric) = 12.588346719223389065090706193069
absolute error = 1.1e-29
relative error = 8.7382404102376211841785694029716e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=725.0MB, alloc=44.3MB, time=7.86
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 12.704811539980854868983000160809
y[1] (numeric) = 12.704811539980854868983000160797
absolute error = 1.2e-29
relative error = 9.4452404604642274265567465099009e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 12.822446851646360888436353300643
y[1] (numeric) = 12.822446851646360888436353300631
absolute error = 1.2e-29
relative error = 9.3585882155239650216198773874834e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 12.941264417849103427205970766319
y[1] (numeric) = 12.941264417849103427205970766306
absolute error = 1.3e-29
relative error = 1.0045386277765784722080394409079e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 13.061276120444717728097399349678
y[1] (numeric) = 13.061276120444717728097399349665
absolute error = 1.3e-29
relative error = 9.9530856557355810926400090634914e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 13.182493960703473438070175951168
y[1] (numeric) = 13.182493960703473438070175951155
absolute error = 1.3e-29
relative error = 9.8615634027616616551298029640122e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 13.304930060510411636294418494051
y[1] (numeric) = 13.304930060510411636294418494038
absolute error = 1.3e-29
relative error = 9.7708142326764596851680718373779e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 13.428596663577543439863282465196
y[1] (numeric) = 13.428596663577543439863282465182
absolute error = 1.4e-29
relative error = 1.0425512323243929852366633639047e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 13.553506136668231408032023200075
y[1] (numeric) = 13.553506136668231408032023200061
absolute error = 1.4e-29
relative error = 1.0329430524345139832129699159910e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 13.679670970833876184144409056144
y[1] (numeric) = 13.679670970833876184144409056129
absolute error = 1.5e-29
relative error = 1.0965176013356730674897971297884e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 13.807103782663032044941253752753
y[1] (numeric) = 13.807103782663032044941253752738
absolute error = 1.5e-29
relative error = 1.0863972804227657676588525922154e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 13.935817315543076269846931825039
y[1] (numeric) = 13.935817315543076269846931825024
absolute error = 1.5e-29
relative error = 1.0763631339562700577931819318206e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 14.065824440934558498222200489047
y[1] (numeric) = 14.065824440934558498222200489033
absolute error = 1.4e-29
relative error = 9.9532025718002029856130536677331e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 14.197138159658357510581014537849
y[1] (numeric) = 14.197138159658357510581014537835
absolute error = 1.4e-29
relative error = 9.8611423249943906450246171165935e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 14.329771603195774150522090176603
y[1] (numeric) = 14.329771603195774150522090176588
absolute error = 1.5e-29
relative error = 1.0467717431487012620458257448038e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 14.463738035001690397750825332584
y[1] (numeric) = 14.46373803500169039775082533257
absolute error = 1.4e-29
relative error = 9.6793788480685544993532398844275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 14.599050851830925909193181507426
y[1] (numeric) = 14.599050851830925909193181507412
absolute error = 1.4e-29
relative error = 9.5896645214056525303004722279782e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 14.735723585077924664960939361653
y[1] (numeric) = 14.735723585077924664960939361638
absolute error = 1.5e-29
relative error = 1.0179344036549174862011349914234e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 14.873769902129905688949333816751
y[1] (numeric) = 14.873769902129905688949333816737
absolute error = 1.4e-29
relative error = 9.4125430822990055091231881030863e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 15.013203607733613160266757797534
y[1] (numeric) = 15.013203607733613160266757797519
absolute error = 1.5e-29
relative error = 9.9912053362635995241245092793552e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 15.154038645375802591646639807897
y[1] (numeric) = 15.154038645375802591646639807882
absolute error = 1.5e-29
relative error = 9.8983514236828167915729101418324e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 15.2962890986776011246097455111
y[1] (numeric) = 15.296289098677601124609745511086
absolute error = 1.4e-29
relative error = 9.1525466795801680707011233303363e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 15.439969192802881378568390330594
y[1] (numeric) = 15.43996919280288137856839033058
absolute error = 1.4e-29
relative error = 9.0673756049499747586219388375458e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 15.585093295880789692431122279052
y[1] (numeric) = 15.585093295880789692431122279038
absolute error = 1.4e-29
relative error = 8.9829426967243519901576413292612e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 15.731675920442571012717479636724
y[1] (numeric) = 15.73167592044257101271747963671
absolute error = 1.4e-29
relative error = 8.8992425669077381556398817100603e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 15.879731724872834111868993019468
y[1] (numeric) = 15.879731724872834111868993019455
absolute error = 1.3e-29
relative error = 8.1865362874095436368403227061623e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 16.029275514875402264487654649923
y[1] (numeric) = 16.02927551487540226448765464991
absolute error = 1.3e-29
relative error = 8.1101606793992715057087477794675e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 16.18032224495389596779102498073
y[1] (numeric) = 16.180322244953895967791024980717
absolute error = 1.3e-29
relative error = 8.0344506142665158378557103066310e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 16.332887019907195765789845226944
y[1] (numeric) = 16.332887019907195765789845226931
absolute error = 1.3e-29
relative error = 7.9594011665880406077796168853920e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 16.486985096339934724716796743092
y[1] (numeric) = 16.486985096339934724716796743079
absolute error = 1.3e-29
relative error = 7.8850074310347767520988663653822e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 16.642631884188171610212698046157
y[1] (numeric) = 16.642631884188171610212698046143
absolute error = 1.4e-29
relative error = 8.4121310243610670827612823832870e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 16.799842948260397334859256656509
y[1] (numeric) = 16.799842948260397334859256656496
absolute error = 1.3e-29
relative error = 7.7381675769451962013823201512813e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 16.958634009794028777987305352163
y[1] (numeric) = 16.95863400979402877798730535215
absolute error = 1.3e-29
relative error = 7.6657117504229290232103831586151e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 17.119020948027545628439586166743
y[1] (numeric) = 17.11902094802754562843958616673
absolute error = 1.3e-29
relative error = 7.5938922205115127163569801789300e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 17.281019801788427465282476812269
y[1] (numeric) = 17.281019801788427465282476812255
absolute error = 1.4e-29
relative error = 8.1013737386905419030425305974223e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 17.444646771097049871498016010925
y[1] (numeric) = 17.444646771097049871498016010912
absolute error = 1.3e-29
relative error = 7.4521428668529370070778526183377e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 17.609918218786699971604181488378
y[1] (numeric) = 17.609918218786699971604181488364
absolute error = 1.4e-29
relative error = 7.9500653132303878734475486619770e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 17.776850672139873396107200104494
y[1] (numeric) = 17.77685067213987339610720010448
absolute error = 1.4e-29
relative error = 7.8754107002434317101191639199259e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 17.945460824541016303845920701474
y[1] (numeric) = 17.94546082454101630384592070146
absolute error = 1.4e-29
relative error = 7.8014157100131599778974380857340e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 18.11576553714587773780777371626
y[1] (numeric) = 18.115765537145877737807773716245
absolute error = 1.5e-29
relative error = 8.2800806674401441036583642478798e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 18.287781840567639251043030753446
y[1] (numeric) = 18.287781840567639251043030753431
absolute error = 1.5e-29
relative error = 8.2021975823911135800942248530485e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 18.46152693657999041704506824997
y[1] (numeric) = 18.461526936579990417045068249955
absolute error = 1.5e-29
relative error = 8.1250050721854102068347944517616e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 18.637018199837320533566907580682
y[1] (numeric) = 18.637018199837320533566907580667
absolute error = 1.5e-29
relative error = 8.0484978010757818183526228351425e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 18.814273179612198540477911123657
y[1] (numeric) = 18.814273179612198540477911123642
absolute error = 1.5e-29
relative error = 7.9726704597095582961320650912994e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 18.993309601550314901100324712728
y[1] (numeric) = 18.993309601550314901100324712712
absolute error = 1.6e-29
relative error = 8.4240189496484655783849528689253e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=767.3MB, alloc=44.3MB, time=8.31
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 19.174145369443060942676256574128
y[1] (numeric) = 19.174145369443060942676256574112
absolute error = 1.6e-29
relative error = 8.3445700925468375647928519982248e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 19.356798567017922915376293819354
y[1] (numeric) = 19.356798567017922915376293819337
absolute error = 1.7e-29
relative error = 8.7824440292344234011714605919360e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 19.541287459746869810747657378403
y[1] (numeric) = 19.541287459746869810747657378387
absolute error = 1.6e-29
relative error = 8.1877921467346643994183272849554e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 19.727630496672915779890735060899
y[1] (numeric) = 19.727630496672915779890735060882
absolute error = 1.7e-29
relative error = 8.6173552383126126897229653557367e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 19.915846312255039809127950820668
y[1] (numeric) = 19.915846312255039809127950820651
absolute error = 1.7e-29
relative error = 8.5359164423453099350173432453115e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 20.105953728231647146669975298563
y[1] (numeric) = 20.105953728231647146669975298547
absolute error = 1.6e-29
relative error = 7.9578418493690760294354306278933e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 20.297971755502758827974833963076
y[1] (numeric) = 20.29797175550275882797483396306
absolute error = 1.6e-29
relative error = 7.8825609734442638593350922514017e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 20.491919596031117520320945259013
y[1] (numeric) = 20.491919596031117520320945258997
absolute error = 1.6e-29
relative error = 7.8079556798079989782753456904407e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 20.687816644762399798762806219384
y[1] (numeric) = 20.687816644762399798762806219368
absolute error = 1.6e-29
relative error = 7.7340205951848334766497790395772e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 20.885682491564726876297103339624
y[1] (numeric) = 20.885682491564726876297103339608
absolute error = 1.6e-29
relative error = 7.6607503759870199000659982940538e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 21.085536923187667740928529654582
y[1] (numeric) = 21.085536923187667740928529654565
absolute error = 1.7e-29
relative error = 8.0623984401863527494041858011978e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 21.28739992524093060158152265589
y[1] (numeric) = 21.287399925240930601581522655873
absolute error = 1.7e-29
relative error = 7.9859447653082010448252281501837e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 21.491291684192940513651429258142
y[1] (numeric) = 21.491291684192940513651429258125
absolute error = 1.7e-29
relative error = 7.9101806675043499762746091609858e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 21.697232589389503043623139836616
y[1] (numeric) = 21.697232589389503043623139836599
absolute error = 1.7e-29
relative error = 7.8351005963375398865542875272342e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 21.905243235092755840805878527866
y[1] (numeric) = 21.90524323509275584080587852785
absolute error = 1.6e-29
relative error = 7.3041873255109962700771894159975e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 22.115344422540612013040455245769
y[1] (numeric) = 22.115344422540612013040455245752
absolute error = 1.7e-29
relative error = 7.6869704921588732111518101391940e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 22.327557162026901252432758671981
y[1] (numeric) = 22.327557162026901252432758671964
absolute error = 1.7e-29
relative error = 7.6139095184637456891014463032443e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (closed_form) = 22.541902675002416726959520286426
y[1] (numeric) = 22.541902675002416726959520286409
absolute error = 1.7e-29
relative error = 7.5415106901565829880773180183344e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 22.758402396197077844386388260106
y[1] (numeric) = 22.758402396197077844386388260089
absolute error = 1.7e-29
relative error = 7.4697686173440253685032324170811e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 22.977077975763421106543177882497
y[1] (numeric) = 22.97707797576342110654317788248
absolute error = 1.7e-29
relative error = 7.3986779423962716955639889520751e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 23.197951281441633404827974381257
y[1] (numeric) = 23.197951281441633404827974381239
absolute error = 1.8e-29
relative error = 7.7593058893955020596788238608052e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 23.421044400746344262073838971462
y[1] (numeric) = 23.421044400746344262073838971443
absolute error = 1.9e-29
relative error = 8.1123624014796447279606420263494e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 23.646379643175395701824637747618
y[1] (numeric) = 23.646379643175395701824637747598
absolute error = 2.0e-29
relative error = 8.4579543684067591182568131362677e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 23.873979542440810623847568694562
y[1] (numeric) = 23.873979542440810623847568694543
absolute error = 1.9e-29
relative error = 7.9584553409806146484750690594270e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 24.103866858722182784579084580015
y[1] (numeric) = 24.103866858722182784579084579996
absolute error = 1.9e-29
relative error = 7.8825526673222116154588806885165e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 24.33606458094271372338008756421
y[1] (numeric) = 24.336064580942713723380087564191
absolute error = 1.9e-29
relative error = 7.8073428580883520463006017815890e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 24.57059592906812424018972480695
y[1] (numeric) = 24.570595929068124240189724806932
absolute error = 1.8e-29
relative error = 7.3258296428639678933780136867245e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 24.807484356428670317641316402232
y[1] (numeric) = 24.807484356428670317641316402213
absolute error = 1.9e-29
relative error = 7.6589789303147519465126786981879e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 25.046753552064495691167646951714
y[1] (numeric) = 25.046753552064495691167646951695
absolute error = 1.9e-29
relative error = 7.5858134510346200462509620901091e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 25.288427443094555604307098296172
y[1] (numeric) = 25.288427443094555604307098296153
absolute error = 1.9e-29
relative error = 7.5133181146810613748970892773721e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 25.532530197109348643560263727964
y[1] (numeric) = 25.532530197109348643560263727945
absolute error = 1.9e-29
relative error = 7.4414873313852281450898988065617e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 25.779086224587695927974479188157
y[1] (numeric) = 25.779086224587695927974479188138
absolute error = 1.9e-29
relative error = 7.3703155474448478482609410799458e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 26.02812018133780933338921927269
y[1] (numeric) = 26.02812018133780933338921927267
absolute error = 2.0e-29
relative error = 7.6839971003130767379707660837788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 26.279656970962892860199012888142
y[1] (numeric) = 26.279656970962892860199012888123
absolute error = 1.9e-29
relative error = 7.2299269434884999933982947731820e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 26.533721747351523706825329504055
y[1] (numeric) = 26.533721747351523706825329504035
absolute error = 2.0e-29
relative error = 7.5375781017211841723772162222844e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 26.790339917193062089080107669377
y[1] (numeric) = 26.790339917193062089080107669356
absolute error = 2.1e-29
relative error = 7.8386463422671866415199748680847e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 27.049537142518341348499043982636
y[1] (numeric) = 27.049537142518341348499043982614
absolute error = 2.2e-29
relative error = 8.1332260452689491216007494363083e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 27.311339343265892420772724659149
y[1] (numeric) = 27.311339343265892420772724659127
absolute error = 2.2e-29
relative error = 8.0552622203877746614787108246887e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 27.575772699873959288860970327214
y[1] (numeric) = 27.575772699873959288860970327191
absolute error = 2.3e-29
relative error = 8.3406547661691185196813394442951e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 27.842863655898564624495725565399
y[1] (numeric) = 27.842863655898564624495725565376
absolute error = 2.3e-29
relative error = 8.2606445530351923504080123555550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 28.112638920657887426818372110231
y[1] (numeric) = 28.112638920657887426818372110209
absolute error = 2.2e-29
relative error = 7.8256616399799580110184242889383e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 28.385125471903217098118984843308
y[1] (numeric) = 28.385125471903217098118984843286
absolute error = 2.2e-29
relative error = 7.7505382253027272995168154386614e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 28.660350558516751054310906965868
y[1] (numeric) = 28.660350558516751054310906965846
absolute error = 2.2e-29
relative error = 7.6761098769821042231532055523585e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 28.938341703236505652149863987642
y[1] (numeric) = 28.93834170323650565214986398762
absolute error = 2.2e-29
relative error = 7.6023706629808329472978828436225e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=809.8MB, alloc=44.3MB, time=8.76
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 29.2191267054086129265611051166
y[1] (numeric) = 29.219126705408612926561105116578
absolute error = 2.2e-29
relative error = 7.5293146923270931032628444101764e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 29.502733643767278370041893023457
y[1] (numeric) = 29.502733643767278370041893023435
absolute error = 2.2e-29
relative error = 7.4569361150191927051239842189600e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 29.789190879242677752233921434877
y[1] (numeric) = 29.789190879242677752233921434855
absolute error = 2.2e-29
relative error = 7.3852291219261541191240511375176e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 30.078527057797073771687539613154
y[1] (numeric) = 30.078527057797073771687539613131
absolute error = 2.3e-29
relative error = 7.6466510330790449324456514533444e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 30.370771113289436153846398566086
y[1] (numeric) = 30.370771113289436153846398566063
absolute error = 2.3e-29
relative error = 7.5730708035713376756305165827645e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 30.665952270368851659649508823945
y[1] (numeric) = 30.665952270368851659649508823921
absolute error = 2.4e-29
relative error = 7.8262692736237428308486676765855e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 30.96410004739701334816275303373
y[1] (numeric) = 30.964100047397013348162753033707
absolute error = 2.3e-29
relative error = 7.4279568806436172399183928592094e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 31.265244259400081344601532358897
y[1] (numeric) = 31.265244259400081344601532358873
absolute error = 2.4e-29
relative error = 7.6762553974879813978000957271131e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 31.569415021050210302281241122151
y[1] (numeric) = 31.569415021050210302281241122127
absolute error = 2.4e-29
relative error = 7.6022948109735354756832099345791e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 31.876642749677041713726379239121
y[1] (numeric) = 31.876642749677041713726379239096
absolute error = 2.5e-29
relative error = 7.8427330620484767213893828978793e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 32.186958168309462222678998645337
y[1] (numeric) = 32.186958168309462222678998645312
absolute error = 2.5e-29
relative error = 7.7671210399168518737663683802265e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 32.500392308747932115372491603845
y[1] (numeric) = 32.50039230874793211537249160382
absolute error = 2.5e-29
relative error = 7.6922148392870022916325346481539e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 32.81697651466769122648013054928
y[1] (numeric) = 32.816976514667691226480130549255
absolute error = 2.5e-29
relative error = 7.6180083161610395844294811000388e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 33.136742444753152582914967864034
y[1] (numeric) = 33.136742444753152582914967864008
absolute error = 2.6e-29
relative error = 7.8462751863277438333447922243151e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 33.459722075863797227457478986324
y[1] (numeric) = 33.459722075863797227457478986298
absolute error = 2.6e-29
relative error = 7.7705367489454208773610828922788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 33.785947706231886814331566095013
y[1] (numeric) = 33.785947706231886814331566094987
absolute error = 2.6e-29
relative error = 7.6955070865761883262955126852676e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 34.115451958692313750653249350389
y[1] (numeric) = 34.115451958692313750653249350362
absolute error = 2.7e-29
relative error = 7.9143023028662060936281806908289e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 34.448267783944911871457741316409
y[1] (numeric) = 34.448267783944911871457741316382
absolute error = 2.7e-29
relative error = 7.8378396758120072072984425155494e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 34.78442846384955388209100856303
y[1] (numeric) = 34.784428463849553882091008563003
absolute error = 2.7e-29
relative error = 7.7620939001657927857027619802448e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 35.123967614754365080455983293164
y[1] (numeric) = 35.123967614754365080455983293137
absolute error = 2.7e-29
relative error = 7.6870586763262567721590679312598e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 35.466919190857386183259170295692
y[1] (numeric) = 35.466919190857386183259170295664
absolute error = 2.8e-29
relative error = 7.8946806316399202844093477351516e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 35.813317487602021425341668911734
y[1] (numeric) = 35.813317487602021425341668911706
absolute error = 2.8e-29
relative error = 7.8183206595404453113507575276921e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 36.163197145106611479734092630969
y[1] (numeric) = 36.163197145106611479734092630941
absolute error = 2.8e-29
relative error = 7.7426782503904783448211599137515e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 36.516593151628474158585378769949
y[1] (numeric) = 36.516593151628474158585378769921
absolute error = 2.8e-29
relative error = 7.6677470660351915126122009209760e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 36.873540847062759301922291319834
y[1] (numeric) = 36.873540847062759301922291319805
absolute error = 2.9e-29
relative error = 7.8647179885112815184050649522247e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 37.234075926476467742644215040193
y[1] (numeric) = 37.234075926476467742644215040164
absolute error = 2.9e-29
relative error = 7.7885644475947991673334570390258e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 37.598234443677987752594765899184
y[1] (numeric) = 37.598234443677987752594765899154
absolute error = 3.0e-29
relative error = 7.9790980730597565530402527803834e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 37.966052814822505926329448641597
y[1] (numeric) = 37.966052814822505926329448641567
absolute error = 3.0e-29
relative error = 7.9017958875850160443232969936994e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 38.337567822053653046672257335396
y[1] (numeric) = 38.337567822053653046672257335366
absolute error = 3.0e-29
relative error = 7.8252225439148817626219662217270e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 38.71281661718174909968248956046
y[1] (numeric) = 38.712816617181749099682489560429
absolute error = 3.1e-29
relative error = 8.0076839426458570732851976691533e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 39.091836725399015266598485317448
y[1] (numeric) = 39.091836725399015266598485317417
absolute error = 3.1e-29
relative error = 7.9300443767223831110198186516298e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 39.474666049032124417053505344034
y[1] (numeric) = 39.474666049032124417053505344002
absolute error = 3.2e-29
relative error = 8.1064650325989534132882699039225e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 39.861342871332465361740206261101
y[1] (numeric) = 39.861342871332465361740206261069
absolute error = 3.2e-29
relative error = 8.0278278891135409811080508934208e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 40.251905860304499894107543068851
y[1] (numeric) = 40.25190586030449989410754306882
absolute error = 3.1e-29
relative error = 7.7014986837111442669547318234957e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 40.646394072572595459984576852157
y[1] (numeric) = 40.646394072572595459984576852126
absolute error = 3.1e-29
relative error = 7.6267528048492260843698562194968e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 41.044846957286720141620521375166
y[1] (numeric) = 41.044846957286720141620521375136
absolute error = 3.0e-29
relative error = 7.3090782945833543173725514787846e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 41.447304360067390528894189239039
y[1] (numeric) = 41.447304360067390528894189239009
absolute error = 3.0e-29
relative error = 7.2381064253007603841140744411584e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 41.853806526990266975767426064963
y[1] (numeric) = 41.853806526990266975767426064933
absolute error = 3.0e-29
relative error = 7.1678068231748283208549742001509e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 42.264394108610794704828685161265
y[1] (numeric) = 42.264394108610794704828685161234
absolute error = 3.1e-29
relative error = 7.3347792281929748961144695924311e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 42.679108164029293227391075798772
y[1] (numeric) = 42.679108164029293227391075798741
absolute error = 3.1e-29
relative error = 7.2635069788377977325349304457225e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 43.097990164996900591474480707947
y[1] (numeric) = 43.097990164996900591474480707916
absolute error = 3.1e-29
relative error = 7.1929108251496649291403161857237e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 43.521082000062783055518172621604
y[1] (numeric) = 43.521082000062783055518172621573
absolute error = 3.1e-29
relative error = 7.1229846721079406357102048739491e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 43.948425978763024912247320706349
y[1] (numeric) = 43.948425978763024912247320706318
absolute error = 3.1e-29
relative error = 7.0537224734692370653954113593884e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=852.1MB, alloc=44.3MB, time=9.22
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 44.380064835851617355166526689092
y[1] (numeric) = 44.38006483585161735516652668906
absolute error = 3.2e-29
relative error = 7.2104446260631394640452965808781e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 44.816041735573969490092875840424
y[1] (numeric) = 44.816041735573969490092875840392
absolute error = 3.2e-29
relative error = 7.1403003836903153363609590540166e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 45.256400275983368846390927167131
y[1] (numeric) = 45.256400275983368846390927167099
absolute error = 3.2e-29
relative error = 7.0708230890784601373348751744439e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 45.701184493300823037557828729065
y[1] (numeric) = 45.701184493300823037557828729032
absolute error = 3.3e-29
relative error = 7.2208194089230564042429280052723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 46.150438866318718558957830086431
y[1] (numeric) = 46.150438866318718558957830086398
absolute error = 3.3e-29
relative error = 7.1505278845969749191947688769106e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 46.604208320848737092255693225917
y[1] (numeric) = 46.604208320848737092255693225884
absolute error = 3.3e-29
relative error = 7.0809056068091614942969973677552e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 47.062538234214474111886054582464
y[1] (numeric) = 47.06253823421447411188605458243
absolute error = 3.4e-29
relative error = 7.2244297217445857247076762831064e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 47.525474439789209059163246411121
y[1] (numeric) = 47.525474439789209059163246411087
absolute error = 3.4e-29
relative error = 7.1540579869592146803589452877805e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 47.993063231579280864830476241162
y[1] (numeric) = 47.993063231579280864830476241128
absolute error = 3.4e-29
relative error = 7.0843571363513445469009937270212e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 48.46535136885352716142011166414
y[1] (numeric) = 48.465351368853527161420111664106
absolute error = 3.4e-29
relative error = 7.0153210571481073953459682453804e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 48.942386080819250133204185354246
y[1] (numeric) = 48.942386080819250133204185354212
absolute error = 3.4e-29
relative error = 6.9469436867780255036402002921524e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 49.424215071345176604216766568584
y[1] (numeric) = 49.42421507134517660421676656855
absolute error = 3.4e-29
relative error = 6.8792190125670363130566487329379e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 49.910886523731884664292814557216
y[1] (numeric) = 49.910886523731884664292814557181
absolute error = 3.5e-29
relative error = 7.0124981617703825480298753213846e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 50.40244910553017387976148654122
y[1] (numeric) = 50.402449105530173879761486541186
absolute error = 3.4e-29
relative error = 6.7457039495863522278204861931233e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 50.89895197340786092983029148288
y[1] (numeric) = 50.898951973407860929830291482845
absolute error = 3.5e-29
relative error = 6.8763694816910449070739032782135e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 51.400444778065487352279404612568
y[1] (numeric) = 51.400444778065487352279404612532
absolute error = 3.6e-29
relative error = 7.0038304445494916703223040041242e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 51.906977669201430973337148919991
y[1] (numeric) = 51.906977669201430973337148919955
absolute error = 3.6e-29
relative error = 6.9354837473730044376435697629550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 52.418601300526917537017237808153
y[1] (numeric) = 52.418601300526917537017237808116
absolute error = 3.7e-29
relative error = 7.0585630066455191616426696653639e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 52.9353668348314340392599029227
y[1] (numeric) = 52.935366834831434039259902922662
absolute error = 3.8e-29
relative error = 7.1785655360748396294045291911961e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 53.457325949099050312431513118509
y[1] (numeric) = 53.457325949099050312431513118471
absolute error = 3.8e-29
relative error = 7.1084737826547490678136244541160e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 53.984530839676160496604750057851
y[1] (numeric) = 53.984530839676160496604750057813
absolute error = 3.8e-29
relative error = 7.0390534860537749481217174803852e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 54.517034227491161176072934038621
y[1] (numeric) = 54.517034227491161176072934038583
absolute error = 3.8e-29
relative error = 6.9702984651424490264995953135631e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 55.054889363326588153261897764787
y[1] (numeric) = 55.054889363326588153261897764748
absolute error = 3.9e-29
relative error = 7.0838395010886819342083174852798e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 55.598150033144239078110261202861
y[1] (numeric) = 55.598150033144239078110261202822
absolute error = 3.9e-29
relative error = 7.0146218852157076304493238003200e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 56.146870563463814449618662535082
y[1] (numeric) = 56.146870563463814449618662535043
absolute error = 3.9e-29
relative error = 6.9460683398049052035455964202705e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 56.701105826795614858150315907712
y[1] (numeric) = 56.701105826795614858150315907673
absolute error = 3.9e-29
relative error = 6.8781727324918437927945523828619e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (closed_form) = 57.260911247127837742734388822998
y[1] (numeric) = 57.260911247127837742734388822958
absolute error = 4.0e-29
relative error = 6.9855681875838761698703100912526e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 57.826342805469022397620692052799
y[1] (numeric) = 57.826342805469022397620692052759
absolute error = 4.0e-29
relative error = 6.9172626279621704825754659556607e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 58.397457045446197477205057110728
y[1] (numeric) = 58.397457045446197477205057110688
absolute error = 4.0e-29
relative error = 6.8496133262910938079183748172582e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 58.974311078959290818741032291737
y[1] (numeric) = 58.974311078959290818741032291696
absolute error = 4.1e-29
relative error = 6.9521795591823163879340048328996e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 59.556962591892367028532192341085
y[1] (numeric) = 59.556962591892367028532192341044
absolute error = 4.1e-29
relative error = 6.8841657155936674469828569208961e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 60.145469849882263960123061503388
y[1] (numeric) = 60.145469849882263960123061503347
absolute error = 4.1e-29
relative error = 6.8168060042314655514084000393295e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 60.739891704145204952943682133229
y[1] (numeric) = 60.739891704145204952943682133187
absolute error = 4.2e-29
relative error = 6.9147308007356395012557849849404e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 61.340287597361969497487219708124
y[1] (numeric) = 61.340287597361969497487219708082
absolute error = 4.2e-29
relative error = 6.8470497360051948314602258851809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 61.946717569622210848991447239727
y[1] (numeric) = 61.946717569622210848991447239685
absolute error = 4.2e-29
relative error = 6.7800202573761878517698986998004e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 62.559242264428515026339091755126
y[1] (numeric) = 62.559242264428515026339091755083
absolute error = 4.3e-29
relative error = 6.8734847871471112881859554666458e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 63.177922934760801607080332059943
y[1] (numeric) = 63.1779229347608016070803320599
absolute error = 4.3e-29
relative error = 6.8061750058486316731794121024774e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 63.802821449201672763710634207787
y[1] (numeric) = 63.802821449201672763710634207743
absolute error = 4.4e-29
relative error = 6.8962467490613686898002797643417e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 64.434000298123323081212027004718
y[1] (numeric) = 64.434000298123323081212027004673
absolute error = 4.5e-29
relative error = 6.9838904602840017373585060319448e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 65.071522599936628851995347043461
y[1] (numeric) = 65.071522599936628851995347043416
absolute error = 4.5e-29
relative error = 6.9154675043739984826287290943910e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 65.71545210740304176238053926293
y[1] (numeric) = 65.715452107403041762380539262885
absolute error = 4.5e-29
relative error = 6.8477045438953338233991980876678e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 66.365853214009918165243590001587
y[1] (numeric) = 66.365853214009918165243590001541
absolute error = 4.6e-29
relative error = 6.9312753128726958050451217787390e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (closed_form) = 67.022790960409921477070149341099
y[1] (numeric) = 67.022790960409921477070149341052
absolute error = 4.7e-29
relative error = 7.0125399623782752907998036001557e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 67.686331040925141645021734653992
y[1] (numeric) = 67.686331040925141645021734653945
absolute error = 4.7e-29
relative error = 6.9437948958383371427509804074356e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=894.4MB, alloc=44.3MB, time=9.67
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 68.356539810116582101381339598584
y[1] (numeric) = 68.356539810116582101381339598537
absolute error = 4.7e-29
relative error = 6.8757137401276311742509099193667e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 69.033484289419671159548483832735
y[1] (numeric) = 69.033484289419671159548483832687
absolute error = 4.8e-29
relative error = 6.9531475187841067327512162777546e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 69.717232173846461408252914213396
y[1] (numeric) = 69.717232173846461408252914213348
absolute error = 4.8e-29
relative error = 6.8849549104742849208165755717527e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 70.407851838755187329511563631169
y[1] (numeric) = 70.40785183875518732951156363112
absolute error = 4.9e-29
relative error = 6.9594510726186531651870951123358e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 71.105412346687858101731879995094
y[1] (numeric) = 71.105412346687858101731879995044
absolute error = 5.0e-29
relative error = 7.0318135216227371218637615628240e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 71.809983454276569352939848696489
y[1] (numeric) = 71.809983454276569352939848696438
absolute error = 5.1e-29
relative error = 7.1020765563151996111068570076040e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 72.521635619219224501063310332678
y[1] (numeric) = 72.521635619219224501063310332627
absolute error = 5.1e-29
relative error = 7.0323841381321938976169581603691e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 73.240440007325363259217722516329
y[1] (numeric) = 73.240440007325363259217722516278
absolute error = 5.1e-29
relative error = 6.9633661396489536862440314382457e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 73.96646849963280189471643767276
y[1] (numeric) = 73.966468499632801894716437672709
absolute error = 5.1e-29
relative error = 6.8950162194445154143283109029104e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 74.699793699595796911761951170653
y[1] (numeric) = 74.699793699595796911761951170601
absolute error = 5.2e-29
relative error = 6.9611972703856843105916659233077e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 75.440488940345450980176545280381
y[1] (numeric) = 75.440488940345450980176545280329
absolute error = 5.2e-29
relative error = 6.8928503420913652696312217514878e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 76.188628292023087156815560466137
y[1] (numeric) = 76.188628292023087156815560466084
absolute error = 5.3e-29
relative error = 6.9564187186644853378923922105268e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 76.944286569187324743196600893995
y[1] (numeric) = 76.944286569187324743196600893941
absolute error = 5.4e-29
relative error = 7.0180649412408140511060405640240e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 77.70753933829559749310302086642
y[1] (numeric) = 77.707539338295597493103020866366
absolute error = 5.4e-29
relative error = 6.9491326658683530402529627775196e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (closed_form) = 78.478462925260862328217071820222
y[1] (numeric) = 78.478462925260862328217071820168
absolute error = 5.4e-29
relative error = 6.8808687106202652549975588934597e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 79.257134423084254238951551456582
y[1] (numeric) = 79.257134423084254238951551456527
absolute error = 5.5e-29
relative error = 6.9394383736362822664383837592810e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 80.043631699564450642330605120616
y[1] (numeric) = 80.04363169956445064233060512056
absolute error = 5.6e-29
relative error = 6.9961843073525508660947489699247e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 80.838033405084516139779959223782
y[1] (numeric) = 80.838033405084516139779959223726
absolute error = 5.6e-29
relative error = 6.9274322544909579516664547455600e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 81.640418980477006365791424660798
y[1] (numeric) = 81.640418980477006365791424660742
absolute error = 5.6e-29
relative error = 6.8593474530540441819731340323516e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 82.450868664968117444400811726181
y[1] (numeric) = 82.450868664968117444400811726124
absolute error = 5.7e-29
relative error = 6.9132079410363166819225996114173e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 83.269463504201675475045050936085
y[1] (numeric) = 83.269463504201675475045050936027
absolute error = 5.8e-29
relative error = 6.9653384997578843299522424442352e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 84.096285358343768453433785661304
y[1] (numeric) = 84.096285358343768453433785661245
absolute error = 5.9e-29
relative error = 7.0157676701883249000945558020573e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 84.931416910268831097381406177663
y[1] (numeric) = 84.931416910268831097381406177604
absolute error = 5.9e-29
relative error = 6.9467815499103568304365015817749e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 85.774941673828001192903868431231
y[1] (numeric) = 85.774941673828001192903868431172
absolute error = 5.9e-29
relative error = 6.8784657673515294019462540160759e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 86.626944002200574303105227123016
y[1] (numeric) = 86.626944002200574303105227122956
absolute error = 6.0e-29
relative error = 6.9262514903533739912778648094504e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 87.4875090963293919922843405557
y[1] (numeric) = 87.48750909632939199228434055564
absolute error = 6.0e-29
relative error = 6.8581218758824335653134282745984e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 88.356723013441007111113671531353
y[1] (numeric) = 88.356723013441007111113671531293
absolute error = 6.0e-29
relative error = 6.7906547406554084327203136577614e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 89.234672675651478166518863585011
y[1] (numeric) = 89.23467267565147816651886358495
absolute error = 6.1e-29
relative error = 6.8359078563241511356086794415927e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 90.121445878658653362867599725013
y[1] (numeric) = 90.121445878658653362867599724952
absolute error = 6.1e-29
relative error = 6.7686441784491163126765906298634e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 91.017131300521813550115456745574
y[1] (numeric) = 91.017131300521813550115456745512
absolute error = 6.2e-29
relative error = 6.8119044309677716239539346680832e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 91.92181851052955205051996320841
y[1] (numeric) = 91.921818510529552050519963208347
absolute error = 6.3e-29
relative error = 6.8536503107565711650583409969537e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 92.835597978156778159295456987861
y[1] (numeric) = 92.835597978156778159295456987797
absolute error = 6.4e-29
relative error = 6.8939072288906368109988895760220e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 93.758561082111740027023002329753
y[1] (numeric) = 93.758561082111740027023002329688
absolute error = 6.5e-29
relative error = 6.9327002515614965470567047895259e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 94.690800119473971633642818281708
y[1] (numeric) = 94.690800119473971633642818281642
absolute error = 6.6e-29
relative error = 6.9700541041712600767264313789372e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 95.632408314924077656341598932635
y[1] (numeric) = 95.63240831492407765634159893257
absolute error = 6.5e-29
relative error = 6.7968590507467451042686680042298e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 96.583479830066279217513027221686
y[1] (numeric) = 96.58347983006627921751302722162
absolute error = 6.6e-29
relative error = 6.8334667705205531438507150398606e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 97.54410977284465277513509238733
y[1] (numeric) = 97.544109772844652775135092387263
absolute error = 6.7e-29
relative error = 6.8686874231592156265180360425507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 98.51439420705400378730014068658
y[1] (numeric) = 98.514394207054003787300140686512
absolute error = 6.8e-29
relative error = 6.9025446024750505366466827389306e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 99.494430161946326246189866862324
y[1] (numeric) = 99.494430161946326246189866862256
absolute error = 6.8e-29
relative error = 6.8345534407621530042969528993691e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 100.48431564193380873545405348757
y[1] (numeric) = 100.4843156419338087354540534875
absolute error = 7e-29
relative error = 6.9662613068330251010643269146058e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 101.48414963638935731968466139449
y[1] (numeric) = 101.48414963638935731968466139442
absolute error = 7e-29
relative error = 6.8976288662618868565365087825310e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 102.49403212954561532644134822903
y[1] (numeric) = 102.49403212954561532644134822895
absolute error = 8e-29
relative error = 7.8053324996410854293108992359056e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 103.51406411049346993105582833176
y[1] (numeric) = 103.51406411049346993105582833168
absolute error = 8e-29
relative error = 7.7284184219263213497468911677225e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 104.54434758328104540320567097554
y[1] (numeric) = 104.54434758328104540320567097546
absolute error = 8e-29
relative error = 7.6522549376733372323044248761112e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=936.8MB, alloc=44.3MB, time=10.13
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 105.58498557711419292299805009791
y[1] (numeric) = 105.58498557711419292299805009783
absolute error = 8e-29
relative error = 7.5768348655568882417637697774673e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 106.63608215665949702404549041811
y[1] (numeric) = 106.63608215665949702404549041804
absolute error = 7e-29
relative error = 6.5643822038737993549644420749469e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 107.69774243245082897276378483542
y[1] (numeric) = 107.69774243245082897276378483534
absolute error = 8e-29
relative error = 7.4281965613324580127143719282733e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 108.77007257140048774790216962363
y[1] (numeric) = 108.77007257140048774790216962356
absolute error = 7e-29
relative error = 6.4355937571016647690069977036150e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 109.85317980741597974316302378673
y[1] (numeric) = 109.85317980741597974316302378666
absolute error = 7e-29
relative error = 6.3721414457658177694154571179024e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 110.94717245212349887972870045537
y[1] (numeric) = 110.94717245212349887972870045529
absolute error = 8e-29
relative error = 7.2106389222782596144153825320543e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 112.05215990569917948564300622207
y[1] (numeric) = 112.052159905699179485643006222
absolute error = 7e-29
relative error = 6.2470906459019243692947630111443e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 113.1682526678092050763613407161
y[1] (numeric) = 113.16825266780920507636134071604
absolute error = 6e-29
relative error = 5.3018402763646314833872270749166e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 114.29556234865986705646433913828
y[1] (numeric) = 114.29556234865986705646433913821
absolute error = 7e-29
relative error = 6.1244722508529449221012387925151e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 115.43420168015867835761360206601
y[1] (numeric) = 115.43420168015867835761360206594
absolute error = 7e-29
relative error = 6.0640606493692153094612090679419e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 116.58428452718765813341426713653
y[1] (numeric) = 116.58428452718765813341426713646
absolute error = 7e-29
relative error = 6.0042397895983894917616943294439e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 117.74592589898991484904834409238
y[1] (numeric) = 117.7459258989899148490483440923
absolute error = 8e-29
relative error = 6.7942902813154812664682771548588e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 118.91924196067066643347662739359
y[1] (numeric) = 118.91924196067066643347662739352
absolute error = 7e-29
relative error = 5.8863476461740828289579931933473e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 120.10435004481384760580862199534
y[1] (numeric) = 120.10435004481384760580862199526
absolute error = 8e-29
relative error = 6.6608744787470277819913330035042e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 121.30136866321546604625365765727
y[1] (numeric) = 121.30136866321546604625365765719
absolute error = 8e-29
relative error = 6.5951440516812511473245825364249e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 122.51041751873488075704811629788
y[1] (numeric) = 122.5104175187348807570481162978
absolute error = 8e-29
relative error = 6.5300569225279161441083400264502e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 123.73161751726518775107096333766
y[1] (numeric) = 123.73161751726518775107096333758
absolute error = 8e-29
relative error = 6.4656069002603161066926623714242e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 124.96509077982391011669179924248
y[1] (numeric) = 124.9650907798239101166917992424
absolute error = 8e-29
relative error = 6.4017878513729935776845928498891e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 126.21096065476520153793352471171
y[1] (numeric) = 126.21096065476520153793352471163
absolute error = 8e-29
relative error = 6.3385936993879883248899160345550e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 127.46935173011478450047850596726
y[1] (numeric) = 127.46935173011478450047850596718
absolute error = 8e-29
relative error = 6.2760184243645059475832435858609e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 128.74038984602885668761799019549
y[1] (numeric) = 128.74038984602885668761799019541
absolute error = 8e-29
relative error = 6.2140560624120007445745225206569e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 130.0242021073782114671668226883
y[1] (numeric) = 130.02420210737821146716682268823
absolute error = 7e-29
relative error = 5.3836131170558328230260213392454e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 131.32091689645883089187895918358
y[1] (numeric) = 131.3209168964588308918789591835
absolute error = 8e-29
relative error = 6.0919464995113250899971108538820e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 132.63066388583022228325601109699
y[1] (numeric) = 132.63066388583022228325601109691
absolute error = 8e-29
relative error = 6.0317876466987140685520092812329e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 133.95357405128278224310585398182
y[1] (numeric) = 133.95357405128278224310585398173
absolute error = 9e-29
relative error = 6.7187457025629195021602226617629e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 135.28977968493548484005862777435
y[1] (numeric) = 135.28977968493548484005862777426
absolute error = 9e-29
relative error = 6.6523872098537757318311480053299e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 136.63941440846520375077355696288
y[1] (numeric) = 136.63941440846520375077355696279
absolute error = 9e-29
relative error = 6.5866792820816013233453988591648e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 138.00261318646899129907518322816
y[1] (numeric) = 138.00261318646899129907518322807
absolute error = 9e-29
relative error = 6.5216156362482854630332672967115e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 139.37951233996065063205819382868
y[1] (numeric) = 139.37951233996065063205819382859
absolute error = 9e-29
relative error = 6.4571900481672619858950749339809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 140.77024956000295070162563718432
y[1] (numeric) = 140.77024956000295070162563718423
absolute error = 9e-29
relative error = 6.3933963519499008480339228758823e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 142.17496392147684728431889649845
y[1] (numeric) = 142.17496392147684728431889649837
absolute error = 8e-29
relative error = 5.6268697239961288166641660187901e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 143.59379589698908697301579351366
y[1] (numeric) = 143.59379589698908697301579351358
absolute error = 8e-29
relative error = 5.5712713422096714239805320496149e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 145.02688737091958491248570083683
y[1] (numeric) = 145.02688737091958491248570083675
absolute error = 8e-29
relative error = 5.5162185061169141789862884379744e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 146.47438165360998102828140547844
y[1] (numeric) = 146.47438165360998102828140547835
absolute error = 9e-29
relative error = 6.1444191799243466089803064005440e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 147.93642349569479361641444906234
y[1] (numeric) = 147.93642349569479361641444906225
absolute error = 9e-29
relative error = 6.0836944596419255750321317378294e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 2 ) = diff ( y , x , 1 ) ;
Iterations = 2000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Time to Timeout = 2 Minutes 49 Seconds
Percent Done = 100 %
> quit
memory used=971.1MB, alloc=44.3MB, time=10.48