|\^/| 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) + c(x) * c(x) * c(x) / c(3.0));
> end;
exact_soln_y := proc(x) return c(1.0) + c(x)*c(x)*c(x)/c(3.0) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> 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)*16*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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)*16*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> 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 mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_x[1] * array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp1[3] := array_x[2] * array_x[2];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, 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_x[1]*array_x[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_x[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> 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..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # 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/multpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = x * x ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.1);");
> omniout_str(ALWAYS,"x_end := c(10.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.005);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(1.0) + c(x) * c(x) * c(x) / c(3.0));");
> 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(0.1);
> x_end := c(10.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.005);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = x * x ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-02T21:49:06-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mult")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = x * x ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"mult diffeq.mxt")
> ;
> logitem_str(html_log_file,"mult maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
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/multpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = x * x ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.1);");
omniout_str(ALWAYS, "x_end := c(10.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.005);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(1.0) + c(x) * c(x) * c(x) / c(3.0));");
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(0.1);
x_end := c(10.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.005);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = x * x ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-05-02T21:49:06-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mult")
;
logitem_str(html_log_file,
"diff ( y , x , 1 ) = x * x ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file,
"mult diffeq.mxt");
logitem_str(html_log_file,
"mult 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/multpostode.ode#################
diff ( y , x , 1 ) = x * x ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(10.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.005);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(1.0) + c(x) * c(x) * c(x) / c(3.0));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 1.0003333333333333333333333333333
y[1] (numeric) = 1.0003333333333333333333333333333
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] = 0.11
y[1] (closed_form) = 1.0004436666666666666666666666667
y[1] (numeric) = 1.0004436666666666666666666666667
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] = 0.12
y[1] (closed_form) = 1.000576
y[1] (numeric) = 1.0005760000000000000000000000001
absolute error = 1e-31
relative error = 9.9942433158500703594729435844953e-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=4.3MB, alloc=40.3MB, time=0.11
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 1.0007323333333333333333333333333
y[1] (numeric) = 1.0007323333333333333333333333335
absolute error = 2e-31
relative error = 1.9985364051726119238677541813546e-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] = 0.14
y[1] (closed_form) = 1.0009146666666666666666666666667
y[1] (numeric) = 1.0009146666666666666666666666669
absolute error = 2e-31
relative error = 1.9981723383678395494254588469746e-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] = 0.15
y[1] (closed_form) = 1.001125
y[1] (numeric) = 1.0011250000000000000000000000003
absolute error = 3e-31
relative error = 2.9966287926083156448994880759146e-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] = 0.16
y[1] (closed_form) = 1.0013653333333333333333333333333
y[1] (numeric) = 1.0013653333333333333333333333337
absolute error = 4e-31
relative error = 3.9945461130403289375572551609537e-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] = 0.17
y[1] (closed_form) = 1.0016376666666666666666666666667
y[1] (numeric) = 1.0016376666666666666666666666671
absolute error = 4e-31
relative error = 3.9934600436019279093937162240636e-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] = 0.18
y[1] (closed_form) = 1.001944
y[1] (numeric) = 1.0019440000000000000000000000005
absolute error = 5e-31
relative error = 4.9902988590180688741087326237794e-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] = 0.19
y[1] (closed_form) = 1.0022863333333333333333333333333
y[1] (numeric) = 1.0022863333333333333333333333339
absolute error = 6e-31
relative error = 5.9863132923758646481261675389503e-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] = 0.2
y[1] (closed_form) = 1.0026666666666666666666666666667
y[1] (numeric) = 1.0026666666666666666666666666673
absolute error = 6e-31
relative error = 5.9840425531914893617021276595743e-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] = 0.21
y[1] (closed_form) = 1.003087
y[1] (numeric) = 1.0030870000000000000000000000007
absolute error = 7e-31
relative error = 6.9784575016922759441603769164589e-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] = 0.22
y[1] (closed_form) = 1.0035493333333333333333333333333
y[1] (numeric) = 1.0035493333333333333333333333341
absolute error = 8e-31
relative error = 7.9717057590259638456571475642456e-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] = 0.23
y[1] (closed_form) = 1.0040556666666666666666666666667
y[1] (numeric) = 1.0040556666666666666666666666675
absolute error = 8e-31
relative error = 7.9676857226043575937190733448707e-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] = 0.24
y[1] (closed_form) = 1.004608
y[1] (numeric) = 1.0046080000000000000000000000009
absolute error = 9e-31
relative error = 8.9587182264126903229916544562655e-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] = 0.25
y[1] (closed_form) = 1.0052083333333333333333333333333
y[1] (numeric) = 1.0052083333333333333333333333343
absolute error = 1.0e-30
relative error = 9.9481865284974093264248704663216e-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] = 0.26
y[1] (closed_form) = 1.0058586666666666666666666666667
y[1] (numeric) = 1.0058586666666666666666666666677
absolute error = 1.0e-30
relative error = 9.9417545738698876184062969747900e-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] = 0.27
y[1] (closed_form) = 1.006561
y[1] (numeric) = 1.0065610000000000000000000000011
absolute error = 1.1e-30
relative error = 1.0928299427456458177894832007201e-28 %
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] = 0.28
y[1] (closed_form) = 1.0073173333333333333333333333333
y[1] (numeric) = 1.0073173333333333333333333333345
absolute error = 1.2e-30
relative error = 1.1912829853022152568935575416155e-28 %
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] = 0.29
y[1] (closed_form) = 1.0081296666666666666666666666667
y[1] (numeric) = 1.0081296666666666666666666666679
absolute error = 1.2e-30
relative error = 1.1903230702135208136254959266152e-28 %
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] = 0.3
y[1] (closed_form) = 1.009
y[1] (numeric) = 1.0090000000000000000000000000013
absolute error = 1.3e-30
relative error = 1.2884043607532210109018830525273e-28 %
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] = 0.31
y[1] (closed_form) = 1.0099303333333333333333333333333
y[1] (numeric) = 1.0099303333333333333333333333347
absolute error = 1.4e-30
relative error = 1.3862342319981807325983871494767e-28 %
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] = 0.32
y[1] (closed_form) = 1.0109226666666666666666666666667
y[1] (numeric) = 1.0109226666666666666666666666681
absolute error = 1.4e-30
relative error = 1.3848734885095068267668347859117e-28 %
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] = 0.33
y[1] (closed_form) = 1.011979
y[1] (numeric) = 1.0119790000000000000000000000015
absolute error = 1.5e-30
relative error = 1.4822441967669289580119745567843e-28 %
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] = 0.34
y[1] (closed_form) = 1.0131013333333333333333333333333
y[1] (numeric) = 1.0131013333333333333333333333349
absolute error = 1.6e-30
relative error = 1.5793089470484031870454551436777e-28 %
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] = 0.35
y[1] (closed_form) = 1.0142916666666666666666666666667
y[1] (numeric) = 1.0142916666666666666666666666683
absolute error = 1.6e-30
relative error = 1.5774555313642525572033027975187e-28 %
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] = 0.36
y[1] (closed_form) = 1.015552
y[1] (numeric) = 1.0155520000000000000000000000017
absolute error = 1.7e-30
relative error = 1.6739664734055961683892109906731e-28 %
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] = 0.37
y[1] (closed_form) = 1.0168843333333333333333333333333
y[1] (numeric) = 1.0168843333333333333333333333351
absolute error = 1.8e-30
relative error = 1.7701128250246750449821726692614e-28 %
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] = 0.38
y[1] (closed_form) = 1.0182906666666666666666666666667
y[1] (numeric) = 1.0182906666666666666666666666685
absolute error = 1.8e-30
relative error = 1.7676681707122262405757098824435e-28 %
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] = 0.39
y[1] (closed_form) = 1.019773
y[1] (numeric) = 1.0197730000000000000000000000019
absolute error = 1.9e-30
relative error = 1.8631597424132625594127320491913e-28 %
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] = 0.4
y[1] (closed_form) = 1.0213333333333333333333333333333
y[1] (numeric) = 1.0213333333333333333333333333353
absolute error = 2.0e-30
relative error = 1.9582245430809399477806788511750e-28 %
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] = 0.41
y[1] (closed_form) = 1.0229736666666666666666666666667
y[1] (numeric) = 1.0229736666666666666666666666687
absolute error = 2.0e-30
relative error = 1.9550845394847244357218709768025e-28 %
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] = 0.42
y[1] (closed_form) = 1.024696
y[1] (numeric) = 1.0246960000000000000000000000021
absolute error = 2.1e-30
relative error = 2.0493883063855036030198224644187e-28 %
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] = 0.43
y[1] (closed_form) = 1.0265023333333333333333333333333
y[1] (numeric) = 1.0265023333333333333333333333355
absolute error = 2.2e-30
relative error = 2.1432001940570357528006917990445e-28 %
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] = 0.44
y[1] (closed_form) = 1.0283946666666666666666666666667
y[1] (numeric) = 1.0283946666666666666666666666689
absolute error = 2.2e-30
relative error = 2.1392565240841389038708874413973e-28 %
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] = 0.45
y[1] (closed_form) = 1.030375
y[1] (numeric) = 1.0303750000000000000000000000023
absolute error = 2.3e-30
relative error = 2.2321970156496421205871648671600e-28 %
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] = 0.46
y[1] (closed_form) = 1.0324453333333333333333333333333
y[1] (numeric) = 1.0324453333333333333333333333357
absolute error = 2.4e-30
relative error = 2.3245782827565365849878734499584e-28 %
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] = 0.47
y[1] (closed_form) = 1.0346076666666666666666666666667
y[1] (numeric) = 1.0346076666666666666666666666691
absolute error = 2.4e-30
relative error = 2.3197199067085977518692270789925e-28 %
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] = 0.48
y[1] (closed_form) = 1.036864
y[1] (numeric) = 1.0368640000000000000000000000025
absolute error = 2.5e-30
relative error = 2.4111165977408801925807048947596e-28 %
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] = 0.49
y[1] (closed_form) = 1.0392163333333333333333333333333
y[1] (numeric) = 1.0392163333333333333333333333359
absolute error = 2.6e-30
relative error = 2.5018852346752312399503600309080e-28 %
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] = 0.5
y[1] (closed_form) = 1.0416666666666666666666666666667
y[1] (numeric) = 1.0416666666666666666666666666693
absolute error = 2.6e-30
relative error = 2.4959999999999999999999999999999e-28 %
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] = 0.51
y[1] (closed_form) = 1.044217
y[1] (numeric) = 1.0442170000000000000000000000027
absolute error = 2.7e-30
relative error = 2.5856694537629630622753699662043e-28 %
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] = 0.52
y[1] (closed_form) = 1.0468693333333333333333333333333
y[1] (numeric) = 1.0468693333333333333333333333361
absolute error = 2.8e-30
relative error = 2.6746413433322464949462014998371e-28 %
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] = 0.53
y[1] (closed_form) = 1.0496256666666666666666666666667
y[1] (numeric) = 1.0496256666666666666666666666695
absolute error = 2.8e-30
relative error = 2.6676176935459848066469411158326e-28 %
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] = 0.54
y[1] (closed_form) = 1.052488
y[1] (numeric) = 1.0524880000000000000000000000029
absolute error = 2.9e-30
relative error = 2.7553758332636571628370109682961e-28 %
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] = 0.55
y[1] (closed_form) = 1.0554583333333333333333333333333
y[1] (numeric) = 1.0554583333333333333333333333363
absolute error = 3.0e-30
relative error = 2.8423670601239587856776282025977e-28 %
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] = 0.56
y[1] (closed_form) = 1.0585386666666666666666666666667
y[1] (numeric) = 1.0585386666666666666666666666697
absolute error = 3.0e-30
relative error = 2.8340958100727543884399121304338e-28 %
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] = 0.57
y[1] (closed_form) = 1.061731
y[1] (numeric) = 1.0617310000000000000000000000031
absolute error = 3.1e-30
relative error = 2.9197602782625730999659989206306e-28 %
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] = 0.58
y[1] (closed_form) = 1.0650373333333333333333333333333
y[1] (numeric) = 1.0650373333333333333333333333365
absolute error = 3.2e-30
relative error = 3.0045895104772540054933911549893e-28 %
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] = 0.59
y[1] (closed_form) = 1.0684596666666666666666666666667
y[1] (numeric) = 1.0684596666666666666666666666699
absolute error = 3.2e-30
relative error = 2.9949656499278244475926247722967e-28 %
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] = 0.6
y[1] (closed_form) = 1.072
y[1] (numeric) = 1.0720000000000000000000000000033
absolute error = 3.3e-30
relative error = 3.0783582089552238805970149253731e-28 %
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] = 0.61
y[1] (closed_form) = 1.0756603333333333333333333333333
y[1] (numeric) = 1.0756603333333333333333333333367
absolute error = 3.4e-30
relative error = 3.1608491032330218244235091560813e-28 %
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] = 0.62
y[1] (closed_form) = 1.0794426666666666666666666666667
y[1] (numeric) = 1.0794426666666666666666666666701
absolute error = 3.4e-30
relative error = 3.1497735868633442937219453989836e-28 %
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] = 0.63
y[1] (closed_form) = 1.083349
y[1] (numeric) = 1.0833490000000000000000000000035
absolute error = 3.5e-30
relative error = 3.2307225095514003335951757005360e-28 %
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] = 0.64
y[1] (closed_form) = 1.0873813333333333333333333333333
y[1] (numeric) = 1.0873813333333333333333333333369
absolute error = 3.6e-30
relative error = 3.3107060877754016990053167487396e-28 %
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] = 0.65
y[1] (closed_form) = 1.0915416666666666666666666666667
y[1] (numeric) = 1.0915416666666666666666666666703
absolute error = 3.6e-30
relative error = 3.2980875672786960338970111081421e-28 %
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] = 0.66
y[1] (closed_form) = 1.095832
y[1] (numeric) = 1.0958320000000000000000000000037
absolute error = 3.7e-30
relative error = 3.3764299637170661196241759685791e-28 %
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] = 0.67
y[1] (closed_form) = 1.1002543333333333333333333333333
y[1] (numeric) = 1.1002543333333333333333333333371
absolute error = 3.8e-30
relative error = 3.4537469063970966712847908195773e-28 %
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] = 0.68
y[1] (closed_form) = 1.1048106666666666666666666666667
y[1] (numeric) = 1.1048106666666666666666666666705
absolute error = 3.8e-30
relative error = 3.4395033598517030972426044643546e-28 %
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] = 0.69
y[1] (closed_form) = 1.109503
y[1] (numeric) = 1.1095030000000000000000000000039
absolute error = 3.9e-30
relative error = 3.5150873859737197646153277638727e-28 %
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] = 0.7
y[1] (closed_form) = 1.1143333333333333333333333333333
y[1] (numeric) = 1.1143333333333333333333333333373
absolute error = 4.0e-30
relative error = 3.5895901884534848938079569249178e-28 %
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] = 0.71
y[1] (closed_form) = 1.1193036666666666666666666666667
y[1] (numeric) = 1.1193036666666666666666666666707
absolute error = 4.0e-30
relative error = 3.5736504034800207629088442189205e-28 %
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] = 0.72
y[1] (closed_form) = 1.124416
y[1] (numeric) = 1.1244160000000000000000000000041
absolute error = 4.1e-30
relative error = 3.6463372986510330696112470829302e-28 %
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] = 0.73
y[1] (closed_form) = 1.1296723333333333333333333333333
y[1] (numeric) = 1.1296723333333333333333333333375
absolute error = 4.2e-30
relative error = 3.7178922383688249424538147787398e-28 %
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] = 0.74
y[1] (closed_form) = 1.1350746666666666666666666666667
y[1] (numeric) = 1.1350746666666666666666666666709
absolute error = 4.2e-30
relative error = 3.7001971089126589029091771936294e-28 %
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] = 0.75
y[1] (closed_form) = 1.140625
y[1] (numeric) = 1.1406250000000000000000000000043
absolute error = 4.3e-30
relative error = 3.7698630136986301369863013698630e-28 %
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] = 0.76
y[1] (closed_form) = 1.1463253333333333333333333333333
y[1] (numeric) = 1.1463253333333333333333333333377
absolute error = 4.4e-30
relative error = 3.8383518814903040905199687348793e-28 %
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] = 0.77
y[1] (closed_form) = 1.1521776666666666666666666666667
y[1] (numeric) = 1.1521776666666666666666666666711
absolute error = 4.4e-30
relative error = 3.8188554832255326363150590490528e-28 %
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] = 0.78
y[1] (closed_form) = 1.158184
y[1] (numeric) = 1.1581840000000000000000000000045
absolute error = 4.5e-30
relative error = 3.8853929945500887596444088331388e-28 %
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] = 0.79
y[1] (closed_form) = 1.1643463333333333333333333333333
y[1] (numeric) = 1.1643463333333333333333333333379
absolute error = 4.6e-30
relative error = 3.9507145497087206870578885606489e-28 %
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] = 0.8
y[1] (closed_form) = 1.1706666666666666666666666666667
y[1] (numeric) = 1.1706666666666666666666666666713
absolute error = 4.6e-30
relative error = 3.9293849658314350797266514806377e-28 %
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] = 0.81
y[1] (closed_form) = 1.177147
y[1] (numeric) = 1.1771470000000000000000000000047
absolute error = 4.7e-30
relative error = 3.9927043946083199464467904178493e-28 %
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] = 0.82
y[1] (closed_form) = 1.1837893333333333333333333333333
y[1] (numeric) = 1.1837893333333333333333333333381
absolute error = 4.8e-30
relative error = 4.0547755118590920456567722635335e-28 %
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] = 0.83
y[1] (closed_form) = 1.1905956666666666666666666666667
y[1] (numeric) = 1.1905956666666666666666666666715
absolute error = 4.8e-30
relative error = 4.0315953890867512536441842696666e-28 %
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] = 0.84
y[1] (closed_form) = 1.197568
y[1] (numeric) = 1.1975680000000000000000000000049
absolute error = 4.9e-30
relative error = 4.0916256947413424540401881145789e-28 %
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] = 0.85
y[1] (closed_form) = 1.2047083333333333333333333333333
y[1] (numeric) = 1.2047083333333333333333333333383
absolute error = 5.0e-30
relative error = 4.1503821810258361290768858299036e-28 %
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] = 0.86
y[1] (closed_form) = 1.2120186666666666666666666666667
y[1] (numeric) = 1.2120186666666666666666666666717
absolute error = 5.0e-30
relative error = 4.1253490045257828812317522062365e-28 %
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] = 0.87
y[1] (closed_form) = 1.219501
y[1] (numeric) = 1.2195010000000000000000000000051
absolute error = 5.1e-30
relative error = 4.1820383911124304121111831806616e-28 %
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] = 0.88
y[1] (closed_form) = 1.2271573333333333333333333333333
y[1] (numeric) = 1.2271573333333333333333333333385
absolute error = 5.2e-30
relative error = 4.2374354605983693479130087095598e-28 %
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] = 0.89
y[1] (closed_form) = 1.2349896666666666666666666666667
y[1] (numeric) = 1.2349896666666666666666666666719
absolute error = 5.2e-30
relative error = 4.2105615458590881597119975902631e-28 %
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] = 0.9
y[1] (closed_form) = 1.243
y[1] (numeric) = 1.2430000000000000000000000000053
absolute error = 5.3e-30
relative error = 4.2638777152051488334674175382140e-28 %
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] = 0.91
y[1] (closed_form) = 1.2511903333333333333333333333333
y[1] (numeric) = 1.2511903333333333333333333333387
absolute error = 5.4e-30
relative error = 4.3158901217001090428288155465823e-28 %
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] = 0.92
y[1] (closed_form) = 1.2595626666666666666666666666667
y[1] (numeric) = 1.2595626666666666666666666666721
absolute error = 5.4e-30
relative error = 4.2872023305443582534466989600622e-28 %
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] = 0.93
y[1] (closed_form) = 1.268119
y[1] (numeric) = 1.2681190000000000000000000000055
absolute error = 5.5e-30
relative error = 4.3371323984578734330137786753451e-28 %
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] = 0.94
y[1] (closed_form) = 1.2768613333333333333333333333333
y[1] (numeric) = 1.2768613333333333333333333333389
absolute error = 5.6e-30
relative error = 4.3857542348634046401279804854822e-28 %
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] = 0.95
y[1] (closed_form) = 1.2857916666666666666666666666667
y[1] (numeric) = 1.2857916666666666666666666666723
absolute error = 5.6e-30
relative error = 4.3552934314138500923555526750704e-28 %
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] = 0.96
y[1] (closed_form) = 1.294912
y[1] (numeric) = 1.2949120000000000000000000000057
absolute error = 5.7e-30
relative error = 4.4018435229575446053476993031187e-28 %
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] = 0.97
y[1] (closed_form) = 1.3042243333333333333333333333333
y[1] (numeric) = 1.3042243333333333333333333333391
absolute error = 5.8e-30
relative error = 4.4470877070483528779430328064728e-28 %
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] = 0.98
y[1] (closed_form) = 1.3137306666666666666666666666667
y[1] (numeric) = 1.3137306666666666666666666666725
absolute error = 5.8e-30
relative error = 4.4149079770790156886545999281435e-28 %
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] = 0.99
y[1] (closed_form) = 1.323433
y[1] (numeric) = 1.3234330000000000000000000000059
absolute error = 5.9e-30
relative error = 4.4581025257795445632684087520864e-28 %
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] = 1
y[1] (closed_form) = 1.3333333333333333333333333333333
y[1] (numeric) = 1.3333333333333333333333333333393
absolute error = 6.0e-30
relative error = 4.5000000000000000000000000000001e-28 %
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] = 1.01
y[1] (closed_form) = 1.3434336666666666666666666666667
y[1] (numeric) = 1.3434336666666666666666666666727
absolute error = 6.0e-30
relative error = 4.4661676634077702881248819877224e-28 %
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] = 1.02
y[1] (closed_form) = 1.353736
y[1] (numeric) = 1.3537360000000000000000000000061
absolute error = 6.1e-30
relative error = 4.5060484466690698925048901706093e-28 %
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] = 1.03
y[1] (closed_form) = 1.3642423333333333333333333333333
y[1] (numeric) = 1.3642423333333333333333333333395
absolute error = 6.2e-30
relative error = 4.5446471264758191787529439417778e-28 %
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] = 1.04
y[1] (closed_form) = 1.3749546666666666666666666666667
y[1] (numeric) = 1.3749546666666666666666666666729
absolute error = 6.2e-30
relative error = 4.5092395773533381949077593830971e-28 %
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] = 1.05
y[1] (closed_form) = 1.385875
y[1] (numeric) = 1.3858750000000000000000000000063
absolute error = 6.3e-30
relative error = 4.5458645260214665824839902588617e-28 %
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] = 1.06
y[1] (closed_form) = 1.3970053333333333333333333333333
y[1] (numeric) = 1.3970053333333333333333333333397
absolute error = 6.4e-30
relative error = 4.5812280363520444684534728571784e-28 %
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] = 1.07
y[1] (closed_form) = 1.4083476666666666666666666666667
y[1] (numeric) = 1.4083476666666666666666666666731
absolute error = 6.4e-30
relative error = 4.5443324482141365188472638029955e-28 %
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] = 1.08
y[1] (closed_form) = 1.419904
y[1] (numeric) = 1.4199040000000000000000000000065
absolute error = 6.5e-30
relative error = 4.5777742720634634454160281258451e-28 %
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] = 1.09
y[1] (closed_form) = 1.4316763333333333333333333333333
y[1] (numeric) = 1.4316763333333333333333333333399
absolute error = 6.6e-30
relative error = 4.6099805146833700075133369297391e-28 %
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] = 1.1
y[1] (closed_form) = 1.4436666666666666666666666666667
y[1] (numeric) = 1.4436666666666666666666666666733
absolute error = 6.6e-30
relative error = 4.5716924497806511198337566381897e-28 %
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] = 1.11
y[1] (closed_form) = 1.455877
y[1] (numeric) = 1.4558770000000000000000000000067
absolute error = 6.7e-30
relative error = 4.6020371226415418335477516301171e-28 %
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] = 1.12
y[1] (closed_form) = 1.4683093333333333333333333333333
y[1] (numeric) = 1.4683093333333333333333333333401
absolute error = 6.8e-30
relative error = 4.6311767184389847007714995568601e-28 %
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] = 1.13
y[1] (closed_form) = 1.4809656666666666666666666666667
y[1] (numeric) = 1.4809656666666666666666666666735
absolute error = 6.8e-30
relative error = 4.5915986798703638639383267269080e-28 %
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] = 1.14
y[1] (closed_form) = 1.493848
y[1] (numeric) = 1.4938480000000000000000000000069
absolute error = 6.9e-30
relative error = 4.6189438282877508287322404956863e-28 %
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=51.4MB, alloc=40.3MB, time=0.70
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 1.5069583333333333333333333333333
y[1] (numeric) = 1.5069583333333333333333333333403
absolute error = 7.0e-30
relative error = 4.6451184781707081040727735228248e-28 %
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] = 1.16
y[1] (closed_form) = 1.5202986666666666666666666666667
y[1] (numeric) = 1.5202986666666666666666666666737
absolute error = 7.0e-30
relative error = 4.6043584418500224517287831162999e-28 %
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] = 1.17
y[1] (closed_form) = 1.533871
y[1] (numeric) = 1.5338710000000000000000000000071
absolute error = 7.1e-30
relative error = 4.6288116797305640435212609143794e-28 %
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] = 1.18
y[1] (closed_form) = 1.5476773333333333333333333333333
y[1] (numeric) = 1.5476773333333333333333333333405
absolute error = 7.2e-30
relative error = 4.6521324858411486287408744975267e-28 %
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] = 1.19
y[1] (closed_form) = 1.5617196666666666666666666666667
y[1] (numeric) = 1.5617196666666666666666666666739
absolute error = 7.2e-30
relative error = 4.6103024465124876231521705026445e-28 %
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] = 1.2
y[1] (closed_form) = 1.576
y[1] (numeric) = 1.5760000000000000000000000000073
absolute error = 7.3e-30
relative error = 4.6319796954314720812182741116751e-28 %
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] = 1.21
y[1] (closed_form) = 1.5905203333333333333333333333333
y[1] (numeric) = 1.5905203333333333333333333333407
absolute error = 7.4e-30
relative error = 4.6525654811915848922396674798877e-28 %
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] = 1.22
y[1] (closed_form) = 1.6052826666666666666666666666667
y[1] (numeric) = 1.6052826666666666666666666666741
absolute error = 7.4e-30
relative error = 4.6097800428917191738609690339063e-28 %
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] = 1.23
y[1] (closed_form) = 1.620289
y[1] (numeric) = 1.6202890000000000000000000000075
absolute error = 7.5e-30
relative error = 4.6288038738768207400037894474381e-28 %
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] = 1.24
y[1] (closed_form) = 1.6355413333333333333333333333333
y[1] (numeric) = 1.6355413333333333333333333333409
absolute error = 7.6e-30
relative error = 4.6467795372133670727571544100384e-28 %
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] = 1.25
y[1] (closed_form) = 1.6510416666666666666666666666667
y[1] (numeric) = 1.6510416666666666666666666666743
absolute error = 7.6e-30
relative error = 4.6031545741324921135646687697160e-28 %
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] = 1.26
y[1] (closed_form) = 1.666792
y[1] (numeric) = 1.6667920000000000000000000000077
absolute error = 7.7e-30
relative error = 4.6196526021243202511171159928773e-28 %
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] = 1.27
y[1] (closed_form) = 1.6827943333333333333333333333333
y[1] (numeric) = 1.6827943333333333333333333333411
absolute error = 7.8e-30
relative error = 4.6351475313976772364537318186834e-28 %
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] = 1.28
y[1] (closed_form) = 1.6990506666666666666666666666667
y[1] (numeric) = 1.6990506666666666666666666666745
absolute error = 7.8e-30
relative error = 4.5907989402709591552302148336953e-28 %
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] = 1.29
y[1] (closed_form) = 1.715563
y[1] (numeric) = 1.7155630000000000000000000000079
absolute error = 7.9e-30
relative error = 4.6049022973799271725958183989746e-28 %
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] = 1.3
y[1] (closed_form) = 1.7323333333333333333333333333333
y[1] (numeric) = 1.7323333333333333333333333333413
absolute error = 8.0e-30
relative error = 4.6180488743505868770444487204157e-28 %
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] = 1.31
y[1] (closed_form) = 1.7493636666666666666666666666667
y[1] (numeric) = 1.7493636666666666666666666666747
absolute error = 8.0e-30
relative error = 4.5730914345806884827263856514682e-28 %
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] = 1.32
y[1] (closed_form) = 1.766656
y[1] (numeric) = 1.7666560000000000000000000000081
absolute error = 8.1e-30
relative error = 4.5849333429937690189827561223011e-28 %
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] = 1.33
y[1] (closed_form) = 1.7842123333333333333333333333333
y[1] (numeric) = 1.7842123333333333333333333333415
absolute error = 8.2e-30
relative error = 4.5958655518765797120185807481435e-28 %
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] = 1.34
y[1] (closed_form) = 1.8020346666666666666666666666667
y[1] (numeric) = 1.8020346666666666666666666666749
absolute error = 8.2e-30
relative error = 4.5504119047654281160702790771320e-28 %
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] = 1.35
y[1] (closed_form) = 1.820125
y[1] (numeric) = 1.8201250000000000000000000000083
absolute error = 8.3e-30
relative error = 4.5601263649474623995604697479569e-28 %
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] = 1.36
y[1] (closed_form) = 1.8384853333333333333333333333333
y[1] (numeric) = 1.8384853333333333333333333333417
absolute error = 8.4e-30
relative error = 4.5689785214495410714907344016525e-28 %
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] = 1.37
y[1] (closed_form) = 1.8571176666666666666666666666667
y[1] (numeric) = 1.8571176666666666666666666666751
absolute error = 8.4e-30
relative error = 4.5231382753884020631972161878810e-28 %
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] = 1.38
y[1] (closed_form) = 1.876024
y[1] (numeric) = 1.8760240000000000000000000000085
absolute error = 8.5e-30
relative error = 4.5308588802701884410860415431786e-28 %
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] = 1.39
y[1] (closed_form) = 1.8952063333333333333333333333333
y[1] (numeric) = 1.8952063333333333333333333333419
absolute error = 8.6e-30
relative error = 4.5377644896712213744888639214130e-28 %
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] = 1.4
y[1] (closed_form) = 1.9146666666666666666666666666667
y[1] (numeric) = 1.9146666666666666666666666666753
absolute error = 8.6e-30
relative error = 4.4916434540389972144846796657381e-28 %
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] = 1.41
y[1] (closed_form) = 1.934407
y[1] (numeric) = 1.9344070000000000000000000000087
absolute error = 8.7e-30
relative error = 4.4975023353410114831056752792975e-28 %
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] = 1.42
y[1] (closed_form) = 1.9544293333333333333333333333333
y[1] (numeric) = 1.9544293333333333333333333333421
absolute error = 8.8e-30
relative error = 4.5025930842899069600538128094681e-28 %
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] = 1.43
y[1] (closed_form) = 1.9747356666666666666666666666667
y[1] (numeric) = 1.9747356666666666666666666666755
absolute error = 8.8e-30
relative error = 4.4562926312331760183261658480198e-28 %
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] = 1.44
y[1] (closed_form) = 1.995328
y[1] (numeric) = 1.9953280000000000000000000000089
absolute error = 8.9e-30
relative error = 4.4604195400455463963819482310678e-28 %
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] = 1.45
y[1] (closed_form) = 2.0162083333333333333333333333333
y[1] (numeric) = 2.0162083333333333333333333333423
absolute error = 9.0e-30
relative error = 4.4638244229060323627270660687347e-28 %
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] = 1.46
y[1] (closed_form) = 2.0373786666666666666666666666667
y[1] (numeric) = 2.0373786666666666666666666666757
absolute error = 9.0e-30
relative error = 4.4174409731720629253014003615102e-28 %
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] = 1.47
y[1] (closed_form) = 2.058841
y[1] (numeric) = 2.0588410000000000000000000000091
absolute error = 9.1e-30
relative error = 4.4199624934611269155801735053848e-28 %
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] = 1.48
y[1] (closed_form) = 2.0805973333333333333333333333333
y[1] (numeric) = 2.0805973333333333333333333333425
absolute error = 9.2e-30
relative error = 4.4218070707899269953244196538431e-28 %
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] = 1.49
y[1] (closed_form) = 2.1026496666666666666666666666667
y[1] (numeric) = 2.1026496666666666666666666666759
absolute error = 9.2e-30
relative error = 4.3754316973710472294560403072377e-28 %
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] = 1.5
y[1] (closed_form) = 2.125
y[1] (numeric) = 2.1250000000000000000000000000093
absolute error = 9.3e-30
relative error = 4.3764705882352941176470588235294e-28 %
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] = 1.51
y[1] (closed_form) = 2.1476503333333333333333333333333
y[1] (numeric) = 2.1476503333333333333333333333427
absolute error = 9.4e-30
relative error = 4.3768763723331125752780053736247e-28 %
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] = 1.52
y[1] (closed_form) = 2.1706026666666666666666666666667
y[1] (numeric) = 2.1706026666666666666666666666761
absolute error = 9.4e-30
relative error = 4.3305945138431599948892842049396e-28 %
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] = 1.53
y[1] (closed_form) = 2.193859
y[1] (numeric) = 2.1938590000000000000000000000095
absolute error = 9.5e-30
relative error = 4.3302691740900395148457580911080e-28 %
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] = 1.54
y[1] (closed_form) = 2.2174213333333333333333333333333
y[1] (numeric) = 2.2174213333333333333333333333429
absolute error = 9.6e-30
relative error = 4.3293531345117992911886840329849e-28 %
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] = 1.55
y[1] (closed_form) = 2.2412916666666666666666666666667
y[1] (numeric) = 2.2412916666666666666666666666763
absolute error = 9.6e-30
relative error = 4.2832444089159896636983882062054e-28 %
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] = 1.56
y[1] (closed_form) = 2.265472
y[1] (numeric) = 2.2654720000000000000000000000097
absolute error = 9.7e-30
relative error = 4.2816684558449629922594496864230e-28 %
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] = 1.57
y[1] (closed_form) = 2.2899643333333333333333333333333
y[1] (numeric) = 2.2899643333333333333333333333431
absolute error = 9.8e-30
relative error = 4.2795426362535777485908441368738e-28 %
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] = 1.58
y[1] (closed_form) = 2.3147706666666666666666666666667
y[1] (numeric) = 2.3147706666666666666666666666765
absolute error = 9.8e-30
relative error = 4.2336807447591640467767001252247e-28 %
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] = 1.59
y[1] (closed_form) = 2.339893
y[1] (numeric) = 2.3398930000000000000000000000099
absolute error = 9.9e-30
relative error = 4.2309626978669537453208330466393e-28 %
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] = 1.6
y[1] (closed_form) = 2.3653333333333333333333333333333
y[1] (numeric) = 2.3653333333333333333333333333433
absolute error = 1.00e-29
relative error = 4.2277339346110484780157835400226e-28 %
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] = 1.61
y[1] (closed_form) = 2.3910936666666666666666666666667
y[1] (numeric) = 2.3910936666666666666666666666767
absolute error = 1.00e-29
relative error = 4.1821866451349110678920845286835e-28 %
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] = 1.62
y[1] (closed_form) = 2.417176
y[1] (numeric) = 2.4171760000000000000000000000101
absolute error = 1.01e-29
relative error = 4.1784297047463651798627820233198e-28 %
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] = 1.63
y[1] (closed_form) = 2.4435823333333333333333333333333
y[1] (numeric) = 2.4435823333333333333333333333435
absolute error = 1.02e-29
relative error = 4.1741994369741582951914723015268e-28 %
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] = 1.64
y[1] (closed_form) = 2.4703146666666666666666666666667
y[1] (numeric) = 2.4703146666666666666666666666769
absolute error = 1.02e-29
relative error = 4.1290286365677570900549241770009e-28 %
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] = 1.65
y[1] (closed_form) = 2.497375
y[1] (numeric) = 2.4973750000000000000000000000103
absolute error = 1.03e-29
relative error = 4.1243305470744281495570348866310e-28 %
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] = 1.66
y[1] (closed_form) = 2.5247653333333333333333333333333
y[1] (numeric) = 2.5247653333333333333333333333437
absolute error = 1.04e-29
relative error = 4.1191947079966243727469853303859e-28 %
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] = 1.67
y[1] (closed_form) = 2.5524876666666666666666666666667
y[1] (numeric) = 2.5524876666666666666666666666771
absolute error = 1.04e-29
relative error = 4.0744565138610529362009323453472e-28 %
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] = 1.68
y[1] (closed_form) = 2.580544
y[1] (numeric) = 2.5805440000000000000000000000105
absolute error = 1.05e-29
relative error = 4.0689095012524490960045633788845e-28 %
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] = 1.69
y[1] (closed_form) = 2.6089363333333333333333333333333
y[1] (numeric) = 2.6089363333333333333333333333439
absolute error = 1.06e-29
relative error = 4.0629584802695453536683979384191e-28 %
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] = 1.7
y[1] (closed_form) = 2.6376666666666666666666666666667
y[1] (numeric) = 2.6376666666666666666666666666773
absolute error = 1.06e-29
relative error = 4.0187033994692278529002906609376e-28 %
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] = 1.71
y[1] (closed_form) = 2.666737
y[1] (numeric) = 2.6667370000000000000000000000107
absolute error = 1.07e-29
relative error = 4.0123941731036843903242051990879e-28 %
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] = 1.72
y[1] (closed_form) = 2.6961493333333333333333333333333
y[1] (numeric) = 2.6961493333333333333333333333441
absolute error = 1.08e-29
relative error = 4.0057128388536342200629836527354e-28 %
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] = 1.73
y[1] (closed_form) = 2.7259056666666666666666666666667
y[1] (numeric) = 2.7259056666666666666666666666775
absolute error = 1.08e-29
relative error = 3.9619859674772311147475511808491e-28 %
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] = 1.74
y[1] (closed_form) = 2.756008
y[1] (numeric) = 2.7560080000000000000000000000109
absolute error = 1.09e-29
relative error = 3.9549957764999230771463653225970e-28 %
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] = 1.75
y[1] (closed_form) = 2.7864583333333333333333333333333
y[1] (numeric) = 2.7864583333333333333333333333443
absolute error = 1.10e-29
relative error = 3.9476635514018691588785046728972e-28 %
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] = 1.76
y[1] (closed_form) = 2.8172586666666666666666666666667
y[1] (numeric) = 2.8172586666666666666666666666777
absolute error = 1.10e-29
relative error = 3.9045048046706396383434676924707e-28 %
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] = 1.77
y[1] (closed_form) = 2.848411
y[1] (numeric) = 2.8484110000000000000000000000111
absolute error = 1.11e-29
relative error = 3.8969095400909489536446811924262e-28 %
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] = 1.78
y[1] (closed_form) = 2.8799173333333333333333333333333
y[1] (numeric) = 2.8799173333333333333333333333445
absolute error = 1.12e-29
relative error = 3.8890005176074498434677291663002e-28 %
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] = 1.79
y[1] (closed_form) = 2.9117796666666666666666666666667
y[1] (numeric) = 2.9117796666666666666666666666779
absolute error = 1.12e-29
relative error = 3.8464448832495224283797114227621e-28 %
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] = 1.8
y[1] (closed_form) = 2.944
y[1] (numeric) = 2.9440000000000000000000000000113
absolute error = 1.13e-29
relative error = 3.8383152173913043478260869565217e-28 %
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] = 1.81
y[1] (closed_form) = 2.9765803333333333333333333333333
y[1] (numeric) = 2.9765803333333333333333333333447
absolute error = 1.14e-29
relative error = 3.8298983139600577441159827591865e-28 %
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] = 1.82
y[1] (closed_form) = 3.0095226666666666666666666666667
y[1] (numeric) = 3.0095226666666666666666666666781
absolute error = 1.14e-29
relative error = 3.7879761220162488669299494670694e-28 %
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] = 1.83
y[1] (closed_form) = 3.042829
y[1] (numeric) = 3.0428290000000000000000000000115
absolute error = 1.15e-29
relative error = 3.7793776778123253064828815552895e-28 %
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] = 1.84
y[1] (closed_form) = 3.0765013333333333333333333333333
y[1] (numeric) = 3.0765013333333333333333333333449
absolute error = 1.16e-29
relative error = 3.7705168121710549125933527955566e-28 %
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] = 1.85
y[1] (closed_form) = 3.1105416666666666666666666666667
y[1] (numeric) = 3.1105416666666666666666666666783
absolute error = 1.16e-29
relative error = 3.7292540152438615996677963377225e-28 %
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] = 1.86
y[1] (closed_form) = 3.144952
y[1] (numeric) = 3.1449520000000000000000000000117
absolute error = 1.17e-29
relative error = 3.7202475586272858854443565434385e-28 %
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] = 1.87
y[1] (closed_form) = 3.1797343333333333333333333333333
y[1] (numeric) = 3.1797343333333333333333333333451
absolute error = 1.18e-29
relative error = 3.7110018520415175146183596260610e-28 %
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] = 1.88
y[1] (closed_form) = 3.2148906666666666666666666666667
y[1] (numeric) = 3.2148906666666666666666666666785
absolute error = 1.18e-29
relative error = 3.6704203108203161289466349918379e-28 %
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] = 1.89
y[1] (closed_form) = 3.250423
y[1] (numeric) = 3.2504230000000000000000000000119
absolute error = 1.19e-29
relative error = 3.6610619602433283298819876674513e-28 %
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] = 1.9
y[1] (closed_form) = 3.2863333333333333333333333333333
y[1] (numeric) = 3.2863333333333333333333333333453
absolute error = 1.20e-29
relative error = 3.6514859519221016330256618318288e-28 %
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] = 1.91
y[1] (closed_form) = 3.3226236666666666666666666666667
y[1] (numeric) = 3.3226236666666666666666666666787
absolute error = 1.20e-29
relative error = 3.6116037215971193848716541375786e-28 %
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] = 1.92
y[1] (closed_form) = 3.359296
y[1] (numeric) = 3.3592960000000000000000000000121
absolute error = 1.21e-29
relative error = 3.6019451694640781878107794013984e-28 %
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] = 1.93
y[1] (closed_form) = 3.3963523333333333333333333333333
y[1] (numeric) = 3.3963523333333333333333333333455
absolute error = 1.22e-29
relative error = 3.5920890421949744711409505315360e-28 %
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] = 1.94
y[1] (closed_form) = 3.4337946666666666666666666666667
y[1] (numeric) = 3.4337946666666666666666666666789
absolute error = 1.22e-29
relative error = 3.5529206560982485460206123759681e-28 %
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] = 1.95
y[1] (closed_form) = 3.471625
y[1] (numeric) = 3.4716250000000000000000000000123
absolute error = 1.23e-29
relative error = 3.5430093976163900190832823245598e-28 %
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] = 1.96
y[1] (closed_form) = 3.5098453333333333333333333333333
y[1] (numeric) = 3.5098453333333333333333333333457
absolute error = 1.24e-29
relative error = 3.5329192093554739734020568427707e-28 %
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] = 1.97
y[1] (closed_form) = 3.5484576666666666666666666666667
y[1] (numeric) = 3.5484576666666666666666666666791
absolute error = 1.24e-29
relative error = 3.4944759568311979298423831649675e-28 %
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] = 1.98
y[1] (closed_form) = 3.587464
y[1] (numeric) = 3.5874640000000000000000000000125
absolute error = 1.25e-29
relative error = 3.4843555224526294898011520115603e-28 %
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] = 1.99
y[1] (closed_form) = 3.6268663333333333333333333333333
y[1] (numeric) = 3.6268663333333333333333333333459
absolute error = 1.26e-29
relative error = 3.4740734402582063726454765955441e-28 %
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] = 2
y[1] (closed_form) = 3.6666666666666666666666666666667
y[1] (numeric) = 3.6666666666666666666666666666793
absolute error = 1.26e-29
relative error = 3.4363636363636363636363636363636e-28 %
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] = 2.01
y[1] (closed_form) = 3.706867
y[1] (numeric) = 3.7068670000000000000000000000127
absolute error = 1.27e-29
relative error = 3.4260738246071412866984437261979e-28 %
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] = 2.02
y[1] (closed_form) = 3.7474693333333333333333333333333
y[1] (numeric) = 3.7474693333333333333333333333461
absolute error = 1.28e-29
relative error = 3.4156383579033957849599480822970e-28 %
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] = 2.03
y[1] (closed_form) = 3.7884756666666666666666666666667
y[1] (numeric) = 3.7884756666666666666666666666795
absolute error = 1.28e-29
relative error = 3.3786676030737780463505682628554e-28 %
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] = 2.04
y[1] (closed_form) = 3.829888
y[1] (numeric) = 3.8298880000000000000000000000129
absolute error = 1.29e-29
relative error = 3.3682447110724908926840680458541e-28 %
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] = 2.05
y[1] (closed_form) = 3.8717083333333333333333333333333
y[1] (numeric) = 3.8717083333333333333333333333463
absolute error = 1.30e-29
relative error = 3.3576909417677381862011816489276e-28 %
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] = 2.06
y[1] (closed_form) = 3.9139386666666666666666666666667
y[1] (numeric) = 3.9139386666666666666666666666797
absolute error = 1.30e-29
relative error = 3.3214623700456556294188224376876e-28 %
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] = 2.07
y[1] (closed_form) = 3.956581
y[1] (numeric) = 3.9565810000000000000000000000131
absolute error = 1.31e-29
relative error = 3.3109394196656153380911448546106e-28 %
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] = 2.08
y[1] (closed_form) = 3.9996373333333333333333333333333
y[1] (numeric) = 3.9996373333333333333333333333465
absolute error = 1.32e-29
relative error = 3.3002992271299264466644975811140e-28 %
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] = 2.09
y[1] (closed_form) = 4.0431096666666666666666666666667
y[1] (numeric) = 4.0431096666666666666666666666799
absolute error = 1.32e-29
relative error = 3.2648137419637970080620288228640e-28 %
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] = 2.1
y[1] (closed_form) = 4.087
y[1] (numeric) = 4.0870000000000000000000000000133
absolute error = 1.33e-29
relative error = 3.2542206997797895767066307805236e-28 %
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] = 2.11
y[1] (closed_form) = 4.1313103333333333333333333333333
y[1] (numeric) = 4.1313103333333333333333333333467
absolute error = 1.34e-29
relative error = 3.2435229791096948982530240002143e-28 %
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] = 2.12
y[1] (closed_form) = 4.1760426666666666666666666666667
y[1] (numeric) = 4.1760426666666666666666666666801
absolute error = 1.34e-29
relative error = 3.2087794760717642731619600310597e-28 %
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] = 2.13
y[1] (closed_form) = 4.221199
y[1] (numeric) = 4.2211990000000000000000000000135
absolute error = 1.35e-29
relative error = 3.1981434658730848747002924998324e-28 %
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] = 2.14
y[1] (closed_form) = 4.2667813333333333333333333333333
y[1] (numeric) = 4.2667813333333333333333333333469
absolute error = 1.36e-29
relative error = 3.1874143382396598091426292918378e-28 %
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] = 2.15
y[1] (closed_form) = 4.3127916666666666666666666666667
y[1] (numeric) = 4.3127916666666666666666666666803
absolute error = 1.36e-29
relative error = 3.1534099143053126841662882703585e-28 %
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=98.3MB, alloc=40.3MB, time=1.28
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 4.359232
y[1] (numeric) = 4.3592320000000000000000000000137
absolute error = 1.37e-29
relative error = 3.1427554211384023607828167897464e-28 %
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] = 2.17
y[1] (closed_form) = 4.4061043333333333333333333333333
y[1] (numeric) = 4.4061043333333333333333333333471
absolute error = 1.38e-29
relative error = 3.1320184353328597983721523313906e-28 %
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] = 2.18
y[1] (closed_form) = 4.4534106666666666666666666666667
y[1] (numeric) = 4.4534106666666666666666666666805
absolute error = 1.38e-29
relative error = 3.0987485846054170316802881866123e-28 %
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] = 2.19
y[1] (closed_form) = 4.501153
y[1] (numeric) = 4.5011530000000000000000000000139
absolute error = 1.39e-29
relative error = 3.0880976496466572009438470542992e-28 %
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] = 2.2
y[1] (closed_form) = 4.5493333333333333333333333333333
y[1] (numeric) = 4.5493333333333333333333333333473
absolute error = 1.40e-29
relative error = 3.0773739742086752637749120750293e-28 %
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] = 2.21
y[1] (closed_form) = 4.5979536666666666666666666666667
y[1] (numeric) = 4.5979536666666666666666666666807
absolute error = 1.40e-29
relative error = 3.0448327701721802184319531710519e-28 %
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] = 2.22
y[1] (closed_form) = 4.647016
y[1] (numeric) = 4.6470160000000000000000000000141
absolute error = 1.41e-29
relative error = 3.0342051759666848575515987033399e-28 %
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] = 2.23
y[1] (closed_form) = 4.6965223333333333333333333333333
y[1] (numeric) = 4.6965223333333333333333333333475
absolute error = 1.42e-29
relative error = 3.0235137815093962788210595825976e-28 %
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] = 2.24
y[1] (closed_form) = 4.7464746666666666666666666666667
y[1] (numeric) = 4.7464746666666666666666666666809
absolute error = 1.42e-29
relative error = 2.9916940460513009514991617638466e-28 %
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] = 2.25
y[1] (closed_form) = 4.796875
y[1] (numeric) = 4.7968750000000000000000000000143
absolute error = 1.43e-29
relative error = 2.9811074918566775244299674267101e-28 %
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] = 2.26
y[1] (closed_form) = 4.8477253333333333333333333333333
y[1] (numeric) = 4.8477253333333333333333333333477
absolute error = 1.44e-29
relative error = 2.9704653233929094992730611250253e-28 %
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] = 2.27
y[1] (closed_form) = 4.8990276666666666666666666666667
y[1] (numeric) = 4.8990276666666666666666666666811
absolute error = 1.44e-29
relative error = 2.9393587829639391707864751121022e-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] = 2.28
y[1] (closed_form) = 4.950784
y[1] (numeric) = 4.9507840000000000000000000000145
absolute error = 1.45e-29
relative error = 2.9288290501060034127928021097265e-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] = 2.29
y[1] (closed_form) = 5.0029963333333333333333333333333
y[1] (numeric) = 5.0029963333333333333333333333479
absolute error = 1.46e-29
relative error = 2.9182511893372698187732698051814e-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] = 2.3
y[1] (closed_form) = 5.0556666666666666666666666666667
y[1] (numeric) = 5.0556666666666666666666666666813
absolute error = 1.46e-29
relative error = 2.8878486187116766664468912771148e-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] = 2.31
y[1] (closed_form) = 5.108797
y[1] (numeric) = 5.1087970000000000000000000000147
absolute error = 1.47e-29
relative error = 2.8773897259961591740677893445365e-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] = 2.32
y[1] (closed_form) = 5.1623893333333333333333333333333
y[1] (numeric) = 5.1623893333333333333333333333481
absolute error = 1.48e-29
relative error = 2.8668895436531714513589572993591e-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] = 2.33
y[1] (closed_form) = 5.2164456666666666666666666666667
y[1] (numeric) = 5.2164456666666666666666666666815
absolute error = 1.48e-29
relative error = 2.8371808978233390973687894892927e-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] = 2.34
y[1] (closed_form) = 5.270968
y[1] (numeric) = 5.2709680000000000000000000000149
absolute error = 1.49e-29
relative error = 2.8268052471576378380593469738386e-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] = 2.35
y[1] (closed_form) = 5.3259583333333333333333333333333
y[1] (numeric) = 5.3259583333333333333333333333483
absolute error = 1.50e-29
relative error = 2.8163945455825633884355710631107e-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] = 2.36
y[1] (closed_form) = 5.3814186666666666666666666666667
y[1] (numeric) = 5.3814186666666666666666666666817
absolute error = 1.50e-29
relative error = 2.7873690803713717126388481451235e-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] = 2.37
y[1] (closed_form) = 5.437351
y[1] (numeric) = 5.4373510000000000000000000000151
absolute error = 1.51e-29
relative error = 2.7770875928370267065709018968980e-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] = 2.38
y[1] (closed_form) = 5.4937573333333333333333333333333
y[1] (numeric) = 5.4937573333333333333333333333485
absolute error = 1.52e-29
relative error = 2.7667767390769353239240272231415e-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] = 2.39
y[1] (closed_form) = 5.5506396666666666666666666666667
y[1] (numeric) = 5.5506396666666666666666666666819
absolute error = 1.52e-29
relative error = 2.7384231210829214338599653289209e-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] = 2.4
y[1] (closed_form) = 5.608
y[1] (numeric) = 5.6080000000000000000000000000153
absolute error = 1.53e-29
relative error = 2.7282453637660485021398002853067e-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] = 2.41
y[1] (closed_form) = 5.6658403333333333333333333333333
y[1] (numeric) = 5.6658403333333333333333333333487
absolute error = 1.54e-29
relative error = 2.7180434135071814295743479299129e-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] = 2.42
y[1] (closed_form) = 5.7241626666666666666666666666667
y[1] (numeric) = 5.7241626666666666666666666666821
absolute error = 1.54e-29
relative error = 2.6903498200144323874327354312316e-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] = 2.43
y[1] (closed_form) = 5.782969
y[1] (numeric) = 5.7829690000000000000000000000155
absolute error = 1.55e-29
relative error = 2.6802841239508633022241689346770e-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] = 2.44
y[1] (closed_form) = 5.8422613333333333333333333333333
y[1] (numeric) = 5.8422613333333333333333333333489
absolute error = 1.56e-29
relative error = 2.6701989366674456648749707875672e-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] = 2.45
y[1] (closed_form) = 5.9020416666666666666666666666667
y[1] (numeric) = 5.9020416666666666666666666666823
absolute error = 1.56e-29
relative error = 2.6431531461570501733157311382360e-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] = 2.46
y[1] (closed_form) = 5.962312
y[1] (numeric) = 5.9623120000000000000000000000157
absolute error = 1.57e-29
relative error = 2.6332067157840783910670894109533e-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] = 2.47
y[1] (closed_form) = 6.0230743333333333333333333333333
y[1] (numeric) = 6.0230743333333333333333333333491
absolute error = 1.58e-29
relative error = 2.6232450615059651430501466499141e-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] = 2.48
y[1] (closed_form) = 6.0843306666666666666666666666667
y[1] (numeric) = 6.0843306666666666666666666666825
absolute error = 1.58e-29
relative error = 2.5968345354011002689312524763063e-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) = 6.146083
y[1] (numeric) = 6.1460830000000000000000000000159
absolute error = 1.59e-29
relative error = 2.5870135499309072135862792611164e-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] = 2.5
y[1] (closed_form) = 6.2083333333333333333333333333333
y[1] (numeric) = 6.2083333333333333333333333333493
absolute error = 1.60e-29
relative error = 2.5771812080536912751677852348993e-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] = 2.51
y[1] (closed_form) = 6.2710836666666666666666666666667
y[1] (numeric) = 6.2710836666666666666666666666827
absolute error = 1.60e-29
relative error = 2.5513931643180649638916740121099e-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] = 2.52
y[1] (closed_form) = 6.334336
y[1] (numeric) = 6.3343360000000000000000000000161
absolute error = 1.61e-29
relative error = 2.5417028714611918281568896882009e-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) = 6.3980923333333333333333333333333
y[1] (numeric) = 6.3980923333333333333333333333495
absolute error = 1.62e-29
relative error = 2.5320047220325100028513707497292e-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) = 6.4623546666666666666666666666667
y[1] (numeric) = 6.4623546666666666666666666666829
absolute error = 1.62e-29
relative error = 2.5068262012236613032277605314554e-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) = 6.527125
y[1] (numeric) = 6.5271250000000000000000000000163
absolute error = 1.63e-29
relative error = 2.4972710036961142922802918589731e-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) = 6.5924053333333333333333333333333
y[1] (numeric) = 6.5924053333333333333333333333497
absolute error = 1.64e-29
relative error = 2.4877111116144961960267815247606e-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) = 6.6581976666666666666666666666667
y[1] (numeric) = 6.6581976666666666666666666666831
absolute error = 1.64e-29
relative error = 2.4631290359708455636617977647905e-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] = 2.58
y[1] (closed_form) = 6.724504
y[1] (numeric) = 6.7245040000000000000000000000165
absolute error = 1.65e-29
relative error = 2.4537125712171485064177224074817e-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] = 2.59
y[1] (closed_form) = 6.7913263333333333333333333333333
y[1] (numeric) = 6.7913263333333333333333333333499
absolute error = 1.66e-29
relative error = 2.4442942637763590509247113683586e-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) = 6.8586666666666666666666666666667
y[1] (numeric) = 6.8586666666666666666666666666833
absolute error = 1.66e-29
relative error = 2.4202954898911353032659409020218e-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] = 2.61
y[1] (closed_form) = 6.926527
y[1] (numeric) = 6.9265270000000000000000000000167
absolute error = 1.67e-29
relative error = 2.4110207034492177681542279413622e-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] = 2.62
y[1] (closed_form) = 6.9949093333333333333333333333333
y[1] (numeric) = 6.9949093333333333333333333333501
absolute error = 1.68e-29
relative error = 2.4017466416529201617481055746827e-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) = 7.0638156666666666666666666666667
y[1] (numeric) = 7.0638156666666666666666666666835
absolute error = 1.68e-29
relative error = 2.3783180072601932279565430336116e-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] = 2.64
y[1] (closed_form) = 7.133248
y[1] (numeric) = 7.1332480000000000000000000000169
absolute error = 1.69e-29
relative error = 2.3691872201835685511004243789085e-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] = 2.65
y[1] (closed_form) = 7.2032083333333333333333333333333
y[1] (numeric) = 7.2032083333333333333333333333503
absolute error = 1.70e-29
relative error = 2.3600594642433637788716833355507e-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] = 2.66
y[1] (closed_form) = 7.2736986666666666666666666666667
y[1] (numeric) = 7.2736986666666666666666666666837
absolute error = 1.70e-29
relative error = 2.3371878296122247938417025432636e-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] = 2.67
y[1] (closed_form) = 7.344721
y[1] (numeric) = 7.3447210000000000000000000000171
absolute error = 1.71e-29
relative error = 2.3282028003514360858635746681188e-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] = 2.68
y[1] (closed_form) = 7.4162773333333333333333333333333
y[1] (numeric) = 7.4162773333333333333333333333505
absolute error = 1.72e-29
relative error = 2.3192228697668264113819547920538e-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] = 2.69
y[1] (closed_form) = 7.4883696666666666666666666666667
y[1] (numeric) = 7.4883696666666666666666666666839
absolute error = 1.72e-29
relative error = 2.2968951541699619619027888981086e-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] = 2.7
y[1] (closed_form) = 7.561
y[1] (numeric) = 7.5610000000000000000000000000173
absolute error = 1.73e-29
relative error = 2.2880571352995635497950006612882e-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] = 2.71
y[1] (closed_form) = 7.6341703333333333333333333333333
y[1] (numeric) = 7.6341703333333333333333333333507
absolute error = 1.74e-29
relative error = 2.2792260639019014115963092431219e-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] = 2.72
y[1] (closed_form) = 7.7078826666666666666666666666667
y[1] (numeric) = 7.7078826666666666666666666666841
absolute error = 1.74e-29
relative error = 2.2574292775949538757898407725286e-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] = 2.73
y[1] (closed_form) = 7.782139
y[1] (numeric) = 7.7821390000000000000000000000175
absolute error = 1.75e-29
relative error = 2.2487390677550221089600172908759e-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] = 2.74
y[1] (closed_form) = 7.8569413333333333333333333333333
y[1] (numeric) = 7.8569413333333333333333333333509
absolute error = 1.76e-29
relative error = 2.2400574540796706979781445061064e-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] = 2.75
y[1] (closed_form) = 7.9322916666666666666666666666667
y[1] (numeric) = 7.9322916666666666666666666666843
absolute error = 1.76e-29
relative error = 2.2187787261982928430728824688115e-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] = 2.76
y[1] (closed_form) = 8.008192
y[1] (numeric) = 8.0081920000000000000000000000177
absolute error = 1.77e-29
relative error = 2.2102367176011763953711399526884e-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] = 2.77
y[1] (closed_form) = 8.0846443333333333333333333333333
y[1] (numeric) = 8.0846443333333333333333333333511
absolute error = 1.78e-29
relative error = 2.2017047709334399497186703698736e-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] = 2.78
y[1] (closed_form) = 8.1616506666666666666666666666667
y[1] (numeric) = 8.1616506666666666666666666666845
absolute error = 1.78e-29
relative error = 2.1809313736861726337057961150996e-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] = 2.79
y[1] (closed_form) = 8.239213
y[1] (numeric) = 8.2392130000000000000000000000179
absolute error = 1.79e-29
relative error = 2.1725375955203488488524328719260e-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] = 2.8
y[1] (closed_form) = 8.3173333333333333333333333333333
y[1] (numeric) = 8.3173333333333333333333333333513
absolute error = 1.80e-29
relative error = 2.1641551779416479640910548252645e-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] = 2.81
y[1] (closed_form) = 8.3960136666666666666666666666667
y[1] (numeric) = 8.3960136666666666666666666666847
absolute error = 1.80e-29
relative error = 2.1438745474489262582985314340246e-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] = 2.82
y[1] (closed_form) = 8.475256
y[1] (numeric) = 8.4752560000000000000000000000181
absolute error = 1.81e-29
relative error = 2.1356287054927898343129694253483e-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] = 2.83
y[1] (closed_form) = 8.5550623333333333333333333333333
y[1] (numeric) = 8.5550623333333333333333333333515
absolute error = 1.82e-29
relative error = 2.1273953702343957205532926761843e-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] = 2.84
y[1] (closed_form) = 8.6354346666666666666666666666667
y[1] (numeric) = 8.6354346666666666666666666666849
absolute error = 1.82e-29
relative error = 2.1075951243373041557761385028138e-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] = 2.85
y[1] (closed_form) = 8.716375
y[1] (numeric) = 8.7163750000000000000000000000183
absolute error = 1.83e-29
relative error = 2.0994966370767664309991252097346e-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] = 2.86
y[1] (closed_form) = 8.7978853333333333333333333333333
y[1] (numeric) = 8.7978853333333333333333333333517
absolute error = 1.84e-29
relative error = 2.0914116634694337154352545929977e-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] = 2.87
y[1] (closed_form) = 8.8799676666666666666666666666667
y[1] (numeric) = 8.8799676666666666666666666666851
absolute error = 1.84e-29
relative error = 2.0720796168064125458715071147218e-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] = 2.88
y[1] (closed_form) = 8.962624
y[1] (numeric) = 8.9626240000000000000000000000185
absolute error = 1.85e-29
relative error = 2.0641276483315600431302261480566e-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] = 2.89
y[1] (closed_form) = 9.0458563333333333333333333333333
y[1] (numeric) = 9.0458563333333333333333333333519
absolute error = 1.86e-29
relative error = 2.0561900736208169567436198872493e-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] = 2.9
y[1] (closed_form) = 9.1296666666666666666666666666667
y[1] (numeric) = 9.1296666666666666666666666666853
absolute error = 1.86e-29
relative error = 2.0373142502464493044652962868305e-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] = 2.91
y[1] (closed_form) = 9.214057
y[1] (numeric) = 9.2140570000000000000000000000187
absolute error = 1.87e-29
relative error = 2.0295077401843726384588243810517e-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] = 2.92
y[1] (closed_form) = 9.2990293333333333333333333333333
y[1] (numeric) = 9.2990293333333333333333333333521
absolute error = 1.88e-29
relative error = 2.0217163884631973057546364695842e-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] = 2.93
y[1] (closed_form) = 9.3845856666666666666666666666667
y[1] (numeric) = 9.3845856666666666666666666666855
absolute error = 1.88e-29
relative error = 2.0032850322605256555990022930154e-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] = 2.94
y[1] (closed_form) = 9.470728
y[1] (numeric) = 9.4707280000000000000000000000189
absolute error = 1.89e-29
relative error = 1.9956227229839142249677110355191e-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] = 2.95
y[1] (closed_form) = 9.5574583333333333333333333333333
y[1] (numeric) = 9.5574583333333333333333333333523
absolute error = 1.90e-29
relative error = 1.9879762314771622511215063279550e-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] = 2.96
y[1] (closed_form) = 9.6447786666666666666666666666667
y[1] (numeric) = 9.6447786666666666666666666666857
absolute error = 1.90e-29
relative error = 1.9699778145937062457559074450507e-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] = 2.97
y[1] (closed_form) = 9.732691
y[1] (numeric) = 9.7326910000000000000000000000191
absolute error = 1.91e-29
relative error = 1.9624582759280038788861169023038e-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] = 2.98
y[1] (closed_form) = 9.8211973333333333333333333333333
y[1] (numeric) = 9.8211973333333333333333333333525
absolute error = 1.92e-29
relative error = 1.9549551188463375409216907429345e-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] = 2.99
y[1] (closed_form) = 9.9102996666666666666666666666667
y[1] (numeric) = 9.9102996666666666666666666666859
absolute error = 1.92e-29
relative error = 1.9373783483641042943235587998869e-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] = 3
y[1] (closed_form) = 10
y[1] (numeric) = 10.000000000000000000000000000019
absolute error = 1.9e-29
relative error = 1.9000000000000000000000000000000e-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] = 3.01
y[1] (closed_form) = 10.090300333333333333333333333333
y[1] (numeric) = 10.090300333333333333333333333353
absolute error = 2.0e-29
relative error = 1.9821015568713993679937045811752e-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] = 3.02
y[1] (closed_form) = 10.181202666666666666666666666667
y[1] (numeric) = 10.181202666666666666666666666687
absolute error = 2.0e-29
relative error = 1.9644044672129107995361910092612e-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] = 3.03
y[1] (closed_form) = 10.272709
y[1] (numeric) = 10.272709000000000000000000000021
absolute error = 2.1e-29
relative error = 2.0442514238454530348323893921263e-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] = 3.04
y[1] (closed_form) = 10.364821333333333333333333333333
y[1] (numeric) = 10.364821333333333333333333333355
absolute error = 2.2e-29
relative error = 2.1225643252766794758063686191858e-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] = 3.05
y[1] (closed_form) = 10.457541666666666666666666666667
y[1] (numeric) = 10.457541666666666666666666666689
absolute error = 2.2e-29
relative error = 2.1037449049928082205425908734127e-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] = 3.06
y[1] (closed_form) = 10.550872
y[1] (numeric) = 10.550872000000000000000000000023
absolute error = 2.3e-29
relative error = 2.1799146080058596104663197506329e-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] = 3.07
y[1] (closed_form) = 10.644814333333333333333333333333
y[1] (numeric) = 10.644814333333333333333333333357
absolute error = 2.4e-29
relative error = 2.2546189391811217750063779098950e-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] = 3.08
y[1] (closed_form) = 10.739370666666666666666666666667
y[1] (numeric) = 10.739370666666666666666666666691
absolute error = 2.4e-29
relative error = 2.2347678225216921463306105584336e-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] = 3.09
y[1] (closed_form) = 10.834543
y[1] (numeric) = 10.834543000000000000000000000025
absolute error = 2.5e-29
relative error = 2.3074346559887205210224372177027e-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] = 3.1
y[1] (closed_form) = 10.930333333333333333333333333333
y[1] (numeric) = 10.930333333333333333333333333359
absolute error = 2.6e-29
relative error = 2.3787014729651428745692415601843e-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] = 3.11
y[1] (closed_form) = 11.026743666666666666666666666667
y[1] (numeric) = 11.026743666666666666666666666693
absolute error = 2.6e-29
relative error = 2.3579037280604237618534163198557e-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] = 3.12
y[1] (closed_form) = 11.123776
y[1] (numeric) = 11.123776000000000000000000000027
absolute error = 2.7e-29
relative error = 2.4272333423470591281233998239447e-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] = 3.13
y[1] (closed_form) = 11.221432333333333333333333333333
y[1] (numeric) = 11.221432333333333333333333333361
absolute error = 2.8e-29
relative error = 2.4952251342126645329917330517849e-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] = 3.14
y[1] (closed_form) = 11.319714666666666666666666666667
y[1] (numeric) = 11.319714666666666666666666666695
absolute error = 2.8e-29
relative error = 2.4735605820924108098837827007653e-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] = 3.15
y[1] (closed_form) = 11.418625
y[1] (numeric) = 11.418625000000000000000000000029
absolute error = 2.9e-29
relative error = 2.5397103416567231168376227435440e-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] = 3.16
y[1] (closed_form) = 11.518165333333333333333333333333
y[1] (numeric) = 11.518165333333333333333333333363
absolute error = 3.0e-29
relative error = 2.6045814703823201472827153954149e-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=145.4MB, alloc=40.3MB, time=1.87
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 11.618337666666666666666666666667
y[1] (numeric) = 11.618337666666666666666666666697
absolute error = 3.0e-29
relative error = 2.5821249873009658610656665082867e-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] = 3.18
y[1] (closed_form) = 11.719144
y[1] (numeric) = 11.719144000000000000000000000031
absolute error = 3.1e-29
relative error = 2.6452443966897240958895973972160e-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] = 3.19
y[1] (closed_form) = 11.820586333333333333333333333333
y[1] (numeric) = 11.820586333333333333333333333365
absolute error = 3.2e-29
relative error = 2.7071415154561283888935120223450e-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] = 3.2
y[1] (closed_form) = 11.922666666666666666666666666667
y[1] (numeric) = 11.922666666666666666666666666699
absolute error = 3.2e-29
relative error = 2.6839633191679713710579288749720e-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] = 3.21
y[1] (closed_form) = 12.025387
y[1] (numeric) = 12.025387000000000000000000000033
absolute error = 3.3e-29
relative error = 2.7441944280046870840830320055396e-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] = 3.22
y[1] (closed_form) = 12.128749333333333333333333333333
y[1] (numeric) = 12.128749333333333333333333333367
absolute error = 3.4e-29
relative error = 2.8032568788076198458274675641194e-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] = 3.23
y[1] (closed_form) = 12.232755666666666666666666666667
y[1] (numeric) = 12.232755666666666666666666666701
absolute error = 3.4e-29
relative error = 2.7794227994471782550385826120889e-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] = 3.24
y[1] (closed_form) = 12.337408
y[1] (numeric) = 12.337408000000000000000000000035
absolute error = 3.5e-29
relative error = 2.8369005872222106944992011287946e-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] = 3.25
y[1] (closed_form) = 12.442708333333333333333333333333
y[1] (numeric) = 12.442708333333333333333333333369
absolute error = 3.6e-29
relative error = 2.8932607785684386772708246128088e-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] = 3.26
y[1] (closed_form) = 12.548658666666666666666666666667
y[1] (numeric) = 12.548658666666666666666666666703
absolute error = 3.6e-29
relative error = 2.8688325147952067971355026098937e-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] = 3.27
y[1] (closed_form) = 12.655261
y[1] (numeric) = 12.655261000000000000000000000037
absolute error = 3.7e-29
relative error = 2.9236852562740507682931233105346e-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] = 3.28
y[1] (closed_form) = 12.762517333333333333333333333333
y[1] (numeric) = 12.762517333333333333333333333371
absolute error = 3.8e-29
relative error = 2.9774690217854617605220621051981e-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] = 3.29
y[1] (closed_form) = 12.870429666666666666666666666667
y[1] (numeric) = 12.870429666666666666666666666705
absolute error = 3.8e-29
relative error = 2.9525043828503109543947108318502e-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] = 3.3
y[1] (closed_form) = 12.979
y[1] (numeric) = 12.979000000000000000000000000039
absolute error = 3.9e-29
relative error = 3.0048539949148624701440788966793e-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] = 3.31
y[1] (closed_form) = 13.088230333333333333333333333333
y[1] (numeric) = 13.088230333333333333333333333373
absolute error = 4.0e-29
relative error = 3.0561809336535973248840796938910e-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] = 3.32
y[1] (closed_form) = 13.198122666666666666666666666667
y[1] (numeric) = 13.198122666666666666666666666707
absolute error = 4.0e-29
relative error = 3.0307340680371511423038751369891e-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] = 3.33
y[1] (closed_form) = 13.308679
y[1] (numeric) = 13.308679000000000000000000000041
absolute error = 4.1e-29
relative error = 3.0806964387675140410254090582544e-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] = 3.34
y[1] (closed_form) = 13.419901333333333333333333333333
y[1] (numeric) = 13.419901333333333333333333333375
absolute error = 4.2e-29
relative error = 3.1296802380862015279595696977803e-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] = 3.35
y[1] (closed_form) = 13.531791666666666666666666666667
y[1] (numeric) = 13.531791666666666666666666666709
absolute error = 4.2e-29
relative error = 3.1038018493486019035419675270889e-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] = 3.36
y[1] (closed_form) = 13.644352
y[1] (numeric) = 13.644352000000000000000000000043
absolute error = 4.3e-29
relative error = 3.1514871501409520950500250946326e-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] = 3.37
y[1] (closed_form) = 13.757584333333333333333333333333
y[1] (numeric) = 13.757584333333333333333333333377
absolute error = 4.4e-29
relative error = 3.1982358918485519974885125787466e-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] = 3.38
y[1] (closed_form) = 13.871490666666666666666666666667
y[1] (numeric) = 13.871490666666666666666666666711
absolute error = 4.4e-29
relative error = 3.1719734423159327841525899932119e-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] = 3.39
y[1] (closed_form) = 13.986073
y[1] (numeric) = 13.986073000000000000000000000045
absolute error = 4.5e-29
relative error = 3.2174864238160347082415485747858e-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] = 3.4
y[1] (closed_form) = 14.101333333333333333333333333333
y[1] (numeric) = 14.101333333333333333333333333379
absolute error = 4.6e-29
relative error = 3.2621028744326777609682299546143e-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] = 3.41
y[1] (closed_form) = 14.217273666666666666666666666667
y[1] (numeric) = 14.217273666666666666666666666713
absolute error = 4.6e-29
relative error = 3.2355007773290617533070862320274e-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] = 3.42
y[1] (closed_form) = 14.333896
y[1] (numeric) = 14.333896000000000000000000000047
absolute error = 4.7e-29
relative error = 3.2789410499420394845895351828979e-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] = 3.43
y[1] (closed_form) = 14.451202333333333333333333333333
y[1] (numeric) = 14.451202333333333333333333333381
absolute error = 4.8e-29
relative error = 3.3215229357963225528155016029002e-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] = 3.44
y[1] (closed_form) = 14.569194666666666666666666666667
y[1] (numeric) = 14.569194666666666666666666666715
absolute error = 4.8e-29
relative error = 3.2946227364111454890757631444464e-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] = 3.45
y[1] (closed_form) = 14.687875
y[1] (numeric) = 14.687875000000000000000000000049
absolute error = 4.9e-29
relative error = 3.3360850361267371896887739036450e-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] = 3.46
y[1] (closed_form) = 14.807245333333333333333333333333
y[1] (numeric) = 14.807245333333333333333333333383
absolute error = 5.0e-29
relative error = 3.3767253040268394733605188234877e-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] = 3.47
y[1] (closed_form) = 14.927307666666666666666666666667
y[1] (numeric) = 14.927307666666666666666666666717
absolute error = 5.0e-29
relative error = 3.3495658504883767496987567952363e-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] = 3.48
y[1] (closed_form) = 15.048064
y[1] (numeric) = 15.048064000000000000000000000051
absolute error = 5.1e-29
relative error = 3.3891402907377321095923037009944e-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] = 3.49
y[1] (closed_form) = 15.169516333333333333333333333333
y[1] (numeric) = 15.169516333333333333333333333385
absolute error = 5.2e-29
relative error = 3.4279273549240165842246475491891e-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] = 3.5
y[1] (closed_form) = 15.291666666666666666666666666667
y[1] (numeric) = 15.291666666666666666666666666719
absolute error = 5.2e-29
relative error = 3.4005449591280653950953678474114e-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] = 3.51
y[1] (closed_form) = 15.414517
y[1] (numeric) = 15.414517000000000000000000000053
absolute error = 5.3e-29
relative error = 3.4383172693636784078281531623728e-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] = 3.52
y[1] (closed_form) = 15.538069333333333333333333333333
y[1] (numeric) = 15.538069333333333333333333333387
absolute error = 5.4e-29
relative error = 3.4753352454256007095519031450669e-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] = 3.53
y[1] (closed_form) = 15.662325666666666666666666666667
y[1] (numeric) = 15.662325666666666666666666666721
absolute error = 5.4e-29
relative error = 3.4477638346472044796582678643062e-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] = 3.54
y[1] (closed_form) = 15.787288
y[1] (numeric) = 15.787288000000000000000000000055
absolute error = 5.5e-29
relative error = 3.4838155863122279140027090149999e-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] = 3.55
y[1] (closed_form) = 15.912958333333333333333333333333
y[1] (numeric) = 15.912958333333333333333333333389
absolute error = 5.6e-29
relative error = 3.5191445127267871310331464660615e-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] = 3.56
y[1] (closed_form) = 16.039338666666666666666666666667
y[1] (numeric) = 16.039338666666666666666666666723
absolute error = 5.6e-29
relative error = 3.4914157724208745431233074946398e-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] = 3.57
y[1] (closed_form) = 16.166431
y[1] (numeric) = 16.166431000000000000000000000057
absolute error = 5.7e-29
relative error = 3.5258245929481899870169241436159e-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] = 3.58
y[1] (closed_form) = 16.294237333333333333333333333333
y[1] (numeric) = 16.294237333333333333333333333391
absolute error = 5.8e-29
relative error = 3.5595406408711529753095532015491e-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] = 3.59
y[1] (closed_form) = 16.422759666666666666666666666667
y[1] (numeric) = 16.422759666666666666666666666725
absolute error = 5.8e-29
relative error = 3.5316841491459443915221800217539e-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] = 3.6
y[1] (closed_form) = 16.552
y[1] (numeric) = 16.552000000000000000000000000059
absolute error = 5.9e-29
relative error = 3.5645239246012566457225712904785e-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] = 3.61
y[1] (closed_form) = 16.681960333333333333333333333333
y[1] (numeric) = 16.681960333333333333333333333393
absolute error = 6.0e-29
relative error = 3.5966995965162447634801353581927e-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] = 3.62
y[1] (closed_form) = 16.812642666666666666666666666667
y[1] (numeric) = 16.812642666666666666666666666727
absolute error = 6.0e-29
relative error = 3.5687429507413547995072279733616e-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] = 3.63
y[1] (closed_form) = 16.944049
y[1] (numeric) = 16.944049000000000000000000000061
absolute error = 6.1e-29
relative error = 3.6000840176984851731720086503527e-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] = 3.64
y[1] (closed_form) = 17.076181333333333333333333333333
y[1] (numeric) = 17.076181333333333333333333333395
absolute error = 6.2e-29
relative error = 3.6307883355029571014159606019645e-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] = 3.65
y[1] (closed_form) = 17.209041666666666666666666666667
y[1] (numeric) = 17.209041666666666666666666666729
absolute error = 6.2e-29
relative error = 3.6027572714924567269628126687279e-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] = 3.66
y[1] (closed_form) = 17.342632
y[1] (numeric) = 17.342632000000000000000000000063
absolute error = 6.3e-29
relative error = 3.6326665987031264919880673244984e-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] = 3.67
y[1] (closed_form) = 17.476954333333333333333333333333
y[1] (numeric) = 17.476954333333333333333333333397
absolute error = 6.4e-29
relative error = 3.6619652817845092498286743821097e-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] = 3.68
y[1] (closed_form) = 17.612010666666666666666666666667
y[1] (numeric) = 17.612010666666666666666666666731
absolute error = 6.4e-29
relative error = 3.6338837859739353628978042862870e-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] = 3.69
y[1] (closed_form) = 17.747803
y[1] (numeric) = 17.747803000000000000000000000065
absolute error = 6.5e-29
relative error = 3.6624251463688209746299302510852e-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] = 3.7
y[1] (closed_form) = 17.884333333333333333333333333333
y[1] (numeric) = 17.884333333333333333333333333399
absolute error = 6.6e-29
relative error = 3.6903807801986841369541311762623e-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] = 3.71
y[1] (closed_form) = 18.021603666666666666666666666667
y[1] (numeric) = 18.021603666666666666666666666733
absolute error = 6.6e-29
relative error = 3.6622711952142031903154160660988e-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] = 3.72
y[1] (closed_form) = 18.159616
y[1] (numeric) = 18.159616000000000000000000000067
absolute error = 6.7e-29
relative error = 3.6895053287470395849780083455509e-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] = 3.73
y[1] (closed_form) = 18.298372333333333333333333333333
y[1] (numeric) = 18.298372333333333333333333333401
absolute error = 6.8e-29
relative error = 3.7161775244963955537247511468097e-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] = 3.74
y[1] (closed_form) = 18.437874666666666666666666666667
y[1] (numeric) = 18.437874666666666666666666666735
absolute error = 6.8e-29
relative error = 3.6880606484941214482710443994774e-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] = 3.75
y[1] (closed_form) = 18.578125
y[1] (numeric) = 18.578125000000000000000000000069
absolute error = 6.9e-29
relative error = 3.7140454163162321278385197645080e-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] = 3.76
y[1] (closed_form) = 18.719125333333333333333333333333
y[1] (numeric) = 18.719125333333333333333333333403
absolute error = 7.0e-29
relative error = 3.7394909619708727131410128564412e-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] = 3.77
y[1] (closed_form) = 18.860877666666666666666666666667
y[1] (numeric) = 18.860877666666666666666666666737
absolute error = 7.0e-29
relative error = 3.7113861421047691435638917686986e-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] = 3.78
y[1] (closed_form) = 19.003384
y[1] (numeric) = 19.003384000000000000000000000071
absolute error = 7.1e-29
relative error = 3.7361766725336918940331890362264e-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] = 3.79
y[1] (closed_form) = 19.146646333333333333333333333333
y[1] (numeric) = 19.146646333333333333333333333405
absolute error = 7.2e-29
relative error = 3.7604496759650110352658974794525e-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] = 3.8
y[1] (closed_form) = 19.290666666666666666666666666667
y[1] (numeric) = 19.290666666666666666666666666739
absolute error = 7.2e-29
relative error = 3.7323748963229195465855681504008e-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] = 3.81
y[1] (closed_form) = 19.435447
y[1] (numeric) = 19.435447000000000000000000000073
absolute error = 7.3e-29
relative error = 3.7560237230458347574923283215457e-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] = 3.82
y[1] (closed_form) = 19.580989333333333333333333333333
y[1] (numeric) = 19.580989333333333333333333333407
absolute error = 7.4e-29
relative error = 3.7791757474698929070114400756871e-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] = 3.83
y[1] (closed_form) = 19.727295666666666666666666666667
y[1] (numeric) = 19.727295666666666666666666666741
absolute error = 7.4e-29
relative error = 3.7511477117990509494906777811934e-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] = 3.84
y[1] (closed_form) = 19.874368
y[1] (numeric) = 19.874368000000000000000000000075
absolute error = 7.5e-29
relative error = 3.7737049047295491358517664561711e-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] = 3.85
y[1] (closed_form) = 20.022208333333333333333333333333
y[1] (numeric) = 20.022208333333333333333333333409
absolute error = 7.6e-29
relative error = 3.7957850969652448427059119769090e-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] = 3.86
y[1] (closed_form) = 20.170818666666666666666666666667
y[1] (numeric) = 20.170818666666666666666666666743
absolute error = 7.6e-29
relative error = 3.7678193064912123216416798551359e-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] = 3.87
y[1] (closed_form) = 20.320201
y[1] (numeric) = 20.320201000000000000000000000077
absolute error = 7.7e-29
relative error = 3.7893325956765880416241945638235e-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] = 3.88
y[1] (closed_form) = 20.470357333333333333333333333333
y[1] (numeric) = 20.470357333333333333333333333411
absolute error = 7.8e-29
relative error = 3.8103878075927415824950914388859e-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] = 3.89
y[1] (closed_form) = 20.621289666666666666666666666667
y[1] (numeric) = 20.621289666666666666666666666745
absolute error = 7.8e-29
relative error = 3.7824986342189493515188970802973e-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] = 3.9
y[1] (closed_form) = 20.773
y[1] (numeric) = 20.773000000000000000000000000079
absolute error = 7.9e-29
relative error = 3.8030135271746979251913541616521e-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] = 3.91
y[1] (closed_form) = 20.925490333333333333333333333333
y[1] (numeric) = 20.925490333333333333333333333413
absolute error = 8.0e-29
relative error = 3.8230884306956343563817086819041e-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] = 3.92
y[1] (closed_form) = 21.078762666666666666666666666667
y[1] (numeric) = 21.078762666666666666666666666747
absolute error = 8.0e-29
relative error = 3.7952891858548053927517061089986e-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] = 3.93
y[1] (closed_form) = 21.232819
y[1] (numeric) = 21.232819000000000000000000000081
absolute error = 8.1e-29
relative error = 3.8148490786833345115408368526101e-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] = 3.94
y[1] (closed_form) = 21.387661333333333333333333333333
y[1] (numeric) = 21.387661333333333333333333333415
absolute error = 8.2e-29
relative error = 3.8339862747031840040357225281169e-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] = 3.95
y[1] (closed_form) = 21.543291666666666666666666666667
y[1] (numeric) = 21.543291666666666666666666666749
absolute error = 8.2e-29
relative error = 3.8062892741166527089832681867325e-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] = 3.96
y[1] (closed_form) = 21.699712
y[1] (numeric) = 21.699712000000000000000000000083
absolute error = 8.3e-29
relative error = 3.8249355567484029281125943053991e-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] = 3.97
y[1] (closed_form) = 21.856924333333333333333333333333
y[1] (numeric) = 21.856924333333333333333333333417
absolute error = 8.4e-29
relative error = 3.8431756782858118814612723873181e-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] = 3.98
y[1] (closed_form) = 22.014930666666666666666666666667
y[1] (numeric) = 22.014930666666666666666666666751
absolute error = 8.4e-29
relative error = 3.8155923028722688686793047966598e-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] = 3.99
y[1] (closed_form) = 22.173733
y[1] (numeric) = 22.173733000000000000000000000085
absolute error = 8.5e-29
relative error = 3.8333644587494581990321611611360e-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] = 4
y[1] (closed_form) = 22.333333333333333333333333333333
y[1] (numeric) = 22.333333333333333333333333333419
absolute error = 8.6e-29
relative error = 3.8507462686567164179104477611941e-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] = 4.01
y[1] (closed_form) = 22.493733666666666666666666666667
y[1] (numeric) = 22.493733666666666666666666666753
absolute error = 8.6e-29
relative error = 3.8232870218181208719151278887285e-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] = 4.02
y[1] (closed_form) = 22.654936
y[1] (numeric) = 22.654936000000000000000000000087
absolute error = 8.7e-29
relative error = 3.8402227223241769475755747003655e-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] = 4.03
y[1] (closed_form) = 22.816942333333333333333333333333
y[1] (numeric) = 22.816942333333333333333333333421
absolute error = 8.8e-29
relative error = 3.8567832058479001283651401319082e-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] = 4.04
y[1] (closed_form) = 22.979754666666666666666666666667
y[1] (numeric) = 22.979754666666666666666666666755
absolute error = 8.8e-29
relative error = 3.8294577673472115977333323430897e-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] = 4.05
y[1] (closed_form) = 23.143375
y[1] (numeric) = 23.143375000000000000000000000089
absolute error = 8.9e-29
relative error = 3.8455929612686135881218707297445e-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] = 4.06
y[1] (closed_form) = 23.307805333333333333333333333333
y[1] (numeric) = 23.307805333333333333333333333423
absolute error = 9.0e-29
relative error = 3.8613674137430585485125612284160e-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] = 4.07
y[1] (closed_form) = 23.473047666666666666666666666667
y[1] (numeric) = 23.473047666666666666666666666757
absolute error = 9.0e-29
relative error = 3.8341846903760245988793132571920e-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] = 4.08
y[1] (closed_form) = 23.639104
y[1] (numeric) = 23.639104000000000000000000000091
absolute error = 9.1e-29
relative error = 3.8495536886677261540877353050268e-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] = 4.09
y[1] (closed_form) = 23.805976333333333333333333333333
y[1] (numeric) = 23.805976333333333333333333333425
absolute error = 9.2e-29
relative error = 3.8645757986065375824605611288449e-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] = 4.1
y[1] (closed_form) = 23.973666666666666666666666666667
y[1] (numeric) = 23.973666666666666666666666666759
absolute error = 9.2e-29
relative error = 3.8375439718580108730412535976974e-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] = 4.11
y[1] (closed_form) = 24.142177
y[1] (numeric) = 24.142177000000000000000000000093
absolute error = 9.3e-29
relative error = 3.8521795279688323053882009066539e-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] = 4.12
y[1] (closed_form) = 24.311509333333333333333333333333
y[1] (numeric) = 24.311509333333333333333333333427
absolute error = 9.4e-29
relative error = 3.8664814558065008660918461006562e-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] = 4.13
y[1] (closed_form) = 24.481665666666666666666666666667
y[1] (numeric) = 24.481665666666666666666666666761
absolute error = 9.4e-29
relative error = 3.8396080266706253660817768159211e-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] = 4.14
y[1] (closed_form) = 24.652648
y[1] (numeric) = 24.652648000000000000000000000095
absolute error = 9.5e-29
relative error = 3.8535414126709633788629927300305e-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] = 4.15
y[1] (closed_form) = 24.824458333333333333333333333333
y[1] (numeric) = 24.824458333333333333333333333429
absolute error = 9.6e-29
relative error = 3.8671538653914905830439402001051e-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] = 4.16
y[1] (closed_form) = 24.997098666666666666666666666667
y[1] (numeric) = 24.997098666666666666666666666763
absolute error = 9.6e-29
relative error = 3.8404456965245673311206676572171e-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] = 4.17
y[1] (closed_form) = 25.170571
y[1] (numeric) = 25.170571000000000000000000000097
absolute error = 9.7e-29
relative error = 3.8537067752654478915079042108342e-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=192.3MB, alloc=40.3MB, time=2.45
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 25.344877333333333333333333333333
y[1] (numeric) = 25.344877333333333333333333333431
absolute error = 9.8e-29
relative error = 3.8666590771426367921396660406011e-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] = 4.19
y[1] (closed_form) = 25.520019666666666666666666666667
y[1] (numeric) = 25.520019666666666666666666666765
absolute error = 9.8e-29
relative error = 3.8401224325075298074156395307898e-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] = 4.2
y[1] (closed_form) = 25.696
y[1] (numeric) = 25.696000000000000000000000000099
absolute error = 9.9e-29
relative error = 3.8527397260273972602739726027397e-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] = 4.21
y[1] (closed_form) = 25.872820333333333333333333333333
y[1] (numeric) = 25.872820333333333333333333333433
absolute error = 1.00e-28
relative error = 3.8650598856887925154815939986236e-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] = 4.22
y[1] (closed_form) = 26.050482666666666666666666666667
y[1] (numeric) = 26.050482666666666666666666666767
absolute error = 1.00e-28
relative error = 3.8387004678403399512188181081430e-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] = 4.23
y[1] (closed_form) = 26.228989
y[1] (numeric) = 26.228989000000000000000000000101
absolute error = 1.01e-28
relative error = 3.8507012222240056603020421412354e-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] = 4.24
y[1] (closed_form) = 26.408341333333333333333333333333
y[1] (numeric) = 26.408341333333333333333333333435
absolute error = 1.02e-28
relative error = 3.8624159962387641561332944499960e-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] = 4.25
y[1] (closed_form) = 26.588541666666666666666666666667
y[1] (numeric) = 26.588541666666666666666666666769
absolute error = 1.02e-28
relative error = 3.8362389813907933398628795298726e-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] = 4.26
y[1] (closed_form) = 26.769592
y[1] (numeric) = 26.769592000000000000000000000103
absolute error = 1.03e-28
relative error = 3.8476492282736322615600566493505e-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] = 4.27
y[1] (closed_form) = 26.951494333333333333333333333333
y[1] (numeric) = 26.951494333333333333333333333437
absolute error = 1.04e-28
relative error = 3.8587841814534884849860458572223e-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] = 4.28
y[1] (closed_form) = 27.134250666666666666666666666667
y[1] (numeric) = 27.134250666666666666666666666771
absolute error = 1.04e-28
relative error = 3.8327942524596711423220679320522e-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] = 4.29
y[1] (closed_form) = 27.317863
y[1] (numeric) = 27.317863000000000000000000000105
absolute error = 1.05e-28
relative error = 3.8436388673594270532801193124074e-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] = 4.3
y[1] (closed_form) = 27.502333333333333333333333333333
y[1] (numeric) = 27.502333333333333333333333333439
absolute error = 1.06e-28
relative error = 3.8542184299513980631946380307126e-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] = 4.31
y[1] (closed_form) = 27.687663666666666666666666666667
y[1] (numeric) = 27.687663666666666666666666666773
absolute error = 1.06e-28
relative error = 3.8284198073242992176864904852752e-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] = 4.32
y[1] (closed_form) = 27.873856
y[1] (numeric) = 27.873856000000000000000000000107
absolute error = 1.07e-28
relative error = 3.8387225649727113464315809050603e-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] = 4.33
y[1] (closed_form) = 28.060912333333333333333333333333
y[1] (numeric) = 28.060912333333333333333333333441
absolute error = 1.08e-28
relative error = 3.8487700869122371252909013875375e-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] = 4.34
y[1] (closed_form) = 28.248834666666666666666666666667
y[1] (numeric) = 28.248834666666666666666666666775
absolute error = 1.08e-28
relative error = 3.8231665579974838844089662978900e-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] = 4.35
y[1] (closed_form) = 28.437625
y[1] (numeric) = 28.437625000000000000000000000109
absolute error = 1.09e-28
relative error = 3.8329501848343523764730704480420e-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] = 4.36
y[1] (closed_form) = 28.627285333333333333333333333333
y[1] (numeric) = 28.627285333333333333333333333443
absolute error = 1.10e-28
relative error = 3.8424879872181616568696419415994e-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] = 4.37
y[1] (closed_form) = 28.817817666666666666666666666667
y[1] (numeric) = 28.817817666666666666666666666777
absolute error = 1.10e-28
relative error = 3.8170829336336629608073606961656e-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] = 4.38
y[1] (closed_form) = 29.009224
y[1] (numeric) = 29.009224000000000000000000000111
absolute error = 1.11e-28
relative error = 3.8263691576169014379702125089592e-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] = 4.39
y[1] (closed_form) = 29.201506333333333333333333333333
y[1] (numeric) = 29.201506333333333333333333333445
absolute error = 1.12e-28
relative error = 3.8354185815460044932156981536535e-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] = 4.4
y[1] (closed_form) = 29.394666666666666666666666666667
y[1] (numeric) = 29.394666666666666666666666666779
absolute error = 1.12e-28
relative error = 3.8102150049895672684387190420030e-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] = 4.41
y[1] (closed_form) = 29.588707
y[1] (numeric) = 29.588707000000000000000000000113
absolute error = 1.13e-28
relative error = 3.8190246028662219001323714483367e-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] = 4.42
y[1] (closed_form) = 29.783629333333333333333333333333
y[1] (numeric) = 29.783629333333333333333333333447
absolute error = 1.14e-28
relative error = 3.8276060558010346802596970272976e-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] = 4.43
y[1] (closed_form) = 29.979435666666666666666666666667
y[1] (numeric) = 29.979435666666666666666666666781
absolute error = 1.14e-28
relative error = 3.8026066023235238350661859801296e-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] = 4.44
y[1] (closed_form) = 30.176128
y[1] (numeric) = 30.176128000000000000000000000115
absolute error = 1.15e-28
relative error = 3.8109594444986447565439807254264e-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] = 4.45
y[1] (closed_form) = 30.373708333333333333333333333333
y[1] (numeric) = 30.373708333333333333333333333449
absolute error = 1.16e-28
relative error = 3.8190924442603183400117151758168e-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] = 4.46
y[1] (closed_form) = 30.572178666666666666666666666667
y[1] (numeric) = 30.572178666666666666666666666783
absolute error = 1.16e-28
relative error = 3.7942994270956766182272736510676e-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] = 4.47
y[1] (closed_form) = 30.771541
y[1] (numeric) = 30.771541000000000000000000000117
absolute error = 1.17e-28
relative error = 3.8022145202282849597945062289861e-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] = 4.48
y[1] (closed_form) = 30.971797333333333333333333333333
y[1] (numeric) = 30.971797333333333333333333333451
absolute error = 1.18e-28
relative error = 3.8099177367728266162833387174431e-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] = 4.49
y[1] (closed_form) = 31.172949666666666666666666666667
y[1] (numeric) = 31.172949666666666666666666666785
absolute error = 1.18e-28
relative error = 3.7853331578107852888565812010795e-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] = 4.5
y[1] (closed_form) = 31.375
y[1] (numeric) = 31.375000000000000000000000000119
absolute error = 1.19e-28
relative error = 3.7928286852589641434262948207171e-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] = 4.51
y[1] (closed_form) = 31.577950333333333333333333333333
y[1] (numeric) = 31.577950333333333333333333333453
absolute error = 1.20e-28
relative error = 3.8001199803436682838956900422005e-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] = 4.52
y[1] (closed_form) = 31.781802666666666666666666666667
y[1] (numeric) = 31.781802666666666666666666666787
absolute error = 1.20e-28
relative error = 3.7757455503258216693561162379209e-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] = 4.53
y[1] (closed_form) = 31.986559
y[1] (numeric) = 31.986559000000000000000000000121
absolute error = 1.21e-28
relative error = 3.7828389105561495376855009630764e-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] = 4.54
y[1] (closed_form) = 32.192221333333333333333333333333
y[1] (numeric) = 32.192221333333333333333333333455
absolute error = 1.22e-28
relative error = 3.7897353754111862882321137122732e-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] = 4.55
y[1] (closed_form) = 32.398791666666666666666666666667
y[1] (numeric) = 32.398791666666666666666666666789
absolute error = 1.22e-28
relative error = 3.7655725329262536797282820475557e-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] = 4.56
y[1] (closed_form) = 32.606272
y[1] (numeric) = 32.606272000000000000000000000123
absolute error = 1.23e-28
relative error = 3.7722803759963727224013833902876e-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] = 4.57
y[1] (closed_form) = 32.814664333333333333333333333333
y[1] (numeric) = 32.814664333333333333333333333457
absolute error = 1.24e-28
relative error = 3.7787983671080875396836046664625e-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] = 4.58
y[1] (closed_form) = 33.023970666666666666666666666667
y[1] (numeric) = 33.023970666666666666666666666791
absolute error = 1.24e-28
relative error = 3.7548482964576276674664358955745e-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] = 4.59
y[1] (closed_form) = 33.234193
y[1] (numeric) = 33.234193000000000000000000000125
absolute error = 1.25e-28
relative error = 3.7611865586746758075335242832585e-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] = 4.6
y[1] (closed_form) = 33.445333333333333333333333333333
y[1] (numeric) = 33.445333333333333333333333333459
absolute error = 1.26e-28
relative error = 3.7673417317812151172061872109712e-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] = 4.61
y[1] (closed_form) = 33.657393666666666666666666666667
y[1] (numeric) = 33.657393666666666666666666666793
absolute error = 1.26e-28
relative error = 3.7436053797827740296111856789544e-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] = 4.62
y[1] (closed_form) = 33.870376
y[1] (numeric) = 33.870376000000000000000000000127
absolute error = 1.27e-28
relative error = 3.7495893166346898540482692013812e-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] = 4.63
y[1] (closed_form) = 34.084282333333333333333333333333
y[1] (numeric) = 34.084282333333333333333333333461
absolute error = 1.28e-28
relative error = 3.7553966590289657167198483969840e-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] = 4.64
y[1] (closed_form) = 34.299114666666666666666666666667
y[1] (numeric) = 34.299114666666666666666666666795
absolute error = 1.28e-28
relative error = 3.7318747508196129921487575034006e-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] = 4.65
y[1] (closed_form) = 34.514875
y[1] (numeric) = 34.514875000000000000000000000129
absolute error = 1.29e-28
relative error = 3.7375189682709266656767553120213e-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] = 4.66
y[1] (closed_form) = 34.731565333333333333333333333333
y[1] (numeric) = 34.731565333333333333333333333463
absolute error = 1.30e-28
relative error = 3.7429928295006494380481708972979e-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] = 4.67
y[1] (closed_form) = 34.949187666666666666666666666667
y[1] (numeric) = 34.949187666666666666666666666797
absolute error = 1.30e-28
relative error = 3.7196858834000748305423178982233e-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] = 4.68
y[1] (closed_form) = 35.167744
y[1] (numeric) = 35.167744000000000000000000000131
absolute error = 1.31e-28
relative error = 3.7250043676387089259976414750972e-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] = 4.69
y[1] (closed_form) = 35.387236333333333333333333333333
y[1] (numeric) = 35.387236333333333333333333333465
absolute error = 1.32e-28
relative error = 3.7301584886882331557040024666521e-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] = 4.7
y[1] (closed_form) = 35.607666666666666666666666666667
y[1] (numeric) = 35.607666666666666666666666666799
absolute error = 1.32e-28
relative error = 3.7070668301770218024208269754640e-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] = 4.71
y[1] (closed_form) = 35.829037
y[1] (numeric) = 35.829037000000000000000000000133
absolute error = 1.33e-28
relative error = 3.7120729758938260048686209456313e-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] = 4.72
y[1] (closed_form) = 36.051349333333333333333333333333
y[1] (numeric) = 36.051349333333333333333333333467
absolute error = 1.34e-28
relative error = 3.7169205169278546097507140925507e-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] = 4.73
y[1] (closed_form) = 36.274605666666666666666666666667
y[1] (numeric) = 36.274605666666666666666666666801
absolute error = 1.34e-28
relative error = 3.6940442917932202286196228533318e-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] = 4.74
y[1] (closed_form) = 36.498808
y[1] (numeric) = 36.498808000000000000000000000135
absolute error = 1.35e-28
relative error = 3.6987509290714370726846750721284e-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] = 4.75
y[1] (closed_form) = 36.723958333333333333333333333333
y[1] (numeric) = 36.723958333333333333333333333469
absolute error = 1.36e-28
relative error = 3.7033044958161962842150049638350e-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] = 4.76
y[1] (closed_form) = 36.950058666666666666666666666667
y[1] (numeric) = 36.950058666666666666666666666803
absolute error = 1.36e-28
relative error = 3.6806436825143155388404615613781e-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] = 4.77
y[1] (closed_form) = 37.177111
y[1] (numeric) = 37.177111000000000000000000000137
absolute error = 1.37e-28
relative error = 3.6850631024019053013559875591194e-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] = 4.78
y[1] (closed_form) = 37.405117333333333333333333333333
y[1] (numeric) = 37.405117333333333333333333333471
absolute error = 1.38e-28
relative error = 3.6893347712352227884113396534193e-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] = 4.79
y[1] (closed_form) = 37.634079666666666666666666666667
y[1] (numeric) = 37.634079666666666666666666666805
absolute error = 1.38e-28
relative error = 3.6668891925163680766330949380020e-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] = 4.8
y[1] (closed_form) = 37.864
y[1] (numeric) = 37.864000000000000000000000000139
absolute error = 1.39e-28
relative error = 3.6710331713500950771181069089372e-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] = 4.81
y[1] (closed_form) = 38.094880333333333333333333333333
y[1] (numeric) = 38.094880333333333333333333333473
absolute error = 1.40e-28
relative error = 3.6750345131678717877759269506740e-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] = 4.82
y[1] (closed_form) = 38.326722666666666666666666666667
y[1] (numeric) = 38.326722666666666666666666666807
absolute error = 1.40e-28
relative error = 3.6528038470077726795459196058924e-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] = 4.83
y[1] (closed_form) = 38.559529
y[1] (numeric) = 38.559529000000000000000000000141
absolute error = 1.41e-28
relative error = 3.6566836695541587139199755266720e-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] = 4.84
y[1] (closed_form) = 38.793301333333333333333333333333
y[1] (numeric) = 38.793301333333333333333333333475
absolute error = 1.42e-28
relative error = 3.6604257724770077143215378490087e-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] = 4.85
y[1] (closed_form) = 39.028041666666666666666666666667
y[1] (numeric) = 39.028041666666666666666666666809
absolute error = 1.42e-28
relative error = 3.6384095623552723308988302214326e-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] = 4.86
y[1] (closed_form) = 39.263752
y[1] (numeric) = 39.263752000000000000000000000143
absolute error = 1.43e-28
relative error = 3.6420360438299426911620672420710e-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] = 4.87
y[1] (closed_form) = 39.500434333333333333333333333333
y[1] (numeric) = 39.500434333333333333333333333477
absolute error = 1.44e-28
relative error = 3.6455295348102628036081594815882e-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] = 4.88
y[1] (closed_form) = 39.738090666666666666666666666667
y[1] (numeric) = 39.738090666666666666666666666811
absolute error = 1.44e-28
relative error = 3.6237271993742494187273147966713e-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] = 4.89
y[1] (closed_form) = 39.976723
y[1] (numeric) = 39.976723000000000000000000000145
absolute error = 1.45e-28
relative error = 3.6271107063978205517245623159257e-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] = 4.9
y[1] (closed_form) = 40.216333333333333333333333333333
y[1] (numeric) = 40.216333333333333333333333333479
absolute error = 1.46e-28
relative error = 3.6303657717842667572876691891355e-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] = 4.91
y[1] (closed_form) = 40.456923666666666666666666666667
y[1] (numeric) = 40.456923666666666666666666666813
absolute error = 1.46e-28
relative error = 3.6087766139345032256571889124771e-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] = 4.92
y[1] (closed_form) = 40.698496
y[1] (numeric) = 40.698496000000000000000000000147
absolute error = 1.47e-28
relative error = 3.6119270844799768522158656673701e-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] = 4.93
y[1] (closed_form) = 40.941052333333333333333333333333
y[1] (numeric) = 40.941052333333333333333333333481
absolute error = 1.48e-28
relative error = 3.6149534895931717501773708682639e-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] = 4.94
y[1] (closed_form) = 41.184594666666666666666666666667
y[1] (numeric) = 41.184594666666666666666666666815
absolute error = 1.48e-28
relative error = 3.5935767050242670026196850433978e-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] = 4.95
y[1] (closed_form) = 41.429125
y[1] (numeric) = 41.429125000000000000000000000149
absolute error = 1.49e-28
relative error = 3.5965036674078923945412798363470e-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] = 4.96
y[1] (closed_form) = 41.674645333333333333333333333333
y[1] (numeric) = 41.674645333333333333333333333483
absolute error = 1.50e-28
relative error = 3.5993107751782826610098085537797e-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] = 4.97
y[1] (closed_form) = 41.921157666666666666666666666667
y[1] (numeric) = 41.921157666666666666666666666817
absolute error = 1.50e-28
relative error = 3.5781454604072519530372702096100e-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] = 4.98
y[1] (closed_form) = 42.168664
y[1] (numeric) = 42.168664000000000000000000000151
absolute error = 1.51e-28
relative error = 3.5808580513719856052352049853892e-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] = 4.99
y[1] (closed_form) = 42.417166333333333333333333333333
y[1] (numeric) = 42.417166333333333333333333333485
absolute error = 1.52e-28
relative error = 3.5834548400879741306623036322739e-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] = 5
y[1] (closed_form) = 42.666666666666666666666666666667
y[1] (numeric) = 42.666666666666666666666666666819
absolute error = 1.52e-28
relative error = 3.5625000000000000000000000000000e-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] = 5.01
y[1] (closed_form) = 42.917167
y[1] (numeric) = 42.917167000000000000000000000153
absolute error = 1.53e-28
relative error = 3.5650069819380202798567761940111e-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] = 5.02
y[1] (closed_form) = 43.168669333333333333333333333333
y[1] (numeric) = 43.168669333333333333333333333487
absolute error = 1.54e-28
relative error = 3.5674020621498888298680320684428e-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] = 5.03
y[1] (closed_form) = 43.421175666666666666666666666667
y[1] (numeric) = 43.421175666666666666666666666821
absolute error = 1.54e-28
relative error = 3.5466566170897552927459119082504e-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] = 5.04
y[1] (closed_form) = 43.674688
y[1] (numeric) = 43.674688000000000000000000000155
absolute error = 1.55e-28
relative error = 3.5489663944479694966567362770857e-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] = 5.05
y[1] (closed_form) = 43.929208333333333333333333333333
y[1] (numeric) = 43.929208333333333333333333333489
absolute error = 1.56e-28
relative error = 3.5511680250706392197294700469790e-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] = 5.06
y[1] (closed_form) = 44.184738666666666666666666666667
y[1] (numeric) = 44.184738666666666666666666666823
absolute error = 1.56e-28
relative error = 3.5306308175064005508508307272550e-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] = 5.07
y[1] (closed_form) = 44.441281
y[1] (numeric) = 44.441281000000000000000000000157
absolute error = 1.57e-28
relative error = 3.5327514524165043757402042483879e-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] = 5.08
y[1] (closed_form) = 44.698837333333333333333333333333
y[1] (numeric) = 44.698837333333333333333333333491
absolute error = 1.58e-28
relative error = 3.5347675560718536810263938856217e-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] = 5.09
y[1] (closed_form) = 44.957409666666666666666666666667
y[1] (numeric) = 44.957409666666666666666666666825
absolute error = 1.58e-28
relative error = 3.5144373568557245391117544294459e-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] = 5.1
y[1] (closed_form) = 45.217
y[1] (numeric) = 45.217000000000000000000000000159
absolute error = 1.59e-28
relative error = 3.5163765840281310126722250481014e-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] = 5.11
y[1] (closed_form) = 45.477610333333333333333333333333
y[1] (numeric) = 45.477610333333333333333333333493
absolute error = 1.60e-28
relative error = 3.5182147616653941601490333364116e-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] = 5.12
y[1] (closed_form) = 45.739242666666666666666666666667
y[1] (numeric) = 45.739242666666666666666666666827
absolute error = 1.60e-28
relative error = 3.4980902759153686031006139381640e-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] = 5.13
y[1] (closed_form) = 46.001899
y[1] (numeric) = 46.001899000000000000000000000161
absolute error = 1.61e-28
relative error = 3.4998555168342072139239295316917e-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] = 5.14
y[1] (closed_form) = 46.265581333333333333333333333333
y[1] (numeric) = 46.265581333333333333333333333495
absolute error = 1.62e-28
relative error = 3.5015230616649047617428258979908e-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] = 5.15
y[1] (closed_form) = 46.530291666666666666666666666667
y[1] (numeric) = 46.530291666666666666666666666829
absolute error = 1.62e-28
relative error = 3.4816029342892219853195991500160e-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] = 5.16
y[1] (closed_form) = 46.796032
y[1] (numeric) = 46.796032000000000000000000000163
absolute error = 1.63e-28
relative error = 3.4832013107436117660574298265289e-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] = 5.17
y[1] (closed_form) = 47.062804333333333333333333333333
y[1] (numeric) = 47.062804333333333333333333333497
absolute error = 1.64e-28
relative error = 3.4847052215255086123816690254887e-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] = 5.18
y[1] (closed_form) = 47.330610666666666666666666666667
y[1] (numeric) = 47.330610666666666666666666666831
absolute error = 1.64e-28
relative error = 3.4649880424107775438801296683037e-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] = 5.19
y[1] (closed_form) = 47.599453
y[1] (numeric) = 47.599453000000000000000000000165
absolute error = 1.65e-28
relative error = 3.4664263893956932656347962654109e-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=239.4MB, alloc=40.3MB, time=3.05
TOP MAIN SOLVE Loop
x[1] = 5.2
y[1] (closed_form) = 47.869333333333333333333333333333
y[1] (numeric) = 47.869333333333333333333333333499
absolute error = 1.66e-28
relative error = 3.4677733830984346275973483371400e-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] = 5.21
y[1] (closed_form) = 48.140253666666666666666666666667
y[1] (numeric) = 48.140253666666666666666666666833
absolute error = 1.66e-28
relative error = 3.4482576919810026482272863802455e-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] = 5.22
y[1] (closed_form) = 48.412216
y[1] (numeric) = 48.412216000000000000000000000167
absolute error = 1.67e-28
relative error = 3.4495425699992745632631235058523e-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] = 5.23
y[1] (closed_form) = 48.685222333333333333333333333333
y[1] (numeric) = 48.685222333333333333333333333501
absolute error = 1.68e-28
relative error = 3.4507390938826084714672522771746e-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] = 5.24
y[1] (closed_form) = 48.959274666666666666666666666667
y[1] (numeric) = 48.959274666666666666666666666835
absolute error = 1.68e-28
relative error = 3.4314233849216066817547623799219e-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] = 5.25
y[1] (closed_form) = 49.234375
y[1] (numeric) = 49.234375000000000000000000000169
absolute error = 1.69e-28
relative error = 3.4325610917169152649952396064741e-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] = 5.26
y[1] (closed_form) = 49.510525333333333333333333333333
y[1] (numeric) = 49.510525333333333333333333333503
absolute error = 1.70e-28
relative error = 3.4336133348507660081651594405758e-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] = 5.27
y[1] (closed_form) = 49.787727666666666666666666666667
y[1] (numeric) = 49.787727666666666666666666666837
absolute error = 1.70e-28
relative error = 3.4144960609201800419585327128439e-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] = 5.28
y[1] (closed_form) = 50.065984
y[1] (numeric) = 50.065984000000000000000000000171
absolute error = 1.71e-28
relative error = 3.4154926426693221489464783115019e-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] = 5.29
y[1] (closed_form) = 50.345296333333333333333333333333
y[1] (numeric) = 50.345296333333333333333333333505
absolute error = 1.72e-28
relative error = 3.4164065469234269213987941634190e-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] = 5.3
y[1] (closed_form) = 50.625666666666666666666666666667
y[1] (numeric) = 50.625666666666666666666666666839
absolute error = 1.72e-28
relative error = 3.3974861236395240885716731302304e-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] = 5.31
y[1] (closed_form) = 50.907097
y[1] (numeric) = 50.907097000000000000000000000173
absolute error = 1.73e-28
relative error = 3.3983473856307304264472201194266e-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] = 5.32
y[1] (closed_form) = 51.189589333333333333333333333333
y[1] (numeric) = 51.189589333333333333333333333507
absolute error = 1.74e-28
relative error = 3.3991286561600858841297730538543e-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] = 5.33
y[1] (closed_form) = 51.473145666666666666666666666667
y[1] (numeric) = 51.473145666666666666666666666841
absolute error = 1.74e-28
relative error = 3.3804034656595723762417292066671e-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] = 5.34
y[1] (closed_form) = 51.757768
y[1] (numeric) = 51.757768000000000000000000000175
absolute error = 1.75e-28
relative error = 3.3811349824822430519028563982898e-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] = 5.35
y[1] (closed_form) = 52.043458333333333333333333333333
y[1] (numeric) = 52.043458333333333333333333333509
absolute error = 1.76e-28
relative error = 3.3817890977332245567206253107379e-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] = 5.36
y[1] (closed_form) = 52.330218666666666666666666666667
y[1] (numeric) = 52.330218666666666666666666666843
absolute error = 1.76e-28
relative error = 3.3632574922166068278611435320074e-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] = 5.37
y[1] (closed_form) = 52.618051
y[1] (numeric) = 52.618051000000000000000000000177
absolute error = 1.77e-28
relative error = 3.3638646174864971718545789542832e-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] = 5.38
y[1] (closed_form) = 52.906957333333333333333333333333
y[1] (numeric) = 52.906957333333333333333333333511
absolute error = 1.78e-28
relative error = 3.3643968387472064795611757979757e-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] = 5.39
y[1] (closed_form) = 53.196939666666666666666666666667
y[1] (numeric) = 53.196939666666666666666666666845
absolute error = 1.78e-28
relative error = 3.3460571438009851932647829822842e-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] = 5.4
y[1] (closed_form) = 53.488
y[1] (numeric) = 53.488000000000000000000000000179
absolute error = 1.79e-28
relative error = 3.3465450194436135207897098414598e-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] = 5.41
y[1] (closed_form) = 53.780140333333333333333333333333
y[1] (numeric) = 53.780140333333333333333333333513
absolute error = 1.80e-28
relative error = 3.3469603999607761033423856009400e-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] = 5.42
y[1] (closed_form) = 54.073362666666666666666666666667
y[1] (numeric) = 54.073362666666666666666666666847
absolute error = 1.80e-28
relative error = 3.3288109176713059112629750268659e-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] = 5.43
y[1] (closed_form) = 54.367669
y[1] (numeric) = 54.367669000000000000000000000181
absolute error = 1.81e-28
relative error = 3.3291844827851641018488396109092e-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] = 5.44
y[1] (closed_form) = 54.663061333333333333333333333333
y[1] (numeric) = 54.663061333333333333333333333515
absolute error = 1.82e-28
relative error = 3.3294878764687310109427704695451e-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] = 5.45
y[1] (closed_form) = 54.959541666666666666666666666667
y[1] (numeric) = 54.959541666666666666666666666849
absolute error = 1.82e-28
relative error = 3.3115268883398318005138628491110e-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] = 5.46
y[1] (closed_form) = 55.257112
y[1] (numeric) = 55.257112000000000000000000000183
absolute error = 1.83e-28
relative error = 3.3117908876598545360097719185903e-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] = 5.47
y[1] (closed_form) = 55.555774333333333333333333333333
y[1] (numeric) = 55.555774333333333333333333333517
absolute error = 1.84e-28
relative error = 3.3119869573953617770653219167623e-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] = 5.48
y[1] (closed_form) = 55.855530666666666666666666666667
y[1] (numeric) = 55.855530666666666666666666666851
absolute error = 1.84e-28
relative error = 3.2942127270810639867880108225869e-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] = 5.49
y[1] (closed_form) = 56.156383
y[1] (numeric) = 56.156383000000000000000000000185
absolute error = 1.85e-28
relative error = 3.2943717190617494007760435710398e-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] = 5.5
y[1] (closed_form) = 56.458333333333333333333333333333
y[1] (numeric) = 56.458333333333333333333333333519
absolute error = 1.86e-28
relative error = 3.2944649446494464944649446494465e-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] = 5.51
y[1] (closed_form) = 56.761383666666666666666666666667
y[1] (numeric) = 56.761383666666666666666666666853
absolute error = 1.86e-28
relative error = 3.2768757205125919205481430858471e-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] = 5.52
y[1] (closed_form) = 57.065536
y[1] (numeric) = 57.065536000000000000000000000187
absolute error = 1.87e-28
relative error = 3.2769340850491617217088787179709e-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] = 5.53
y[1] (closed_form) = 57.370792333333333333333333333333
y[1] (numeric) = 57.370792333333333333333333333521
absolute error = 1.88e-28
relative error = 3.2769287707879370000217939003887e-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] = 5.54
y[1] (closed_form) = 57.677154666666666666666666666667
y[1] (numeric) = 57.677154666666666666666666666855
absolute error = 1.88e-28
relative error = 3.2595227882947346501096471101926e-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] = 5.55
y[1] (closed_form) = 57.984625
y[1] (numeric) = 57.984625000000000000000000000189
absolute error = 1.89e-28
relative error = 3.2594847340997721378727550622255e-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] = 5.56
y[1] (closed_form) = 58.293205333333333333333333333333
y[1] (numeric) = 58.293205333333333333333333333523
absolute error = 1.90e-28
relative error = 3.2593850160329720760594533784887e-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] = 5.57
y[1] (closed_form) = 58.602897666666666666666666666667
y[1] (numeric) = 58.602897666666666666666666666857
absolute error = 1.90e-28
relative error = 3.2421604999930236669241378183728e-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] = 5.58
y[1] (closed_form) = 58.913704
y[1] (numeric) = 58.913704000000000000000000000191
absolute error = 1.91e-28
relative error = 3.2420300716451303078821864603862e-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] = 5.59
y[1] (closed_form) = 59.225626333333333333333333333333
y[1] (numeric) = 59.225626333333333333333333333525
absolute error = 1.92e-28
relative error = 3.2418399244844907479492590591936e-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] = 5.6
y[1] (closed_form) = 59.538666666666666666666666666667
y[1] (numeric) = 59.538666666666666666666666666859
absolute error = 1.92e-28
relative error = 3.2247950911452501455636673086397e-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] = 5.61
y[1] (closed_form) = 59.852827
y[1] (numeric) = 59.852827000000000000000000000193
absolute error = 1.93e-28
relative error = 3.2245761758254125573717679200015e-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] = 5.62
y[1] (closed_form) = 60.168109333333333333333333333333
y[1] (numeric) = 60.168109333333333333333333333527
absolute error = 1.94e-28
relative error = 3.2242994195684881306557923641587e-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] = 5.63
y[1] (closed_form) = 60.484515666666666666666666666667
y[1] (numeric) = 60.484515666666666666666666666861
absolute error = 1.94e-28
relative error = 3.2074324785726012840079670638789e-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] = 5.64
y[1] (closed_form) = 60.802048
y[1] (numeric) = 60.802048000000000000000000000195
absolute error = 1.95e-28
relative error = 3.2071288125031577883692338784378e-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] = 5.65
y[1] (closed_form) = 61.120708333333333333333333333333
y[1] (numeric) = 61.120708333333333333333333333529
absolute error = 1.96e-28
relative error = 3.2067691187588494625048657131346e-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] = 5.66
y[1] (closed_form) = 61.440498666666666666666666666667
y[1] (numeric) = 61.440498666666666666666666666863
absolute error = 1.96e-28
relative error = 3.1900782749723342089193980934269e-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] = 5.67
y[1] (closed_form) = 61.761421
y[1] (numeric) = 61.761421000000000000000000000197
absolute error = 1.97e-28
relative error = 3.1896934495726709396793185830358e-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] = 5.68
y[1] (closed_form) = 62.083477333333333333333333333333
y[1] (numeric) = 62.083477333333333333333333333531
absolute error = 1.98e-28
relative error = 3.1892543476087078283931174989167e-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] = 5.69
y[1] (closed_form) = 62.406669666666666666666666666667
y[1] (numeric) = 62.406669666666666666666666666865
absolute error = 1.98e-28
relative error = 3.1727378028274744928572244647205e-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] = 5.7
y[1] (closed_form) = 62.731
y[1] (numeric) = 62.731000000000000000000000000199
absolute error = 1.99e-28
relative error = 3.1722752705998629066968484481357e-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] = 5.71
y[1] (closed_form) = 63.056470333333333333333333333333
y[1] (numeric) = 63.056470333333333333333333333533
absolute error = 2.00e-28
relative error = 3.1717601531253908698801203118405e-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] = 5.72
y[1] (closed_form) = 63.383082666666666666666666666667
y[1] (numeric) = 63.383082666666666666666666666867
absolute error = 2.00e-28
relative error = 3.1554161076671731039399114531339e-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] = 5.73
y[1] (closed_form) = 63.710839
y[1] (numeric) = 63.710839000000000000000000000201
absolute error = 2.01e-28
relative error = 3.1548791878254813125283124901243e-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] = 5.74
y[1] (closed_form) = 64.039741333333333333333333333333
y[1] (numeric) = 64.039741333333333333333333333535
absolute error = 2.02e-28
relative error = 3.1542913165212451618063999675535e-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] = 5.75
y[1] (closed_form) = 64.369791666666666666666666666667
y[1] (numeric) = 64.369791666666666666666666666869
absolute error = 2.02e-28
relative error = 3.1381179707096043369204628206165e-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] = 5.76
y[1] (closed_form) = 64.700992
y[1] (numeric) = 64.700992000000000000000000000203
absolute error = 2.03e-28
relative error = 3.1375098545629717702009885721690e-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] = 5.77
y[1] (closed_form) = 65.033344333333333333333333333333
y[1] (numeric) = 65.033344333333333333333333333537
absolute error = 2.04e-28
relative error = 3.1368523653709479382814866053867e-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] = 5.78
y[1] (closed_form) = 65.366850666666666666666666666667
y[1] (numeric) = 65.366850666666666666666666666871
absolute error = 2.04e-28
relative error = 3.1208479209176320931518846515026e-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] = 5.79
y[1] (closed_form) = 65.701513
y[1] (numeric) = 65.701513000000000000000000000205
absolute error = 2.05e-28
relative error = 3.1201716770205885517430930395773e-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] = 5.8
y[1] (closed_form) = 66.037333333333333333333333333333
y[1] (numeric) = 66.037333333333333333333333333539
absolute error = 2.06e-28
relative error = 3.1194475852043288644806977871103e-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] = 5.81
y[1] (closed_form) = 66.374313666666666666666666666667
y[1] (numeric) = 66.374313666666666666666666666873
absolute error = 2.06e-28
relative error = 3.1036102464959072696701481523417e-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] = 5.82
y[1] (closed_form) = 66.712456
y[1] (numeric) = 66.712456000000000000000000000207
absolute error = 2.07e-28
relative error = 3.1028688255758414890316734853833e-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] = 5.83
y[1] (closed_form) = 67.051762333333333333333333333333
y[1] (numeric) = 67.051762333333333333333333333541
absolute error = 2.08e-28
relative error = 3.1020810305622242978878303109180e-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] = 5.84
y[1] (closed_form) = 67.392234666666666666666666666667
y[1] (numeric) = 67.392234666666666666666666666875
absolute error = 2.08e-28
relative error = 3.0864090058565797966515469556769e-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] = 5.85
y[1] (closed_form) = 67.733875
y[1] (numeric) = 67.733875000000000000000000000209
absolute error = 2.09e-28
relative error = 3.0856052455289173991595785712836e-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] = 5.86
y[1] (closed_form) = 68.076685333333333333333333333333
y[1] (numeric) = 68.076685333333333333333333333543
absolute error = 2.10e-28
relative error = 3.0847565355414680001850462206209e-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] = 5.87
y[1] (closed_form) = 68.420667666666666666666666666667
y[1] (numeric) = 68.420667666666666666666666666877
absolute error = 2.10e-28
relative error = 3.0692480380794101478197111815186e-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] = 5.88
y[1] (closed_form) = 68.765824
y[1] (numeric) = 68.765824000000000000000000000211
absolute error = 2.11e-28
relative error = 3.0683846673603445804706710123913e-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] = 5.89
y[1] (closed_form) = 69.112156333333333333333333333333
y[1] (numeric) = 69.112156333333333333333333333545
absolute error = 2.12e-28
relative error = 3.0674777238537808801981671637323e-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] = 5.9
y[1] (closed_form) = 69.459666666666666666666666666667
y[1] (numeric) = 69.459666666666666666666666666879
absolute error = 2.12e-28
relative error = 3.0521309728907423492770384731667e-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] = 5.91
y[1] (closed_form) = 69.808357
y[1] (numeric) = 69.808357000000000000000000000213
absolute error = 2.13e-28
relative error = 3.0512106165168734740455215125605e-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] = 5.92
y[1] (closed_form) = 70.158229333333333333333333333333
y[1] (numeric) = 70.158229333333333333333333333547
absolute error = 2.14e-28
relative error = 3.0502480184220536770673345765929e-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] = 5.93
y[1] (closed_form) = 70.509285666666666666666666666667
y[1] (numeric) = 70.509285666666666666666666666881
absolute error = 2.14e-28
relative error = 3.0350612401845493097393786767291e-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] = 5.94
y[1] (closed_form) = 70.861528
y[1] (numeric) = 70.861528000000000000000000000215
absolute error = 2.15e-28
relative error = 3.0340864227483212047022186707574e-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] = 5.95
y[1] (closed_form) = 71.214958333333333333333333333333
y[1] (numeric) = 71.214958333333333333333333333549
absolute error = 2.16e-28
relative error = 3.0330706505363163988838955299068e-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] = 5.96
y[1] (closed_form) = 71.569578666666666666666666666667
y[1] (numeric) = 71.569578666666666666666666666883
absolute error = 2.16e-28
relative error = 3.0180420791075776255326657970731e-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] = 5.97
y[1] (closed_form) = 71.925391
y[1] (numeric) = 71.925391000000000000000000000217
absolute error = 2.17e-28
relative error = 3.0170152290169684305226787018787e-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] = 5.98
y[1] (closed_form) = 72.282397333333333333333333333333
y[1] (numeric) = 72.282397333333333333333333333551
absolute error = 2.18e-28
relative error = 3.0159486685905529272428853955370e-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] = 5.99
y[1] (closed_form) = 72.640599666666666666666666666667
y[1] (numeric) = 72.640599666666666666666666666885
absolute error = 2.18e-28
relative error = 3.0010765467294990530066246378592e-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] = 6
y[1] (closed_form) = 73
y[1] (numeric) = 73.000000000000000000000000000219
absolute error = 2.19e-28
relative error = 3.0000000000000000000000000000000e-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] = 6.01
y[1] (closed_form) = 73.360600333333333333333333333333
y[1] (numeric) = 73.360600333333333333333333333553
absolute error = 2.20e-28
relative error = 2.9988849464204448236044742291072e-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] = 6.02
y[1] (closed_form) = 73.722402666666666666666666666667
y[1] (numeric) = 73.722402666666666666666666666887
absolute error = 2.20e-28
relative error = 2.9841675263179159905115771050471e-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] = 6.03
y[1] (closed_form) = 74.085409
y[1] (numeric) = 74.085409000000000000000000000221
absolute error = 2.21e-28
relative error = 2.9830435302044428208528888596674e-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] = 6.04
y[1] (closed_form) = 74.449621333333333333333333333333
y[1] (numeric) = 74.449621333333333333333333333555
absolute error = 2.22e-28
relative error = 2.9818821912611115855059822466794e-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] = 6.05
y[1] (closed_form) = 74.815041666666666666666666666667
y[1] (numeric) = 74.815041666666666666666666666889
absolute error = 2.22e-28
relative error = 2.9673177352370651846414574609272e-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] = 6.06
y[1] (closed_form) = 75.181672
y[1] (numeric) = 75.181672000000000000000000000223
absolute error = 2.23e-28
relative error = 2.9661484517130717710029114542704e-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] = 6.07
y[1] (closed_form) = 75.549514333333333333333333333333
y[1] (numeric) = 75.549514333333333333333333333557
absolute error = 2.24e-28
relative error = 2.9649429513429521583114699307818e-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] = 6.08
y[1] (closed_form) = 75.918570666666666666666666666667
y[1] (numeric) = 75.918570666666666666666666666891
absolute error = 2.24e-28
relative error = 2.9505297324881142827276270462977e-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] = 6.09
y[1] (closed_form) = 76.288843
y[1] (numeric) = 76.288843000000000000000000000225
absolute error = 2.25e-28
relative error = 2.9493172415788243111774548737094e-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] = 6.1
y[1] (closed_form) = 76.660333333333333333333333333333
y[1] (numeric) = 76.660333333333333333333333333559
absolute error = 2.26e-28
relative error = 2.9480696231427813601993208134585e-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] = 6.11
y[1] (closed_form) = 77.033043666666666666666666666667
y[1] (numeric) = 77.033043666666666666666666666893
absolute error = 2.26e-28
relative error = 2.9338059259080467939968151589458e-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] = 6.12
y[1] (closed_form) = 77.406976
y[1] (numeric) = 77.406976000000000000000000000227
absolute error = 2.27e-28
relative error = 2.9325522288843837537329968813147e-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] = 6.13
y[1] (closed_form) = 77.782132333333333333333333333333
y[1] (numeric) = 77.782132333333333333333333333561
absolute error = 2.28e-28
relative error = 2.9312644583065921519242484811111e-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] = 6.14
y[1] (closed_form) = 78.158514666666666666666666666667
y[1] (numeric) = 78.158514666666666666666666666895
absolute error = 2.28e-28
relative error = 2.9171485790432796692861068700623e-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] = 6.15
y[1] (closed_form) = 78.536125
y[1] (numeric) = 78.536125000000000000000000000229
absolute error = 2.29e-28
relative error = 2.9158556014827571388326072874107e-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] = 6.16
y[1] (closed_form) = 78.914965333333333333333333333333
y[1] (numeric) = 78.914965333333333333333333333563
absolute error = 2.30e-28
relative error = 2.9145295702594576737992273337120e-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] = 6.17
y[1] (closed_form) = 79.295037666666666666666666666667
y[1] (numeric) = 79.295037666666666666666666666897
absolute error = 2.30e-28
relative error = 2.9005598177133514025318599907511e-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] = 6.18
y[1] (closed_form) = 79.676344
y[1] (numeric) = 79.676344000000000000000000000231
absolute error = 2.31e-28
relative error = 2.8992294124338837635421625269352e-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] = 6.19
y[1] (closed_form) = 80.058886333333333333333333333333
y[1] (numeric) = 80.058886333333333333333333333565
absolute error = 2.32e-28
relative error = 2.8978669405173131332466407570438e-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] = 6.2
y[1] (closed_form) = 80.442666666666666666666666666667
y[1] (numeric) = 80.442666666666666666666666666899
absolute error = 2.32e-28
relative error = 2.8840416362792547901611085327852e-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=286.5MB, alloc=40.3MB, time=3.62
TOP MAIN SOLVE Loop
x[1] = 6.21
y[1] (closed_form) = 80.827687
y[1] (numeric) = 80.827687000000000000000000000233
absolute error = 2.33e-28
relative error = 2.8826755861515621497371315351384e-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] = 6.22
y[1] (closed_form) = 81.213949333333333333333333333333
y[1] (numeric) = 81.213949333333333333333333333567
absolute error = 2.34e-28
relative error = 2.8812784247146245582573318849560e-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] = 6.23
y[1] (closed_form) = 81.601455666666666666666666666667
y[1] (numeric) = 81.601455666666666666666666666901
absolute error = 2.34e-28
relative error = 2.8675959036302648963774408485123e-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] = 6.24
y[1] (closed_form) = 81.990208
y[1] (numeric) = 81.990208000000000000000000000235
absolute error = 2.35e-28
relative error = 2.8661959242742743133423932770118e-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] = 6.25
y[1] (closed_form) = 82.380208333333333333333333333333
y[1] (numeric) = 82.380208333333333333333333333569
absolute error = 2.36e-28
relative error = 2.8647657583612568755136878042612e-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] = 6.26
y[1] (closed_form) = 82.771458666666666666666666666667
y[1] (numeric) = 82.771458666666666666666666666903
absolute error = 2.36e-28
relative error = 2.8512243689024271393775445365273e-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] = 6.27
y[1] (closed_form) = 83.163961
y[1] (numeric) = 83.163961000000000000000000000237
absolute error = 2.37e-28
relative error = 2.8497921112728144346082794204571e-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] = 6.28
y[1] (closed_form) = 83.557717333333333333333333333333
y[1] (numeric) = 83.557717333333333333333333333571
absolute error = 2.38e-28
relative error = 2.8483305623411955980032516605528e-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] = 6.29
y[1] (closed_form) = 83.952729666666666666666666666667
y[1] (numeric) = 83.952729666666666666666666666905
absolute error = 2.38e-28
relative error = 2.8349286669412206406359890088783e-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] = 6.3
y[1] (closed_form) = 84.349
y[1] (numeric) = 84.349000000000000000000000000239
absolute error = 2.39e-28
relative error = 2.8334657198069923769102182598490e-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] = 6.31
y[1] (closed_form) = 84.746530333333333333333333333333
y[1] (numeric) = 84.746530333333333333333333333573
absolute error = 2.40e-28
relative error = 2.8319743481651526099253361369670e-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] = 6.32
y[1] (closed_form) = 85.145322666666666666666666666667
y[1] (numeric) = 85.145322666666666666666666666907
absolute error = 2.40e-28
relative error = 2.8187103235202960923655042973431e-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] = 6.33
y[1] (closed_form) = 85.545379
y[1] (numeric) = 85.545379000000000000000000000241
absolute error = 2.41e-28
relative error = 2.8172182158430790282663894679805e-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] = 6.34
y[1] (closed_form) = 85.946701333333333333333333333333
y[1] (numeric) = 85.946701333333333333333333333575
absolute error = 2.42e-28
relative error = 2.8156985229884952264834643411407e-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] = 6.35
y[1] (closed_form) = 86.349291666666666666666666666667
y[1] (numeric) = 86.349291666666666666666666666909
absolute error = 2.42e-28
relative error = 2.8025707603276035366049615346198e-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] = 6.36
y[1] (closed_form) = 86.753152
y[1] (numeric) = 86.753152000000000000000000000243
absolute error = 2.43e-28
relative error = 2.8010509635430883249060506758302e-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] = 6.37
y[1] (closed_form) = 87.158284333333333333333333333333
y[1] (numeric) = 87.158284333333333333333333333577
absolute error = 2.44e-28
relative error = 2.7995043944053771014071475546446e-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] = 6.38
y[1] (closed_form) = 87.564690666666666666666666666667
y[1] (numeric) = 87.564690666666666666666666666911
absolute error = 2.44e-28
relative error = 2.7865112997296718595157335716354e-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] = 6.39
y[1] (closed_form) = 87.972373
y[1] (numeric) = 87.972373000000000000000000000245
absolute error = 2.45e-28
relative error = 2.7849652299364483438454024651580e-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] = 6.4
y[1] (closed_form) = 88.381333333333333333333333333333
y[1] (numeric) = 88.381333333333333333333333333579
absolute error = 2.46e-28
relative error = 2.7833931750294179766466523851190e-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] = 6.41
y[1] (closed_form) = 88.791573666666666666666666666667
y[1] (numeric) = 88.791573666666666666666666666913
absolute error = 2.46e-28
relative error = 2.7705331693242768333110708354341e-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] = 6.42
y[1] (closed_form) = 89.203096
y[1] (numeric) = 89.203096000000000000000000000247
absolute error = 2.47e-28
relative error = 2.7689621893840994039040976784034e-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] = 6.43
y[1] (closed_form) = 89.615902333333333333333333333333
y[1] (numeric) = 89.615902333333333333333333333581
absolute error = 2.48e-28
relative error = 2.7673659868707751336707513744947e-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] = 6.44
y[1] (closed_form) = 90.029994666666666666666666666667
y[1] (numeric) = 90.029994666666666666666666666915
absolute error = 2.48e-28
relative error = 2.7546375062912366272715984906719e-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] = 6.45
y[1] (closed_form) = 90.445375
y[1] (numeric) = 90.445375000000000000000000000249
absolute error = 2.49e-28
relative error = 2.7530429278445691667484379383689e-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] = 6.46
y[1] (closed_form) = 90.862045333333333333333333333333
y[1] (numeric) = 90.862045333333333333333333333583
absolute error = 2.50e-28
relative error = 2.7514238655189712216324897756356e-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] = 6.47
y[1] (closed_form) = 91.280007666666666666666666666667
y[1] (numeric) = 91.280007666666666666666666666917
absolute error = 2.50e-28
relative error = 2.7388253615506013888992406343758e-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] = 6.48
y[1] (closed_form) = 91.699264
y[1] (numeric) = 91.699264000000000000000000000251
absolute error = 2.51e-28
relative error = 2.7372084469511118431659386055705e-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] = 6.49
y[1] (closed_form) = 92.119816333333333333333333333333
y[1] (numeric) = 92.119816333333333333333333333585
absolute error = 2.52e-28
relative error = 2.7355677641403894968686234426528e-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] = 6.5
y[1] (closed_form) = 92.541666666666666666666666666667
y[1] (numeric) = 92.541666666666666666666666666919
absolute error = 2.52e-28
relative error = 2.7230977037370553804592525889239e-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] = 6.51
y[1] (closed_form) = 92.964817
y[1] (numeric) = 92.964817000000000000000000000253
absolute error = 2.53e-28
relative error = 2.7214596679085594284556059525186e-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] = 6.52
y[1] (closed_form) = 93.389269333333333333333333333333
y[1] (numeric) = 93.389269333333333333333333333587
absolute error = 2.54e-28
relative error = 2.7197985572989170832931669294425e-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] = 6.53
y[1] (closed_form) = 93.815025666666666666666666666667
y[1] (numeric) = 93.815025666666666666666666666921
absolute error = 2.54e-28
relative error = 2.7074554229989249376708763678250e-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] = 6.54
y[1] (closed_form) = 94.242088
y[1] (numeric) = 94.242088000000000000000000000255
absolute error = 2.55e-28
relative error = 2.7057974352181161351178891537293e-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] = 6.55
y[1] (closed_form) = 94.670458333333333333333333333333
y[1] (numeric) = 94.670458333333333333333333333589
absolute error = 2.56e-28
relative error = 2.7041170446078084020402351842422e-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] = 6.56
y[1] (closed_form) = 95.100138666666666666666666666667
y[1] (numeric) = 95.100138666666666666666666666923
absolute error = 2.56e-28
relative error = 2.6918993346297819628836433242355e-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] = 6.57
y[1] (closed_form) = 95.531131
y[1] (numeric) = 95.531131000000000000000000000257
absolute error = 2.57e-28
relative error = 2.6902225202379316539233687079451e-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] = 6.58
y[1] (closed_form) = 95.963437333333333333333333333333
y[1] (numeric) = 95.963437333333333333333333333591
absolute error = 2.58e-28
relative error = 2.6885239542204532398436526756065e-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] = 6.59
y[1] (closed_form) = 96.397059666666666666666666666667
y[1] (numeric) = 96.397059666666666666666666666925
absolute error = 2.58e-28
relative error = 2.6764301825402496111404559818887e-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] = 6.6
y[1] (closed_form) = 96.832
y[1] (numeric) = 96.832000000000000000000000000259
absolute error = 2.59e-28
relative error = 2.6747356245869134170522141440846e-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] = 6.61
y[1] (closed_form) = 97.268260333333333333333333333333
y[1] (numeric) = 97.268260333333333333333333333593
absolute error = 2.60e-28
relative error = 2.6730199461673659144056313457044e-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] = 6.62
y[1] (closed_form) = 97.705842666666666666666666666667
y[1] (numeric) = 97.705842666666666666666666666927
absolute error = 2.60e-28
relative error = 2.6610486425772531760707261423138e-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] = 6.63
y[1] (closed_form) = 98.144749
y[1] (numeric) = 98.144749000000000000000000000261
absolute error = 2.61e-28
relative error = 2.6593373833988815845868636334278e-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] = 6.64
y[1] (closed_form) = 98.584981333333333333333333333333
y[1] (numeric) = 98.584981333333333333333333333595
absolute error = 2.62e-28
relative error = 2.6576056155463625994363766240202e-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] = 6.65
y[1] (closed_form) = 99.026541666666666666666666666667
y[1] (numeric) = 99.026541666666666666666666666929
absolute error = 2.62e-28
relative error = 2.6457553256976138972842718513597e-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] = 6.66
y[1] (closed_form) = 99.469432
y[1] (numeric) = 99.469432000000000000000000000263
absolute error = 2.63e-28
relative error = 2.6440283684338320138391862939360e-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] = 6.67
y[1] (closed_form) = 99.913654333333333333333333333333
y[1] (numeric) = 99.913654333333333333333333333597
absolute error = 2.64e-28
relative error = 2.6422814955725620992283260262963e-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] = 6.68
y[1] (closed_form) = 100.35921066666666666666666666667
y[1] (numeric) = 100.35921066666666666666666666693
absolute error = 2.6e-28
relative error = 2.5906939509873652786003046549801e-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] = 6.69
y[1] (closed_form) = 100.806103
y[1] (numeric) = 100.80610300000000000000000000027
absolute error = 2.7e-28
relative error = 2.6784092625820482317424769411035e-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] = 6.7
y[1] (closed_form) = 101.25433333333333333333333333333
y[1] (numeric) = 101.25433333333333333333333333361
absolute error = 2.8e-28
relative error = 2.7653137478889792371026096002477e-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] = 6.71
y[1] (closed_form) = 101.70390366666666666666666666667
y[1] (numeric) = 101.70390366666666666666666666695
absolute error = 2.8e-28
relative error = 2.7530899985677704780069880700186e-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] = 6.72
y[1] (closed_form) = 102.154816
y[1] (numeric) = 102.15481600000000000000000000029
absolute error = 2.9e-28
relative error = 2.8388284699176590949955800419630e-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] = 6.73
y[1] (closed_form) = 102.60707233333333333333333333333
y[1] (numeric) = 102.60707233333333333333333333363
absolute error = 3.0e-28
relative error = 2.9237750690849877316936213659373e-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] = 6.74
y[1] (closed_form) = 103.06067466666666666666666666667
y[1] (numeric) = 103.06067466666666666666666666697
absolute error = 3.0e-28
relative error = 2.9109066185555470715205616223017e-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] = 6.75
y[1] (closed_form) = 103.515625
y[1] (numeric) = 103.51562500000000000000000000031
absolute error = 3.1e-28
relative error = 2.9947169811320754716981132075472e-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] = 6.76
y[1] (closed_form) = 103.97192533333333333333333333333
y[1] (numeric) = 103.97192533333333333333333333365
absolute error = 3.2e-28
relative error = 3.0777539126459573497173801173815e-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] = 6.77
y[1] (closed_form) = 104.42957766666666666666666666667
y[1] (numeric) = 104.42957766666666666666666666699
absolute error = 3.2e-28
relative error = 3.0642659594145059790579829118846e-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] = 6.78
y[1] (closed_form) = 104.888584
y[1] (numeric) = 104.88858400000000000000000000033
absolute error = 3.3e-28
relative error = 3.1461955859753049960136748533091e-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] = 6.79
y[1] (closed_form) = 105.34894633333333333333333333333
y[1] (numeric) = 105.34894633333333333333333333367
absolute error = 3.4e-28
relative error = 3.2273697254095934811738458804837e-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] = 6.8
y[1] (closed_form) = 105.81066666666666666666666666667
y[1] (numeric) = 105.81066666666666666666666666701
absolute error = 3.4e-28
relative error = 3.2132866251669648932684795483756e-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] = 6.81
y[1] (closed_form) = 106.273747
y[1] (numeric) = 106.27374700000000000000000000035
absolute error = 3.5e-28
relative error = 3.2933815724028249422691382096465e-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] = 6.82
y[1] (closed_form) = 106.73818933333333333333333333333
y[1] (numeric) = 106.73818933333333333333333333369
absolute error = 3.6e-28
relative error = 3.3727384945209613324025907528356e-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] = 6.83
y[1] (closed_form) = 107.20399566666666666666666666667
y[1] (numeric) = 107.20399566666666666666666666703
absolute error = 3.6e-28
relative error = 3.3580837893333870046330082839853e-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] = 6.84
y[1] (closed_form) = 107.671168
y[1] (numeric) = 107.67116800000000000000000000037
absolute error = 3.7e-28
relative error = 3.4363888390251325220136926535431e-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] = 6.85
y[1] (closed_form) = 108.13970833333333333333333333333
y[1] (numeric) = 108.13970833333333333333333333371
absolute error = 3.8e-28
relative error = 3.5139728584127091767478258256200e-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] = 6.86
y[1] (closed_form) = 108.60961866666666666666666666667
y[1] (numeric) = 108.60961866666666666666666666705
absolute error = 3.8e-28
relative error = 3.4987693048279308938800681300000e-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] = 6.87
y[1] (closed_form) = 109.080901
y[1] (numeric) = 109.08090100000000000000000000039
absolute error = 3.9e-28
relative error = 3.5753280035704875595041152071159e-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] = 6.88
y[1] (closed_form) = 109.55355733333333333333333333333
y[1] (numeric) = 109.55355733333333333333333333373
absolute error = 4.0e-28
relative error = 3.6511822138549026030105603873409e-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] = 6.89
y[1] (closed_form) = 110.02758966666666666666666666667
y[1] (numeric) = 110.02758966666666666666666666707
absolute error = 4.0e-28
relative error = 3.6354518099670934352831971062384e-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] = 6.9
y[1] (closed_form) = 110.503
y[1] (numeric) = 110.50300000000000000000000000041
absolute error = 4.1e-28
relative error = 3.7103065075156330597359347710017e-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] = 6.91
y[1] (closed_form) = 110.97979033333333333333333333333
y[1] (numeric) = 110.97979033333333333333333333375
absolute error = 4.2e-28
relative error = 3.7844728192268976203478200239648e-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] = 6.92
y[1] (closed_form) = 111.45796266666666666666666666667
y[1] (numeric) = 111.45796266666666666666666666709
absolute error = 4.2e-28
relative error = 3.7682368307419986096521986788632e-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] = 6.93
y[1] (closed_form) = 111.937519
y[1] (numeric) = 111.93751900000000000000000000043
absolute error = 4.3e-28
relative error = 3.8414287170327582479293649522463e-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] = 6.94
y[1] (closed_form) = 112.41846133333333333333333333333
y[1] (numeric) = 112.41846133333333333333333333377
absolute error = 4.4e-28
relative error = 3.9139478941572656998709322309886e-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] = 6.95
y[1] (closed_form) = 112.90079166666666666666666666667
y[1] (numeric) = 112.90079166666666666666666666711
absolute error = 4.4e-28
relative error = 3.8972268794985568081711856906819e-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] = 6.96
y[1] (closed_form) = 113.384512
y[1] (numeric) = 113.38451200000000000000000000045
absolute error = 4.5e-28
relative error = 3.9687960203947431550439622653224e-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] = 6.97
y[1] (closed_form) = 113.86962433333333333333333333333
y[1] (numeric) = 113.86962433333333333333333333379
absolute error = 4.6e-28
relative error = 4.0397077156716593833907821240932e-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] = 6.98
y[1] (closed_form) = 114.35613066666666666666666666667
y[1] (numeric) = 114.35613066666666666666666666713
absolute error = 4.6e-28
relative error = 4.0225215501636769848502977213942e-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] = 6.99
y[1] (closed_form) = 114.844033
y[1] (numeric) = 114.84403300000000000000000000047
absolute error = 4.7e-28
relative error = 4.0925069219747794820127920794979e-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] = 7
y[1] (closed_form) = 115.33333333333333333333333333333
y[1] (numeric) = 115.33333333333333333333333333381
absolute error = 4.8e-28
relative error = 4.1618497109826589595375722543354e-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] = 7.01
y[1] (closed_form) = 115.82403366666666666666666666667
y[1] (numeric) = 115.82403366666666666666666666715
absolute error = 4.8e-28
relative error = 4.1442176101499440957995070804259e-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] = 7.02
y[1] (closed_form) = 116.316136
y[1] (numeric) = 116.31613600000000000000000000049
absolute error = 4.9e-28
relative error = 4.2126571329707857558129338134135e-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] = 7.03
y[1] (closed_form) = 116.80964233333333333333333333333
y[1] (numeric) = 116.80964233333333333333333333383
absolute error = 5.0e-28
relative error = 4.2804685470500556022876501859107e-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] = 7.04
y[1] (closed_form) = 117.30455466666666666666666666667
y[1] (numeric) = 117.30455466666666666666666666717
absolute error = 5.0e-28
relative error = 4.2624090890656635600259045354941e-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] = 7.05
y[1] (closed_form) = 117.800875
y[1] (numeric) = 117.80087500000000000000000000051
absolute error = 5.1e-28
relative error = 4.3293396589796128424343197790339e-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] = 7.06
y[1] (closed_form) = 118.29860533333333333333333333333
y[1] (numeric) = 118.29860533333333333333333333385
absolute error = 5.2e-28
relative error = 4.3956562170346916684980022418750e-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] = 7.07
y[1] (closed_form) = 118.79774766666666666666666666667
y[1] (numeric) = 118.79774766666666666666666666719
absolute error = 5.2e-28
relative error = 4.3771873643519105663852330668344e-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] = 7.08
y[1] (closed_form) = 119.298304
y[1] (numeric) = 119.29830400000000000000000000053
absolute error = 5.3e-28
relative error = 4.4426448845408565070631683079082e-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] = 7.09
y[1] (closed_form) = 119.80027633333333333333333333333
y[1] (numeric) = 119.80027633333333333333333333387
absolute error = 5.4e-28
relative error = 4.5075021237638825813615471654909e-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] = 7.1
y[1] (closed_form) = 120.30366666666666666666666666667
y[1] (numeric) = 120.30366666666666666666666666721
absolute error = 5.4e-28
relative error = 4.4886412439631931417995018162371e-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] = 7.11
y[1] (closed_form) = 120.808477
y[1] (numeric) = 120.80847700000000000000000000055
absolute error = 5.5e-28
relative error = 4.5526606547651453299920335888350e-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] = 7.12
y[1] (closed_form) = 121.31470933333333333333333333333
y[1] (numeric) = 121.31470933333333333333333333389
absolute error = 5.6e-28
relative error = 4.6160931603215755139206422366019e-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] = 7.13
y[1] (closed_form) = 121.82236566666666666666666666667
y[1] (numeric) = 121.82236566666666666666666666723
absolute error = 5.6e-28
relative error = 4.5968570462035327902582705003399e-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] = 7.14
y[1] (closed_form) = 122.331448
y[1] (numeric) = 122.33144800000000000000000000057
absolute error = 5.7e-28
relative error = 4.6594723541570439025621604675194e-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] = 7.15
y[1] (closed_form) = 122.84195833333333333333333333333
y[1] (numeric) = 122.84195833333333333333333333391
absolute error = 5.8e-28
relative error = 4.7215137878717471330880090848439e-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] = 7.16
y[1] (closed_form) = 123.35389866666666666666666666667
y[1] (numeric) = 123.35389866666666666666666666725
absolute error = 5.8e-28
relative error = 4.7019186768251745784573175603669e-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] = 7.17
y[1] (closed_form) = 123.867271
y[1] (numeric) = 123.86727100000000000000000000059
absolute error = 5.9e-28
relative error = 4.7631629827381923995080185467233e-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] = 7.18
y[1] (closed_form) = 124.38207733333333333333333333333
y[1] (numeric) = 124.38207733333333333333333333393
absolute error = 6.0e-28
relative error = 4.8238461108190957158050573588535e-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] = 7.19
y[1] (closed_form) = 124.89831966666666666666666666667
y[1] (numeric) = 124.89831966666666666666666666727
absolute error = 6.0e-28
relative error = 4.8039077034927496849510590827029e-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] = 7.2
y[1] (closed_form) = 125.416
y[1] (numeric) = 125.41600000000000000000000000061
absolute error = 6.1e-28
relative error = 4.8638132295719844357976653696498e-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] = 7.21
y[1] (closed_form) = 125.93512033333333333333333333333
y[1] (numeric) = 125.93512033333333333333333333395
absolute error = 6.2e-28
relative error = 4.9231699494068322656755524440535e-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] = 7.22
y[1] (closed_form) = 126.45568266666666666666666666667
y[1] (numeric) = 126.45568266666666666666666666729
absolute error = 6.2e-28
relative error = 4.9029034277115180546730036500164e-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=333.6MB, alloc=40.3MB, time=4.20
TOP MAIN SOLVE Loop
x[1] = 7.23
y[1] (closed_form) = 126.977689
y[1] (numeric) = 126.97768900000000000000000000063
absolute error = 6.3e-28
relative error = 4.9615015437869561478631100302983e-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] = 7.24
y[1] (closed_form) = 127.50114133333333333333333333333
y[1] (numeric) = 127.50114133333333333333333333397
absolute error = 6.4e-28
relative error = 5.0195629098473115890329912445439e-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] = 7.25
y[1] (closed_form) = 128.02604166666666666666666666667
y[1] (numeric) = 128.02604166666666666666666666731
absolute error = 6.4e-28
relative error = 4.9989829543143077987063178877994e-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] = 7.26
y[1] (closed_form) = 128.552392
y[1] (numeric) = 128.55239200000000000000000000065
absolute error = 6.5e-28
relative error = 5.0563042031921117422692531462192e-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] = 7.27
y[1] (closed_form) = 129.08019433333333333333333333333
y[1] (numeric) = 129.08019433333333333333333333399
absolute error = 6.6e-28
relative error = 5.1131004520773588443853778621133e-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] = 7.28
y[1] (closed_form) = 129.60945066666666666666666666667
y[1] (numeric) = 129.60945066666666666666666666733
absolute error = 6.6e-28
relative error = 5.0922212585979326939615761352710e-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] = 7.29
y[1] (closed_form) = 130.140163
y[1] (numeric) = 130.14016300000000000000000000067
absolute error = 6.7e-28
relative error = 5.1482953805736358267816215967088e-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] = 7.3
y[1] (closed_form) = 130.67233333333333333333333333333
y[1] (numeric) = 130.67233333333333333333333333401
absolute error = 6.8e-28
relative error = 5.2038559552264315067968991140692e-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] = 7.31
y[1] (closed_form) = 131.20596366666666666666666666667
y[1] (numeric) = 131.20596366666666666666666666735
absolute error = 6.8e-28
relative error = 5.1826912511962013433987938317569e-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] = 7.32
y[1] (closed_form) = 131.741056
y[1] (numeric) = 131.74105600000000000000000000069
absolute error = 6.9e-28
relative error = 5.2375472077588325996111644952960e-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] = 7.33
y[1] (closed_form) = 132.27761233333333333333333333333
y[1] (numeric) = 132.27761233333333333333333333403
absolute error = 7.0e-28
relative error = 5.2919007808822030521632462587768e-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] = 7.34
y[1] (closed_form) = 132.81563466666666666666666666667
y[1] (numeric) = 132.81563466666666666666666666737
absolute error = 7.0e-28
relative error = 5.2704638407731234372949224873384e-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] = 7.35
y[1] (closed_form) = 133.355125
y[1] (numeric) = 133.35512500000000000000000000071
absolute error = 7.1e-28
relative error = 5.3241298375296787431304196220430e-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] = 7.36
y[1] (closed_form) = 133.89608533333333333333333333333
y[1] (numeric) = 133.89608533333333333333333333405
absolute error = 7.2e-28
relative error = 5.3773043342347554218762123829681e-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] = 7.37
y[1] (closed_form) = 134.43851766666666666666666666667
y[1] (numeric) = 134.43851766666666666666666666739
absolute error = 7.2e-28
relative error = 5.3556079946165626793965964411989e-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] = 7.38
y[1] (closed_form) = 134.982424
y[1] (numeric) = 134.98242400000000000000000000073
absolute error = 7.3e-28
relative error = 5.4081115034650733491050657084066e-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] = 7.39
y[1] (closed_form) = 135.52780633333333333333333333333
y[1] (numeric) = 135.52780633333333333333333333407
absolute error = 7.4e-28
relative error = 5.4601341231773153051280726231486e-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] = 7.4
y[1] (closed_form) = 136.07466666666666666666666666667
y[1] (numeric) = 136.07466666666666666666666666741
absolute error = 7.4e-28
relative error = 5.4381907972093752449635494238456e-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] = 7.41
y[1] (closed_form) = 136.623007
y[1] (numeric) = 136.62300700000000000000000000075
absolute error = 7.5e-28
relative error = 5.4895585777877074539868676730267e-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] = 7.42
y[1] (closed_form) = 137.17282933333333333333333333333
y[1] (numeric) = 137.17282933333333333333333333409
absolute error = 7.6e-28
relative error = 5.5404558154383576564851686566268e-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] = 7.43
y[1] (closed_form) = 137.72413566666666666666666666667
y[1] (numeric) = 137.72413566666666666666666666743
absolute error = 7.6e-28
relative error = 5.5182775068520004047608145332898e-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] = 7.44
y[1] (closed_form) = 138.276928
y[1] (numeric) = 138.27692800000000000000000000077
absolute error = 7.7e-28
relative error = 5.5685356272884511868820227189311e-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] = 7.45
y[1] (closed_form) = 138.83120833333333333333333333333
y[1] (numeric) = 138.83120833333333333333333333411
absolute error = 7.8e-28
relative error = 5.6183332938169221677762774880409e-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] = 7.46
y[1] (closed_form) = 139.38697866666666666666666666667
y[1] (numeric) = 139.38697866666666666666666666745
absolute error = 7.8e-28
relative error = 5.5959316104075297937442917910437e-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] = 7.47
y[1] (closed_form) = 139.944241
y[1] (numeric) = 139.94424100000000000000000000079
absolute error = 7.9e-28
relative error = 5.6451054673982618548769005792814e-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] = 7.48
y[1] (closed_form) = 140.50299733333333333333333333333
y[1] (numeric) = 140.50299733333333333333333333413
absolute error = 8.0e-28
relative error = 5.6938287095901384708775085870530e-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] = 7.49
y[1] (closed_form) = 141.06324966666666666666666666667
y[1] (numeric) = 141.06324966666666666666666666747
absolute error = 8.0e-28
relative error = 5.6712148762374676518924847586512e-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] = 7.5
y[1] (closed_form) = 141.625
y[1] (numeric) = 141.62500000000000000000000000081
absolute error = 8.1e-28
relative error = 5.7193292144748455428067078552515e-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] = 7.51
y[1] (closed_form) = 142.18825033333333333333333333333
y[1] (numeric) = 142.18825033333333333333333333415
absolute error = 8.2e-28
relative error = 5.7670025341592277979855864836803e-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] = 7.52
y[1] (closed_form) = 142.75300266666666666666666666667
y[1] (numeric) = 142.75300266666666666666666666749
absolute error = 8.2e-28
relative error = 5.7441874053937004402718833178634e-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] = 7.53
y[1] (closed_form) = 143.319259
y[1] (numeric) = 143.31925900000000000000000000083
absolute error = 8.3e-28
relative error = 5.7912663363686523107128261108299e-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] = 7.54
y[1] (closed_form) = 143.88702133333333333333333333333
y[1] (numeric) = 143.88702133333333333333333333417
absolute error = 8.4e-28
relative error = 5.8379136089976370905669638992505e-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] = 7.55
y[1] (closed_form) = 144.45629166666666666666666666667
y[1] (numeric) = 144.45629166666666666666666666751
absolute error = 8.4e-28
relative error = 5.8149076811296150421508697411644e-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] = 7.56
y[1] (closed_form) = 145.027072
y[1] (numeric) = 145.02707200000000000000000000085
absolute error = 8.5e-28
relative error = 5.8609747013302454316942977377355e-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] = 7.57
y[1] (closed_form) = 145.59936433333333333333333333333
y[1] (numeric) = 145.59936433333333333333333333419
absolute error = 8.6e-28
relative error = 5.9066191939624608205420896835281e-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] = 7.58
y[1] (closed_form) = 146.17317066666666666666666666667
y[1] (numeric) = 146.17317066666666666666666666753
absolute error = 8.6e-28
relative error = 5.8834326167908350677905524988360e-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] = 7.59
y[1] (closed_form) = 146.748493
y[1] (numeric) = 146.74849300000000000000000000087
absolute error = 8.7e-28
relative error = 5.9285106253186531871233594201202e-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] = 7.6
y[1] (closed_form) = 147.32533333333333333333333333333
y[1] (numeric) = 147.32533333333333333333333333421
absolute error = 8.8e-28
relative error = 5.9731750140279110177928213296651e-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] = 7.61
y[1] (closed_form) = 147.90369366666666666666666666667
y[1] (numeric) = 147.90369366666666666666666666755
absolute error = 8.8e-28
relative error = 5.9498176021436796166016868079973e-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] = 7.62
y[1] (closed_form) = 148.483576
y[1] (numeric) = 148.48357600000000000000000000089
absolute error = 8.9e-28
relative error = 5.9939289177679826353320046656204e-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] = 7.63
y[1] (closed_form) = 149.06498233333333333333333333333
y[1] (numeric) = 149.06498233333333333333333333423
absolute error = 9.0e-28
relative error = 6.0376353044973023811917087694644e-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] = 7.64
y[1] (closed_form) = 149.64791466666666666666666666667
y[1] (numeric) = 149.64791466666666666666666666757
absolute error = 9.0e-28
relative error = 6.0141165481971834760659901299347e-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] = 7.65
y[1] (closed_form) = 150.232375
y[1] (numeric) = 150.23237500000000000000000000091
absolute error = 9.1e-28
relative error = 6.0572829258673438398347892722857e-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] = 7.66
y[1] (closed_form) = 150.81836533333333333333333333333
y[1] (numeric) = 150.81836533333333333333333333425
absolute error = 9.2e-28
relative error = 6.1000528547478223120731521167353e-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] = 7.67
y[1] (closed_form) = 151.40588766666666666666666666667
y[1] (numeric) = 151.40588766666666666666666666759
absolute error = 9.2e-28
relative error = 6.0763819305723476455824220116247e-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] = 7.68
y[1] (closed_form) = 151.994944
y[1] (numeric) = 151.99494400000000000000000000093
absolute error = 9.3e-28
relative error = 6.1186245774069958537568197005290e-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] = 7.69
y[1] (closed_form) = 152.58553633333333333333333333333
y[1] (numeric) = 152.58553633333333333333333333427
absolute error = 9.4e-28
relative error = 6.1604790505602508952525030610755e-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] = 7.7
y[1] (closed_form) = 153.17766666666666666666666666667
y[1] (numeric) = 153.17766666666666666666666666761
absolute error = 9.4e-28
relative error = 6.1366648314702099740388611916879e-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] = 7.71
y[1] (closed_form) = 153.771337
y[1] (numeric) = 153.77133700000000000000000000095
absolute error = 9.5e-28
relative error = 6.1780044222415780907205092454909e-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] = 7.72
y[1] (closed_form) = 154.36654933333333333333333333333
y[1] (numeric) = 154.36654933333333333333333333429
absolute error = 9.6e-28
relative error = 6.2189639150837791178800464128188e-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] = 7.73
y[1] (closed_form) = 154.96330566666666666666666666667
y[1] (numeric) = 154.96330566666666666666666666763
absolute error = 9.6e-28
relative error = 6.1950149802883335067041258285667e-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] = 7.74
y[1] (closed_form) = 155.561608
y[1] (numeric) = 155.56160800000000000000000000097
absolute error = 9.7e-28
relative error = 6.2354716724193285530964683779818e-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] = 7.75
y[1] (closed_form) = 156.16145833333333333333333333333
y[1] (numeric) = 156.16145833333333333333333333431
absolute error = 9.8e-28
relative error = 6.2755561484841410132408364740021e-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] = 7.76
y[1] (closed_form) = 156.76285866666666666666666666667
y[1] (numeric) = 156.76285866666666666666666666765
absolute error = 9.8e-28
relative error = 6.2514807929334009593292778602386e-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] = 7.77
y[1] (closed_form) = 157.365811
y[1] (numeric) = 157.36581100000000000000000000099
absolute error = 9.9e-28
relative error = 6.2910742410243099118905821290496e-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] = 7.78
y[1] (closed_form) = 157.97031733333333333333333333333
y[1] (numeric) = 157.97031733333333333333333333433
absolute error = 1.00e-27
relative error = 6.3303031663214231858477919286408e-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] = 7.79
y[1] (closed_form) = 158.57637966666666666666666666667
y[1] (numeric) = 158.57637966666666666666666666767
absolute error = 1.00e-27
relative error = 6.3061094098757738697187518715349e-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] = 7.8
y[1] (closed_form) = 159.184
y[1] (numeric) = 159.18400000000000000000000000101
absolute error = 1.01e-27
relative error = 6.3448587797768619961805206553422e-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] = 7.81
y[1] (closed_form) = 159.79318033333333333333333333333
y[1] (numeric) = 159.79318033333333333333333333435
absolute error = 1.02e-27
relative error = 6.3832511367021397352458143389980e-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] = 7.82
y[1] (closed_form) = 160.40392266666666666666666666667
y[1] (numeric) = 160.40392266666666666666666666769
absolute error = 1.02e-27
relative error = 6.3589467329901208899779026185410e-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] = 7.83
y[1] (closed_form) = 161.016229
y[1] (numeric) = 161.01622900000000000000000000103
absolute error = 1.03e-27
relative error = 6.3968707154357713842621416751724e-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] = 7.84
y[1] (closed_form) = 161.63010133333333333333333333333
y[1] (numeric) = 161.63010133333333333333333333437
absolute error = 1.04e-27
relative error = 6.4344450162484585379541843756894e-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] = 7.85
y[1] (closed_form) = 162.24554166666666666666666666667
y[1] (numeric) = 162.24554166666666666666666666771
absolute error = 1.04e-27
relative error = 6.4100374612245380137564129266006e-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] = 7.86
y[1] (closed_form) = 162.862552
y[1] (numeric) = 162.86255200000000000000000000105
absolute error = 1.05e-27
relative error = 6.4471542850439921879647323713803e-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] = 7.87
y[1] (closed_form) = 163.48113433333333333333333333333
y[1] (numeric) = 163.48113433333333333333333333439
absolute error = 1.06e-27
relative error = 6.4839285849258329202156685957096e-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] = 7.88
y[1] (closed_form) = 164.10129066666666666666666666667
y[1] (numeric) = 164.10129066666666666666666666773
absolute error = 1.06e-27
relative error = 6.4594251251389710784155685048115e-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] = 7.89
y[1] (closed_form) = 164.723023
y[1] (numeric) = 164.72302300000000000000000000107
absolute error = 1.07e-27
relative error = 6.4957525700581636362999481863564e-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] = 7.9
y[1] (closed_form) = 165.34633333333333333333333333333
y[1] (numeric) = 165.34633333333333333333333333441
absolute error = 1.08e-27
relative error = 6.5317444797687278621237443023635e-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] = 7.91
y[1] (closed_form) = 165.97122366666666666666666666667
y[1] (numeric) = 165.97122366666666666666666666775
absolute error = 1.08e-27
relative error = 6.5071521203522045892971675405151e-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] = 7.92
y[1] (closed_form) = 166.597696
y[1] (numeric) = 166.59769600000000000000000000109
absolute error = 1.09e-27
relative error = 6.5427075294006466932171739037736e-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] = 7.93
y[1] (closed_form) = 167.22575233333333333333333333333
y[1] (numeric) = 167.22575233333333333333333333443
absolute error = 1.10e-27
relative error = 6.5779342275426290652039663819165e-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] = 7.94
y[1] (closed_form) = 167.85539466666666666666666666667
y[1] (numeric) = 167.85539466666666666666666666777
absolute error = 1.10e-27
relative error = 6.5532597399351978726196594646632e-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] = 7.95
y[1] (closed_form) = 168.486625
y[1] (numeric) = 168.48662500000000000000000000111
absolute error = 1.11e-27
relative error = 6.5880600314713408260151213783290e-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] = 7.96
y[1] (closed_form) = 169.11944533333333333333333333333
y[1] (numeric) = 169.11944533333333333333333333445
absolute error = 1.12e-27
relative error = 6.6225382763790836778524912222987e-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] = 7.97
y[1] (closed_form) = 169.75385766666666666666666666667
y[1] (numeric) = 169.75385766666666666666666666779
absolute error = 1.12e-27
relative error = 6.5977882057871270016282968202667e-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] = 7.98
y[1] (closed_form) = 170.389864
y[1] (numeric) = 170.38986400000000000000000000113
absolute error = 1.13e-27
relative error = 6.6318498851551404489647341933438e-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] = 7.99
y[1] (closed_form) = 171.02746633333333333333333333333
y[1] (numeric) = 171.02746633333333333333333333447
absolute error = 1.14e-27
relative error = 6.6655960264191405248341017443478e-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] = 8
y[1] (closed_form) = 171.66666666666666666666666666667
y[1] (numeric) = 171.66666666666666666666666666781
absolute error = 1.14e-27
relative error = 6.6407766990291262135922330097086e-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] = 8.01
y[1] (closed_form) = 172.307467
y[1] (numeric) = 172.30746700000000000000000000115
absolute error = 1.15e-27
relative error = 6.6741158698595459011651538003283e-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] = 8.02
y[1] (closed_form) = 172.94986933333333333333333333333
y[1] (numeric) = 172.94986933333333333333333333449
absolute error = 1.16e-27
relative error = 6.7071458594992327718979407998321e-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] = 8.03
y[1] (closed_form) = 173.59387566666666666666666666667
y[1] (numeric) = 173.59387566666666666666666666783
absolute error = 1.16e-27
relative error = 6.6822633894494131222490304943111e-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] = 8.04
y[1] (closed_form) = 174.239488
y[1] (numeric) = 174.23948800000000000000000000117
absolute error = 1.17e-27
relative error = 6.7148957646156535997167301134402e-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] = 8.05
y[1] (closed_form) = 174.88670833333333333333333333333
y[1] (numeric) = 174.88670833333333333333333333451
absolute error = 1.18e-27
relative error = 6.7472251679122746368422795614591e-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] = 8.06
y[1] (closed_form) = 175.53553866666666666666666666667
y[1] (numeric) = 175.53553866666666666666666666785
absolute error = 1.18e-27
relative error = 6.7222854640322255275273639934671e-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] = 8.07
y[1] (closed_form) = 176.185981
y[1] (numeric) = 176.18598100000000000000000000119
absolute error = 1.19e-27
relative error = 6.7542263762745118750395923952655e-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] = 8.08
y[1] (closed_form) = 176.83803733333333333333333333333
y[1] (numeric) = 176.83803733333333333333333333453
absolute error = 1.20e-27
relative error = 6.7858703822755237093485648879404e-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] = 8.09
y[1] (closed_form) = 177.49170966666666666666666666667
y[1] (numeric) = 177.49170966666666666666666666787
absolute error = 1.20e-27
relative error = 6.7608791546017917392720139610501e-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] = 8.1
y[1] (closed_form) = 178.147
y[1] (numeric) = 178.14700000000000000000000000121
absolute error = 1.21e-27
relative error = 6.7921435668296406899919729212392e-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] = 8.11
y[1] (closed_form) = 178.80391033333333333333333333333
y[1] (numeric) = 178.80391033333333333333333333455
absolute error = 1.22e-27
relative error = 6.8231169985355894463091076581993e-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] = 8.12
y[1] (closed_form) = 179.46244266666666666666666666667
y[1] (numeric) = 179.46244266666666666666666666789
absolute error = 1.22e-27
relative error = 6.7980797646113988775010692673657e-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] = 8.13
y[1] (closed_form) = 180.122599
y[1] (numeric) = 180.12259900000000000000000000123
absolute error = 1.23e-27
relative error = 6.8286822798953728177106749386844e-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] = 8.14
y[1] (closed_form) = 180.78438133333333333333333333333
y[1] (numeric) = 180.78438133333333333333333333457
absolute error = 1.24e-27
relative error = 6.8589996041398443520408540307089e-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] = 8.15
y[1] (closed_form) = 181.44779166666666666666666666667
y[1] (numeric) = 181.44779166666666666666666666791
absolute error = 1.24e-27
relative error = 6.8339216951065125023336602562673e-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] = 8.16
y[1] (closed_form) = 182.112832
y[1] (numeric) = 182.11283200000000000000000000125
absolute error = 1.25e-27
relative error = 6.8638765663695790530565138869511e-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] = 8.17
y[1] (closed_form) = 182.77950433333333333333333333333
y[1] (numeric) = 182.77950433333333333333333333459
absolute error = 1.26e-27
relative error = 6.8935519034024152157264211715147e-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] = 8.18
y[1] (closed_form) = 183.44781066666666666666666666667
y[1] (numeric) = 183.44781066666666666666666666793
absolute error = 1.26e-27
relative error = 6.8684384698898341717649498540757e-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] = 8.19
y[1] (closed_form) = 184.117753
y[1] (numeric) = 184.11775300000000000000000000127
absolute error = 1.27e-27
relative error = 6.8977596093082887015246161514908e-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] = 8.2
y[1] (closed_form) = 184.78933333333333333333333333333
y[1] (numeric) = 184.78933333333333333333333333461
absolute error = 1.28e-27
relative error = 6.9268067420918956361117524821059e-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] = 8.21
y[1] (closed_form) = 185.46255366666666666666666666667
y[1] (numeric) = 185.46255366666666666666666666795
absolute error = 1.28e-27
relative error = 6.9016627599151592256464508475143e-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] = 8.22
y[1] (closed_form) = 186.137416
y[1] (numeric) = 186.13741600000000000000000000129
absolute error = 1.29e-27
relative error = 6.9303637480387070593050459022167e-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] = 8.23
y[1] (closed_form) = 186.81392233333333333333333333333
y[1] (numeric) = 186.81392233333333333333333333463
absolute error = 1.30e-27
relative error = 6.9587961312669260783342009554403e-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=380.7MB, alloc=40.3MB, time=4.78
TOP MAIN SOLVE Loop
x[1] = 8.24
y[1] (closed_form) = 187.49207466666666666666666666667
y[1] (numeric) = 187.49207466666666666666666666797
absolute error = 1.30e-27
relative error = 6.9336264069359134369384473751551e-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] = 8.25
y[1] (closed_form) = 188.171875
y[1] (numeric) = 188.17187500000000000000000000131
absolute error = 1.31e-27
relative error = 6.9617205015361620858590052312547e-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] = 8.26
y[1] (closed_form) = 188.85332533333333333333333333333
y[1] (numeric) = 188.85332533333333333333333333465
absolute error = 1.32e-27
relative error = 6.9895512703848321258754077608900e-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] = 8.27
y[1] (closed_form) = 189.53642766666666666666666666667
y[1] (numeric) = 189.53642766666666666666666666799
absolute error = 1.32e-27
relative error = 6.9643604464333024264044595276154e-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] = 8.28
y[1] (closed_form) = 190.221184
y[1] (numeric) = 190.22118400000000000000000000133
absolute error = 1.33e-27
relative error = 6.9918605910895812739762990855950e-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] = 8.29
y[1] (closed_form) = 190.90759633333333333333333333333
y[1] (numeric) = 190.90759633333333333333333333467
absolute error = 1.34e-27
relative error = 7.0191025697075937378144036101907e-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] = 8.3
y[1] (closed_form) = 191.59566666666666666666666666667
y[1] (numeric) = 191.59566666666666666666666666801
absolute error = 1.34e-27
relative error = 6.9938951298481002527892941211265e-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] = 8.31
y[1] (closed_form) = 192.285397
y[1] (numeric) = 192.28539700000000000000000000135
absolute error = 1.35e-27
relative error = 7.0208139622792052170243588492578e-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] = 8.32
y[1] (closed_form) = 192.97678933333333333333333333333
y[1] (numeric) = 192.97678933333333333333333333469
absolute error = 1.36e-27
relative error = 7.0474796720285365994136275815472e-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] = 8.33
y[1] (closed_form) = 193.66984566666666666666666666667
y[1] (numeric) = 193.66984566666666666666666666803
absolute error = 1.36e-27
relative error = 7.0222599461392317902692189371066e-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] = 8.34
y[1] (closed_form) = 194.364568
y[1] (numeric) = 194.36456800000000000000000000137
absolute error = 1.37e-27
relative error = 7.0486098062893850076625077056226e-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] = 8.35
y[1] (closed_form) = 195.06095833333333333333333333333
y[1] (numeric) = 195.06095833333333333333333333471
absolute error = 1.38e-27
relative error = 7.0747114737422895364120147911028e-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] = 8.36
y[1] (closed_form) = 195.75901866666666666666666666667
y[1] (numeric) = 195.75901866666666666666666666805
absolute error = 1.38e-27
relative error = 7.0494836426914658828421861588952e-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] = 8.37
y[1] (closed_form) = 196.458751
y[1] (numeric) = 196.45875100000000000000000000139
absolute error = 1.39e-27
relative error = 7.0752765805784848952847104275849e-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] = 8.38
y[1] (closed_form) = 197.16015733333333333333333333333
y[1] (numeric) = 197.16015733333333333333333333473
absolute error = 1.40e-27
relative error = 7.1008261452797379927701146488570e-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] = 8.39
y[1] (closed_form) = 197.86323966666666666666666666667
y[1] (numeric) = 197.86323966666666666666666666807
absolute error = 1.40e-27
relative error = 7.0755942455937313833429113013326e-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] = 8.4
y[1] (closed_form) = 198.568
y[1] (numeric) = 198.56800000000000000000000000141
absolute error = 1.41e-27
relative error = 7.1008420289271181660690544297168e-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] = 8.41
y[1] (closed_form) = 199.27444033333333333333333333333
y[1] (numeric) = 199.27444033333333333333333333475
absolute error = 1.42e-27
relative error = 7.1258511509289213560138113113190e-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] = 8.42
y[1] (closed_form) = 199.98256266666666666666666666667
y[1] (numeric) = 199.98256266666666666666666666809
absolute error = 1.42e-27
relative error = 7.1006190793087946694445799747793e-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] = 8.43
y[1] (closed_form) = 200.692369
y[1] (numeric) = 200.69236900000000000000000000143
absolute error = 1.43e-27
relative error = 7.1253332008851816383711131537841e-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] = 8.44
y[1] (closed_form) = 201.40386133333333333333333333333
y[1] (numeric) = 201.40386133333333333333333333477
absolute error = 1.44e-27
relative error = 7.1498132680620701240974552384617e-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] = 8.45
y[1] (closed_form) = 202.11704166666666666666666666667
y[1] (numeric) = 202.11704166666666666666666666811
absolute error = 1.44e-27
relative error = 7.1245847857542937683178208006127e-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] = 8.46
y[1] (closed_form) = 202.831912
y[1] (numeric) = 202.83191200000000000000000000145
absolute error = 1.45e-27
relative error = 7.1487764706374211963253592955333e-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] = 8.47
y[1] (closed_form) = 203.54847433333333333333333333333
y[1] (numeric) = 203.54847433333333333333333333479
absolute error = 1.46e-27
relative error = 7.1727386057882562725766962802570e-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] = 8.48
y[1] (closed_form) = 204.26673066666666666666666666667
y[1] (numeric) = 204.26673066666666666666666666813
absolute error = 1.46e-27
relative error = 7.1475173428144095620648891702696e-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] = 8.49
y[1] (closed_form) = 204.986683
y[1] (numeric) = 204.98668300000000000000000000147
absolute error = 1.47e-27
relative error = 7.1711975553065561824813761194428e-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] = 8.5
y[1] (closed_form) = 205.70833333333333333333333333333
y[1] (numeric) = 205.70833333333333333333333333481
absolute error = 1.48e-27
relative error = 7.1946526230504354871379380190400e-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] = 8.51
y[1] (closed_form) = 206.43168366666666666666666666667
y[1] (numeric) = 206.43168366666666666666666666815
absolute error = 1.48e-27
relative error = 7.1694420823007674899052277425675e-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] = 8.52
y[1] (closed_form) = 207.156736
y[1] (numeric) = 207.15673600000000000000000000149
absolute error = 1.49e-27
relative error = 7.1926215327123130574909232012615e-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] = 8.53
y[1] (closed_form) = 207.88349233333333333333333333333
y[1] (numeric) = 207.88349233333333333333333333483
absolute error = 1.50e-27
relative error = 7.2155801461849920143651233028722e-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] = 8.54
y[1] (closed_form) = 208.61195466666666666666666666667
y[1] (numeric) = 208.61195466666666666666666666817
absolute error = 1.50e-27
relative error = 7.1903837073805025657653905241837e-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] = 8.55
y[1] (closed_form) = 209.342125
y[1] (numeric) = 209.34212500000000000000000000151
absolute error = 1.51e-27
relative error = 7.2130728586040673849087946346202e-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] = 8.56
y[1] (closed_form) = 210.07400533333333333333333333333
y[1] (numeric) = 210.07400533333333333333333333485
absolute error = 1.52e-27
relative error = 7.2355453859612546445854408234448e-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] = 8.57
y[1] (closed_form) = 210.80759766666666666666666666667
y[1] (numeric) = 210.80759766666666666666666666819
absolute error = 1.52e-27
relative error = 7.2103663094887852974647610463336e-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] = 8.58
y[1] (closed_form) = 211.542904
y[1] (numeric) = 211.54290400000000000000000000153
absolute error = 1.53e-27
relative error = 7.2325753833841668354897879250065e-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] = 8.59
y[1] (closed_form) = 212.27992633333333333333333333333
y[1] (numeric) = 212.27992633333333333333333333487
absolute error = 1.54e-27
relative error = 7.2545719541178347152212047985151e-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] = 8.6
y[1] (closed_form) = 213.01866666666666666666666666667
y[1] (numeric) = 213.01866666666666666666666666821
absolute error = 1.54e-27
relative error = 7.2294133847424951803910768383364e-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] = 8.61
y[1] (closed_form) = 213.759127
y[1] (numeric) = 213.75912700000000000000000000155
absolute error = 1.55e-27
relative error = 7.2511523683384054988211099870370e-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] = 8.62
y[1] (closed_form) = 214.50130933333333333333333333333
y[1] (numeric) = 214.50130933333333333333333333489
absolute error = 1.56e-27
relative error = 7.2726828794120429984383871546470e-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] = 8.63
y[1] (closed_form) = 215.24521566666666666666666666667
y[1] (numeric) = 215.24521566666666666666666666823
absolute error = 1.56e-27
relative error = 7.2475478498711408447302275074802e-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] = 8.64
y[1] (closed_form) = 215.990848
y[1] (numeric) = 215.99084800000000000000000000157
absolute error = 1.57e-27
relative error = 7.2688265013895403568210445657401e-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] = 8.65
y[1] (closed_form) = 216.73820833333333333333333333333
y[1] (numeric) = 216.73820833333333333333333333491
absolute error = 1.58e-27
relative error = 7.2899006231980709446515448648976e-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] = 8.66
y[1] (closed_form) = 217.48729866666666666666666666667
y[1] (numeric) = 217.48729866666666666666666666825
absolute error = 1.58e-27
relative error = 7.2647920576805607051112759541132e-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] = 8.67
y[1] (closed_form) = 218.238121
y[1] (numeric) = 218.23812100000000000000000000159
absolute error = 1.59e-27
relative error = 7.2856199123891833727802302696695e-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] = 8.68
y[1] (closed_form) = 218.99067733333333333333333333333
y[1] (numeric) = 218.99067733333333333333333333493
absolute error = 1.60e-27
relative error = 7.3062470945490720676523410969191e-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] = 8.69
y[1] (closed_form) = 219.74496966666666666666666666667
y[1] (numeric) = 219.74496966666666666666666666827
absolute error = 1.60e-27
relative error = 7.2811678120643941809216295613373e-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] = 8.7
y[1] (closed_form) = 220.501
y[1] (numeric) = 220.50100000000000000000000000161
absolute error = 1.61e-27
relative error = 7.3015541879628663815583602795452e-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] = 8.71
y[1] (closed_form) = 221.25877033333333333333333333333
y[1] (numeric) = 221.25877033333333333333333333495
absolute error = 1.62e-27
relative error = 7.3217436649377503922401955076702e-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] = 8.72
y[1] (closed_form) = 222.01828266666666666666666666667
y[1] (numeric) = 222.01828266666666666666666666829
absolute error = 1.62e-27
relative error = 7.2966963825777903503826759924731e-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] = 8.73
y[1] (closed_form) = 222.779539
y[1] (numeric) = 222.77953900000000000000000000163
absolute error = 1.63e-27
relative error = 7.3166503859225599708238915064817e-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] = 8.74
y[1] (closed_form) = 223.54254133333333333333333333333
y[1] (numeric) = 223.54254133333333333333333333497
absolute error = 1.64e-27
relative error = 7.3364111824895539942744738472033e-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] = 8.75
y[1] (closed_form) = 224.30729166666666666666666666667
y[1] (numeric) = 224.30729166666666666666666666831
absolute error = 1.64e-27
relative error = 7.3113985185873174356235632851138e-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] = 8.76
y[1] (closed_form) = 225.073792
y[1] (numeric) = 225.07379200000000000000000000165
absolute error = 1.65e-27
relative error = 7.3309290492604309967817132614001e-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] = 8.77
y[1] (closed_form) = 225.84204433333333333333333333333
y[1] (numeric) = 225.84204433333333333333333333499
absolute error = 1.66e-27
relative error = 7.3502699858220819358417278939115e-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] = 8.78
y[1] (closed_form) = 226.61205066666666666666666666667
y[1] (numeric) = 226.61205066666666666666666666833
absolute error = 1.66e-27
relative error = 7.3252944630105519895917509253023e-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] = 8.79
y[1] (closed_form) = 227.383813
y[1] (numeric) = 227.38381300000000000000000000167
absolute error = 1.67e-27
relative error = 7.3444102197371454932897971941389e-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] = 8.8
y[1] (closed_form) = 228.15733333333333333333333333333
y[1] (numeric) = 228.15733333333333333333333333501
absolute error = 1.68e-27
relative error = 7.3633399174838415596255215699109e-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] = 8.81
y[1] (closed_form) = 228.93261366666666666666666666667
y[1] (numeric) = 228.93261366666666666666666666835
absolute error = 1.68e-27
relative error = 7.3384039656583603034360732651166e-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] = 8.82
y[1] (closed_form) = 229.709656
y[1] (numeric) = 229.70965600000000000000000000169
absolute error = 1.69e-27
relative error = 7.3571134510775637572675656264097e-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] = 8.83
y[1] (closed_form) = 230.48846233333333333333333333333
y[1] (numeric) = 230.48846233333333333333333333503
absolute error = 1.70e-27
relative error = 7.3756403370050394149374826190686e-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] = 8.84
y[1] (closed_form) = 231.26903466666666666666666666667
y[1] (numeric) = 231.26903466666666666666666666837
absolute error = 1.70e-27
relative error = 7.3507462961924356427460275759874e-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] = 8.85
y[1] (closed_form) = 232.051375
y[1] (numeric) = 232.05137500000000000000000000171
absolute error = 1.71e-27
relative error = 7.3690578217862316049624786752503e-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] = 8.86
y[1] (closed_form) = 232.83548533333333333333333333333
y[1] (numeric) = 232.83548533333333333333333333505
absolute error = 1.72e-27
relative error = 7.3871901335726523335097134735718e-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] = 8.87
y[1] (closed_form) = 233.62136766666666666666666666667
y[1] (numeric) = 233.62136766666666666666666666839
absolute error = 1.72e-27
relative error = 7.3623402567102227519847738585064e-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] = 8.88
y[1] (closed_form) = 234.409024
y[1] (numeric) = 234.40902400000000000000000000173
absolute error = 1.73e-27
relative error = 7.3802619475946455030673221863677e-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] = 8.89
y[1] (closed_form) = 235.19845633333333333333333333333
y[1] (numeric) = 235.19845633333333333333333333507
absolute error = 1.74e-27
relative error = 7.3980077383416046768300147389432e-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] = 8.9
y[1] (closed_form) = 235.98966666666666666666666666667
y[1] (numeric) = 235.98966666666666666666666666841
absolute error = 1.74e-27
relative error = 7.3732041939689449679293867386848e-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] = 8.91
y[1] (closed_form) = 236.782657
y[1] (numeric) = 236.78265700000000000000000000175
absolute error = 1.75e-27
relative error = 7.3907439935518588255388991601695e-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] = 8.92
y[1] (closed_form) = 237.57742933333333333333333333333
y[1] (numeric) = 237.57742933333333333333333333509
absolute error = 1.76e-27
relative error = 7.4081111363934728883785323894293e-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] = 8.93
y[1] (closed_form) = 238.37398566666666666666666666667
y[1] (numeric) = 238.37398566666666666666666666843
absolute error = 1.76e-27
relative error = 7.3833560112600486129388976375675e-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] = 8.94
y[1] (closed_form) = 239.172328
y[1] (numeric) = 239.17232800000000000000000000177
absolute error = 1.77e-27
relative error = 7.4005216857696012391533856709377e-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] = 8.95
y[1] (closed_form) = 239.97245833333333333333333333333
y[1] (numeric) = 239.97245833333333333333333333511
absolute error = 1.78e-27
relative error = 7.4175178783537485812173931765435e-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] = 8.96
y[1] (closed_form) = 240.77437866666666666666666666667
y[1] (numeric) = 240.77437866666666666666666666845
absolute error = 1.78e-27
relative error = 7.3928131799449934828060110759071e-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] = 8.97
y[1] (closed_form) = 241.578091
y[1] (numeric) = 241.57809100000000000000000000179
absolute error = 1.79e-27
relative error = 7.4096123228327025731816052805881e-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] = 8.98
y[1] (closed_form) = 242.38359733333333333333333333333
y[1] (numeric) = 242.38359733333333333333333333513
absolute error = 1.80e-27
relative error = 7.4262450916783158781184412159728e-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] = 8.99
y[1] (closed_form) = 243.19089966666666666666666666667
y[1] (numeric) = 243.19089966666666666666666666847
absolute error = 1.80e-27
relative error = 7.4015927506629466133573071105282e-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] = 9
y[1] (closed_form) = 244
y[1] (numeric) = 244.00000000000000000000000000181
absolute error = 1.81e-27
relative error = 7.4180327868852459016393442622951e-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] = 9.01
y[1] (closed_form) = 244.81090033333333333333333333333
y[1] (numeric) = 244.81090033333333333333333333515
absolute error = 1.82e-27
relative error = 7.4343094916194370272191896858363e-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] = 9.02
y[1] (closed_form) = 245.62360266666666666666666666667
y[1] (numeric) = 245.62360266666666666666666666849
absolute error = 1.82e-27
relative error = 7.4097113642205785413608079857601e-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] = 9.03
y[1] (closed_form) = 246.438109
y[1] (numeric) = 246.43810900000000000000000000183
absolute error = 1.83e-27
relative error = 7.4257995544025214054860321948015e-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] = 9.04
y[1] (closed_form) = 247.25442133333333333333333333333
y[1] (numeric) = 247.25442133333333333333333333517
absolute error = 1.84e-27
relative error = 7.4417273918811918946689708267894e-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] = 9.05
y[1] (closed_form) = 248.07254166666666666666666666667
y[1] (numeric) = 248.07254166666666666666666666851
absolute error = 1.84e-27
relative error = 7.4171852621738164290317633904463e-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] = 9.06
y[1] (closed_form) = 248.892472
y[1] (numeric) = 248.89247200000000000000000000185
absolute error = 1.85e-27
relative error = 7.4329287066585123554881965252850e-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] = 9.07
y[1] (closed_form) = 249.71421433333333333333333333333
y[1] (numeric) = 249.71421433333333333333333333519
absolute error = 1.86e-27
relative error = 7.4485147149739812635388852106769e-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] = 9.08
y[1] (closed_form) = 250.53777066666666666666666666667
y[1] (numeric) = 250.53777066666666666666666666853
absolute error = 1.86e-27
relative error = 7.4240302971110761806198557590208e-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] = 9.09
y[1] (closed_form) = 251.363143
y[1] (numeric) = 251.36314300000000000000000000187
absolute error = 1.87e-27
relative error = 7.4394359398983167552133926014762e-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] = 9.1
y[1] (closed_form) = 252.19033333333333333333333333333
y[1] (numeric) = 252.19033333333333333333333333521
absolute error = 1.88e-27
relative error = 7.4546870022773804441354479619230e-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] = 9.11
y[1] (closed_form) = 253.01934366666666666666666666667
y[1] (numeric) = 253.01934366666666666666666666855
absolute error = 1.88e-27
relative error = 7.4302619426471755490852582784938e-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] = 9.12
y[1] (closed_form) = 253.850176
y[1] (numeric) = 253.85017600000000000000000000189
absolute error = 1.89e-27
relative error = 7.4453365752245923201565950460479e-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] = 9.13
y[1] (closed_form) = 254.68283233333333333333333333333
y[1] (numeric) = 254.68283233333333333333333333523
absolute error = 1.90e-27
relative error = 7.4602594238203180445494679115900e-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] = 9.14
y[1] (closed_form) = 255.51731466666666666666666666667
y[1] (numeric) = 255.51731466666666666666666666857
absolute error = 1.90e-27
relative error = 7.4358953031368217363753760175709e-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] = 9.15
y[1] (closed_form) = 256.353625
y[1] (numeric) = 256.35362500000000000000000000191
absolute error = 1.91e-27
relative error = 7.4506455682068080761487183963168e-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] = 9.16
y[1] (closed_form) = 257.19176533333333333333333333333
y[1] (numeric) = 257.19176533333333333333333333525
absolute error = 1.92e-27
relative error = 7.4652467877872544016754004524272e-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] = 9.17
y[1] (closed_form) = 258.03173766666666666666666666667
y[1] (numeric) = 258.03173766666666666666666666859
absolute error = 1.92e-27
relative error = 7.4409451231162696777973745201289e-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] = 9.18
y[1] (closed_form) = 258.873544
y[1] (numeric) = 258.87354400000000000000000000193
absolute error = 1.93e-27
relative error = 7.4553775182217924903133400143817e-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] = 9.19
y[1] (closed_form) = 259.71718633333333333333333333333
y[1] (numeric) = 259.71718633333333333333333333527
absolute error = 1.94e-27
relative error = 7.4696635497587446911596309852215e-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] = 9.2
y[1] (closed_form) = 260.56266666666666666666666666667
y[1] (numeric) = 260.56266666666666666666666666861
absolute error = 1.94e-27
relative error = 7.4454257964814606339102045829025e-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] = 9.21
y[1] (closed_form) = 261.409987
y[1] (numeric) = 261.40998700000000000000000000195
absolute error = 1.95e-27
relative error = 7.4595466775337852719452528032144e-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] = 9.22
y[1] (closed_form) = 262.25914933333333333333333333333
y[1] (numeric) = 262.25914933333333333333333333529
absolute error = 1.96e-27
relative error = 7.4735238216944926972538236759426e-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] = 9.23
y[1] (closed_form) = 263.11015566666666666666666666667
y[1] (numeric) = 263.11015566666666666666666666863
absolute error = 1.96e-27
relative error = 7.4493513754106744748267774642986e-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] = 9.24
y[1] (closed_form) = 263.963008
y[1] (numeric) = 263.96300800000000000000000000197
absolute error = 1.97e-27
relative error = 7.4631669601219273876436504315029e-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
memory used=427.7MB, alloc=40.3MB, time=5.36
x[1] = 9.25
y[1] (closed_form) = 264.81770833333333333333333333333
y[1] (numeric) = 264.81770833333333333333333333531
absolute error = 1.98e-27
relative error = 7.4768413806667322253908938932049e-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] = 9.26
y[1] (closed_form) = 265.67425866666666666666666666667
y[1] (numeric) = 265.67425866666666666666666666865
absolute error = 1.98e-27
relative error = 7.4527355790394627317400525577953e-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] = 9.27
y[1] (closed_form) = 266.532661
y[1] (numeric) = 266.53266100000000000000000000199
absolute error = 1.99e-27
relative error = 7.4662519502628610307537506632255e-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] = 9.28
y[1] (closed_form) = 267.39291733333333333333333333333
y[1] (numeric) = 267.39291733333333333333333333533
absolute error = 2.00e-27
relative error = 7.4796296773515137932748435600549e-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] = 9.29
y[1] (closed_form) = 268.25502966666666666666666666667
y[1] (numeric) = 268.25502966666666666666666666867
absolute error = 2.00e-27
relative error = 7.4555918018953727253444514166791e-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] = 9.3
y[1] (closed_form) = 269.119
y[1] (numeric) = 269.11900000000000000000000000201
absolute error = 2.01e-27
relative error = 7.4688149108758578918619644097964e-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] = 9.31
y[1] (closed_form) = 269.98483033333333333333333333333
y[1] (numeric) = 269.98483033333333333333333333535
absolute error = 2.02e-27
relative error = 7.4819018442852241682304592592228e-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] = 9.32
y[1] (closed_form) = 270.85252266666666666666666666667
y[1] (numeric) = 270.85252266666666666666666666869
absolute error = 2.02e-27
relative error = 7.4579331220997254929265516360312e-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] = 9.33
y[1] (closed_form) = 271.722079
y[1] (numeric) = 271.72207900000000000000000000203
absolute error = 2.03e-27
relative error = 7.4708687916376497325416091785460e-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] = 9.34
y[1] (closed_form) = 272.59350133333333333333333333333
y[1] (numeric) = 272.59350133333333333333333333537
absolute error = 2.04e-27
relative error = 7.4836707038934251726793428178866e-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] = 9.35
y[1] (closed_form) = 273.46679166666666666666666666667
y[1] (numeric) = 273.46679166666666666666666666871
absolute error = 2.04e-27
relative error = 7.4597723093434714726940489270253e-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] = 9.36
y[1] (closed_form) = 274.341952
y[1] (numeric) = 274.34195200000000000000000000205
absolute error = 2.05e-27
relative error = 7.4724262368738996214476158571621e-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] = 9.37
y[1] (closed_form) = 275.21898433333333333333333333333
y[1] (numeric) = 275.21898433333333333333333333539
absolute error = 2.06e-27
relative error = 7.4849487762988656137435809857464e-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] = 9.38
y[1] (closed_form) = 276.09789066666666666666666666667
y[1] (numeric) = 276.09789066666666666666666666873
absolute error = 2.06e-27
relative error = 7.4611218326439176273219192238377e-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] = 9.39
y[1] (closed_form) = 276.978673
y[1] (numeric) = 276.97867300000000000000000000207
absolute error = 2.07e-27
relative error = 7.4734995932340249171458771484547e-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] = 9.4
y[1] (closed_form) = 277.86133333333333333333333333333
y[1] (numeric) = 277.86133333333333333333333333541
absolute error = 2.08e-27
relative error = 7.4857482869152958789995969212462e-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] = 9.41
y[1] (closed_form) = 278.74587366666666666666666666667
y[1] (numeric) = 278.74587366666666666666666666875
absolute error = 2.08e-27
relative error = 7.4619938678888975744849919877019e-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] = 9.42
y[1] (closed_form) = 279.632296
y[1] (numeric) = 279.63229600000000000000000000209
absolute error = 2.09e-27
relative error = 7.4741009171558638562979148874850e-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] = 9.43
y[1] (closed_form) = 280.52060233333333333333333333333
y[1] (numeric) = 280.52060233333333333333333333543
absolute error = 2.10e-27
relative error = 7.4860811738334983635967215418084e-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] = 9.44
y[1] (closed_form) = 281.41079466666666666666666666667
y[1] (numeric) = 281.41079466666666666666666666877
absolute error = 2.10e-27
relative error = 7.4624003051747420293225804519718e-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] = 9.45
y[1] (closed_form) = 282.302875
y[1] (numeric) = 282.30287500000000000000000000211
absolute error = 2.11e-27
relative error = 7.4742419821264661225997078492382e-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] = 9.46
y[1] (closed_form) = 283.19684533333333333333333333333
y[1] (numeric) = 283.19684533333333333333333333545
absolute error = 2.12e-27
relative error = 7.4859590950057381524315849959045e-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] = 9.47
y[1] (closed_form) = 284.09270766666666666666666666667
y[1] (numeric) = 284.09270766666666666666666666879
absolute error = 2.12e-27
relative error = 7.4623527559442001540147476013530e-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] = 9.48
y[1] (closed_form) = 284.990464
y[1] (numeric) = 284.99046400000000000000000000213
absolute error = 2.13e-27
relative error = 7.4739342857450837372579596207121e-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] = 9.49
y[1] (closed_form) = 285.89011633333333333333333333333
y[1] (numeric) = 285.89011633333333333333333333547
absolute error = 2.14e-27
relative error = 7.4853934352346369852177319470328e-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] = 9.5
y[1] (closed_form) = 286.79166666666666666666666666667
y[1] (numeric) = 286.79166666666666666666666666881
absolute error = 2.14e-27
relative error = 7.4618625599302629667296237105912e-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] = 9.51
y[1] (closed_form) = 287.695117
y[1] (numeric) = 287.69511700000000000000000000215
absolute error = 2.15e-27
relative error = 7.4731890565942417437693250803419e-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] = 9.52
y[1] (closed_form) = 288.60046933333333333333333333333
y[1] (numeric) = 288.60046933333333333333333333549
absolute error = 2.16e-27
relative error = 7.4843953129722792042398711368232e-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] = 9.53
y[1] (closed_form) = 289.50772566666666666666666666667
y[1] (numeric) = 289.50772566666666666666666666883
absolute error = 2.16e-27
relative error = 7.4609407919116475115090682260514e-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] = 9.54
y[1] (closed_form) = 290.416888
y[1] (numeric) = 290.41688800000000000000000000217
absolute error = 2.17e-27
relative error = 7.4720172609245781877533237667639e-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] = 9.55
y[1] (closed_form) = 291.32795833333333333333333333333
y[1] (numeric) = 291.32795833333333333333333333551
absolute error = 2.18e-27
relative error = 7.4829755869351708577003208440202e-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] = 9.56
y[1] (closed_form) = 292.24093866666666666666666666667
y[1] (numeric) = 292.24093866666666666666666666885
absolute error = 2.18e-27
relative error = 7.4595982682855147686723371415030e-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] = 9.57
y[1] (closed_form) = 293.155831
y[1] (numeric) = 293.15583100000000000000000000219
absolute error = 2.19e-27
relative error = 7.4704296091589595569054193569836e-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] = 9.58
y[1] (closed_form) = 294.07263733333333333333333333333
y[1] (numeric) = 294.07263733333333333333333333553
absolute error = 2.20e-27
relative error = 7.4811448625404921499712193556098e-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] = 9.59
y[1] (closed_form) = 294.99135966666666666666666666667
y[1] (numeric) = 294.99135966666666666666666666887
absolute error = 2.20e-27
relative error = 7.4578455534628150391283946295109e-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] = 9.6
y[1] (closed_form) = 295.912
y[1] (numeric) = 295.91200000000000000000000000221
absolute error = 2.21e-27
relative error = 7.4684365622212008975641406904755e-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] = 9.61
y[1] (closed_form) = 296.83456033333333333333333333333
y[1] (numeric) = 296.83456033333333333333333333555
absolute error = 2.22e-27
relative error = 7.4789134981689087481716990229938e-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] = 9.62
y[1] (closed_form) = 297.75904266666666666666666666667
y[1] (numeric) = 297.75904266666666666666666666889
absolute error = 2.22e-27
relative error = 7.4556929660914815228539020647576e-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] = 9.63
y[1] (closed_form) = 298.685449
y[1] (numeric) = 298.68544900000000000000000000223
absolute error = 2.23e-27
relative error = 7.4660483376945490237122331325889e-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] = 9.64
y[1] (closed_form) = 299.61378133333333333333333333333
y[1] (numeric) = 299.61378133333333333333333333557
absolute error = 2.24e-27
relative error = 7.4762916112590388365580121779535e-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] = 9.65
y[1] (closed_form) = 300.54404166666666666666666666667
y[1] (numeric) = 300.54404166666666666666666666891
absolute error = 2.24e-27
relative error = 7.4531505851125257987008836891209e-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] = 9.66
y[1] (closed_form) = 301.476232
y[1] (numeric) = 301.47623200000000000000000000225
absolute error = 2.25e-27
relative error = 7.4632749158149223518224149756522e-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] = 9.67
y[1] (closed_form) = 302.41035433333333333333333333333
y[1] (numeric) = 302.41035433333333333333333333559
absolute error = 2.26e-27
relative error = 7.4732890842385100299415122649962e-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] = 9.68
y[1] (closed_form) = 303.34641066666666666666666666667
y[1] (numeric) = 303.34641066666666666666666666893
absolute error = 2.26e-27
relative error = 7.4502282556539276759444146689271e-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] = 9.69
y[1] (closed_form) = 304.284403
y[1] (numeric) = 304.28440300000000000000000000227
absolute error = 2.27e-27
relative error = 7.4601260453037417103498400475032e-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] = 9.7
y[1] (closed_form) = 305.22433333333333333333333333333
y[1] (numeric) = 305.22433333333333333333333333561
absolute error = 2.28e-27
relative error = 7.4699155702963830974594642410556e-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] = 9.71
y[1] (closed_form) = 306.16620366666666666666666666667
y[1] (numeric) = 306.16620366666666666666666666895
absolute error = 2.28e-27
relative error = 7.4469355947670562127828846547923e-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] = 9.72
y[1] (closed_form) = 307.110016
y[1] (numeric) = 307.11001600000000000000000000229
absolute error = 2.29e-27
relative error = 7.4566112490450327741834378986845e-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] = 9.73
y[1] (closed_form) = 308.05577233333333333333333333333
y[1] (numeric) = 308.05577233333333333333333333563
absolute error = 2.30e-27
relative error = 7.4661804990015676998886988339581e-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] = 9.74
y[1] (closed_form) = 309.00347466666666666666666666667
y[1] (numeric) = 309.00347466666666666666666666897
absolute error = 2.30e-27
relative error = 7.4432819970102083771174508389346e-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] = 9.75
y[1] (closed_form) = 309.953125
y[1] (numeric) = 309.95312500000000000000000000231
absolute error = 2.31e-27
relative error = 7.4527398296113323587235973181429e-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] = 9.76
y[1] (closed_form) = 310.90472533333333333333333333333
y[1] (numeric) = 310.90472533333333333333333333565
absolute error = 2.32e-27
relative error = 7.4620930817717088069646751032120e-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] = 9.77
y[1] (closed_form) = 311.85827766666666666666666666667
y[1] (numeric) = 311.85827766666666666666666666899
absolute error = 2.32e-27
relative error = 7.4392766398837066622975310410043e-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] = 9.78
y[1] (closed_form) = 312.813784
y[1] (numeric) = 312.81378400000000000000000000233
absolute error = 2.33e-27
relative error = 7.4485208746427874802345666455670e-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] = 9.79
y[1] (closed_form) = 313.77124633333333333333333333333
y[1] (numeric) = 313.77124633333333333333333333567
absolute error = 2.34e-27
relative error = 7.4576623171968809434321875971260e-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] = 9.8
y[1] (closed_form) = 314.73066666666666666666666666667
y[1] (numeric) = 314.73066666666666666666666666901
absolute error = 2.34e-27
relative error = 7.4349284891208567748932420524638e-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] = 9.81
y[1] (closed_form) = 315.692047
y[1] (numeric) = 315.69204700000000000000000000235
absolute error = 2.35e-27
relative error = 7.4439632620836976612210949995836e-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] = 9.82
y[1] (closed_form) = 316.65538933333333333333333333333
y[1] (numeric) = 316.65538933333333333333333333569
absolute error = 2.36e-27
relative error = 7.4528969962222907289894138629999e-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] = 9.83
y[1] (closed_form) = 317.62069566666666666666666666667
y[1] (numeric) = 317.62069566666666666666666666903
absolute error = 2.36e-27
relative error = 7.4302463038389311002149254365285e-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] = 9.84
y[1] (closed_form) = 318.587968
y[1] (numeric) = 318.58796800000000000000000000237
absolute error = 2.37e-27
relative error = 7.4390756652806172516847842791100e-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] = 9.85
y[1] (closed_form) = 319.55720833333333333333333333333
y[1] (numeric) = 319.55720833333333333333333333571
absolute error = 2.38e-27
relative error = 7.4478057071940561503528384914908e-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] = 9.86
y[1] (closed_form) = 320.52841866666666666666666666667
y[1] (numeric) = 320.52841866666666666666666666905
absolute error = 2.38e-27
relative error = 7.4252386415542128487044938634125e-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] = 9.87
y[1] (closed_form) = 321.501601
y[1] (numeric) = 321.50160100000000000000000000239
absolute error = 2.39e-27
relative error = 7.4338665579460053761909571330564e-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] = 9.88
y[1] (closed_form) = 322.47675733333333333333333333333
y[1] (numeric) = 322.47675733333333333333333333573
absolute error = 2.40e-27
relative error = 7.4423968407720034627984020743978e-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] = 9.89
y[1] (closed_form) = 323.45388966666666666666666666667
y[1] (numeric) = 323.45388966666666666666666666907
absolute error = 2.40e-27
relative error = 7.4199138630650094238213360424895e-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] = 9.9
y[1] (closed_form) = 324.433
y[1] (numeric) = 324.43300000000000000000000000241
absolute error = 2.41e-27
relative error = 7.4283442189912863364700878147414e-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] = 9.91
y[1] (closed_form) = 325.41409033333333333333333333333
y[1] (numeric) = 325.41409033333333333333333333575
absolute error = 2.42e-27
relative error = 7.4366785947132993998371947161875e-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] = 9.92
y[1] (closed_form) = 326.39716266666666666666666666667
y[1] (numeric) = 326.39716266666666666666666666909
absolute error = 2.42e-27
relative error = 7.4142801372064214675853064605071e-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] = 9.93
y[1] (closed_form) = 327.382219
y[1] (numeric) = 327.38221900000000000000000000243
absolute error = 2.43e-27
relative error = 7.4225167372330627400384258498779e-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] = 9.94
y[1] (closed_form) = 328.36926133333333333333333333333
y[1] (numeric) = 328.36926133333333333333333333577
absolute error = 2.44e-27
relative error = 7.4306589785306173156784232658140e-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] = 9.95
y[1] (closed_form) = 329.35829166666666666666666666667
y[1] (numeric) = 329.35829166666666666666666666911
absolute error = 2.44e-27
relative error = 7.4083454454805360777947116608951e-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] = 9.96
y[1] (closed_form) = 330.349312
y[1] (numeric) = 330.34931200000000000000000000245
absolute error = 2.45e-27
relative error = 7.4163920159761071335302190670220e-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] = 9.97
y[1] (closed_form) = 331.34232433333333333333333333333
y[1] (numeric) = 331.34232433333333333333333333579
absolute error = 2.46e-27
relative error = 7.4243458180284208444713904156805e-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] = 9.98
y[1] (closed_form) = 332.33733066666666666666666666667
y[1] (numeric) = 332.33733066666666666666666666913
absolute error = 2.46e-27
relative error = 7.4021175865655987014447063942636e-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] = 9.99
y[1] (closed_form) = 333.334333
y[1] (numeric) = 333.33433300000000000000000000247
absolute error = 2.47e-27
relative error = 7.4099777774766453475406027257324e-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
Finished!
diff ( y , x , 1 ) = x * x ;
Iterations = 1980
Total Elapsed Time = 5 Seconds
Elapsed Time(since restart) = 5 Seconds
Time to Timeout = 2 Minutes 54 Seconds
Percent Done = 100.1 %
> quit
memory used=462.6MB, alloc=40.3MB, time=5.78