|\^/| Maple 2019 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
\ 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
> 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 7
# Begin Function number 8
> 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 8
# Begin Function number 9
> 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 9
# Begin Function number 10
> 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 10
# Begin Function number 11
> 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 11
# Begin Function number 12
> 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 12
# Begin Function number 13
> 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 13
# Begin Function number 14
> 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 14
# Begin Function number 15
> 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 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> 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 17
# Begin Function number 18
> 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 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> 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 21
# Begin Function number 22
> 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 22
# Begin Function number 23
> 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 23
# Begin Function number 24
> 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 24
# Begin Function number 25
> 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 25
# Begin Function number 26
> 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 26
# Begin Function number 27
> 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 27
# Begin Function number 28
> 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 28
# Begin Function number 29
> 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> 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 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(10.0)* ln(c(0.2)* c(x) + c(0.3)));
> end;
exact_soln_y := proc(x) return c(10.0)*ln(c(0.2)*c(x) + c(0.3)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else
omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else
omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_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/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := round(-log10(relerr));
> 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)*22*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 * c(100.0),20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_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/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := round(-log10(relerr))
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)*22*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*c(100.0), 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_2D0[1] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre 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_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 3
> #emit pre div CONST - LINEAR $eq_no = 1 i = 4
> #emit pre div CONST - LINEAR $eq_no = 1 i = 5
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[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_tmp4[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
> array_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[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_tmp4[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
> array_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[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_tmp4[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
> array_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[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_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit div CONST LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp3[kkk] := array_const_2D0[1] * array_tmp2[kkk];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[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_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_0D2[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
array_tmp3[1] := array_const_2D0[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D2[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[1];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[1];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[1];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := array_const_2D0[1]*array_tmp2[kkk];
array_tmp4[kkk] := array_tmp3[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_tmp4[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_const_0D3);
> array_const_0D3[1] := c(0.3);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############R:\Temp/div_c_lin_backpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(3.1);");
> omniout_str(ALWAYS,"x_end := c(2.5);");
> 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,"glob_display_interval := c(0.1);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=12;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=2;");
> omniout_str(ALWAYS,"glob_max_iter:=1000000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"glob_h_reason:=1;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(10.0)* ln(c(0.2)* c(x) + c(0.3)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(3.1);
> x_end := c(2.5);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_display_interval := c(0.1);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-1.5);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(1.0);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=12;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=2;
> glob_max_iter:=1000000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> glob_h_reason:=1;
> #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 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2020-05-26T00:32:57-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_c_lin_back")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 310 | ")
> ;
> logitem_str(html_log_file,"div_c_lin_back diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_c_lin_back maple results")
> ;
> logitem_str(html_log_file,"Missing Real Singularity")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_const_0D3);
array_const_0D3[1] := c(0.3);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############R:Temp/div_c_lin_backpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 / ( 0.2 \
* x + 0.3 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(3.1);");
omniout_str(ALWAYS, "x_end := c(2.5);");
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, "glob_display_interval := c(0.1);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=12;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=2;");
omniout_str(ALWAYS, "glob_max_iter:=1000000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "glob_h_reason:=1;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(10.0)* ln(c(0.2)* c(x) + c(0.3)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(3.1);
x_end := c(2.5);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_display_interval := c(0.1);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-1.5);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(1.0);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 12;
glob_max_minutes := 3.0;
glob_subiter_method := 2;
glob_max_iter := 1000000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_h_reason := 1;
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 ) = 2.0 / ( 0.2\
* x + 0.3 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2020-05-26T00:32:57-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_c_lin_back");
logitem_str(html_log_file, "diff ( y , x , 1 ) = 2\
.0 / ( 0.2 * x + 0.3 ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 310 | ");
logitem_str(html_log_file, "div_c_lin_back diffeq.mxt");
logitem_str(html_log_file, "div_c_lin_back maple results");
logitem_str(html_log_file, "Missing Real Singularity");
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#################
##############R:Temp/div_c_lin_backpostode.ode#################
diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(3.1);
x_end := c(2.5);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_display_interval := c(0.1);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-1.5);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(1.0);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=12;
glob_max_minutes:=(3.0);
glob_subiter_method:=2;
glob_max_iter:=1000000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
glob_h_reason:=1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(10.0)* ln(c(0.2)* c(x) + c(0.3)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 3.099
y[1] (closed_form) = -0.83599023876313609666781622552507
y[1] (numeric) = -0.8359902387631360966676402781906
absolute error = 1.7594733447e-22
relative error = 2.1046577616781449676824066436226e-20 %
Desired digits = 12
Estimated correct digits = 14
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.599
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.098
y[1] (closed_form) = -0.83816486093110569104586988002992
y[1] (numeric) = -0.83816486093110569104551775568261
absolute error = 3.5212434731e-22
relative error = 4.2011346898846362771617381867514e-20 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.598
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.097
y[1] (closed_form) = -0.84033995610009434246951917331244
y[1] (numeric) = -0.84033995610009434246899064192405
absolute error = 5.2853138839e-22
relative error = 6.2894949187331717708351133588475e-20 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.597
Order of pole (given) = 1
NO 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=4.4MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = 3.096
y[1] (closed_form) = -0.84251552447591126431969680287931
y[1] (numeric) = -0.84251552447591126431899163407111
absolute error = 7.0516880820e-22
relative error = 8.3698019527729402058476050069840e-20 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.596
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.095
y[1] (closed_form) = -0.84469156626450002481356329997542
y[1] (numeric) = -0.84469156626450002481268126301762
absolute error = 8.8203695780e-22
relative error = 1.0442118674164741632541946240944e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.595
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.094
y[1] (closed_form) = -0.84686808167193866397465732113378
y[1] (numeric) = -0.84686808167193866397359818494488
absolute error = 1.05913618890e-21
relative error = 1.2506507351286503569836771908746e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.594
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.093
y[1] (closed_form) = -0.8490450709044398107303673210923
y[1] (numeric) = -0.84904507090443981072913085423849
absolute error = 1.23646685381e-21
relative error = 1.4563029645680194837713710899837e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.593
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.092
y[1] (closed_form) = -0.85122253416835080013689094965987
y[1] (numeric) = -0.85122253416835080013547692035443
absolute error = 1.41402930544e-21
relative error = 1.6611746619484346457560434973332e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.592
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.091
y[1] (closed_form) = -0.85340047167015379073184876871264
y[1] (numeric) = -0.85340047167015379073025694481531
absolute error = 1.59182389733e-21
relative error = 1.8652718743109071739486361198779e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.591
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -0.85557888361646588201471913954212
y[1] (numeric) = -0.85557888361646588201294928855849
absolute error = 1.76985098363e-21
relative error = 2.0686005902214142335406229030183e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.089
y[1] (closed_form) = -0.85775777021403923205526138525992
y[1] (numeric) = -0.85775777021403923205331327434079
absolute error = 1.94811091913e-21
relative error = 2.2711667405168258807965417616204e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.589
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.088
y[1] (closed_form) = -0.85993713166976117523009458789123
y[1] (numeric) = -0.85993713166976117522796798383203
absolute error = 2.12660405920e-21
relative error = 2.4729761989352876945199026711134e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.588
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.087
y[1] (closed_form) = -0.86211696819065434008759963516081
y[1] (numeric) = -0.86211696819065434008529430440097
absolute error = 2.30533075984e-21
relative error = 2.6740347828650829467279083067068e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.587
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.086
y[1] (closed_form) = -0.86429727998387676734131238779213
y[1] (numeric) = -0.86429727998387676733882809641442
absolute error = 2.48429137771e-21
relative error = 2.8743482540594641066581781556777e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.586
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.085
y[1] (closed_form) = -0.86647806725672202799197609440387
y[1] (numeric) = -0.86647806725672202798931260813382
absolute error = 2.66348627005e-21
relative error = 3.0739223192141762871898962443123e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.585
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.084
y[1] (closed_form) = -0.86865933021661934157842143779858
y[1] (numeric) = -0.86865933021661934157557852200384
absolute error = 2.84291579474e-21
relative error = 3.2727626306978782047914723793482e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.584
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.083
y[1] (closed_form) = -0.87084106907113369455744285359683
y[1] (numeric) = -0.87084106907113369455442027328656
absolute error = 3.02258031027e-21
relative error = 3.4708747871686605688120285779398e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.583
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.082
y[1] (closed_form) = -0.87302328402796595881284001977781
y[1] (numeric) = -0.87302328402796595880963753960203
absolute error = 3.20248017578e-21
relative error = 3.6682643342619181170813093490489e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.582
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.081
y[1] (closed_form) = -0.8752059752949530102937936737447
y[1] (numeric) = -0.87520597529495301029041105799368
absolute error = 3.38261575102e-21
relative error = 3.8649367651769347969955368826408e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.581
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -0.87738914308006784778274517204131
y[1] (numeric) = -0.87738914308006784777918218464493
absolute error = 3.56298739638e-21
relative error = 4.0608975213349006250473172449708e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.079
y[1] (closed_form) = -0.87957278759141971179294946680611
y[1] (numeric) = -0.87957278759141971178920587133324
absolute error = 3.74359547287e-21
relative error = 4.2561519929706827264203335760954e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.579
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.078
y[1] (closed_form) = -0.88175690903725420359587143246197
y[1] (numeric) = -0.88175690903725420359194699211983
absolute error = 3.92444034214e-21
relative error = 4.4507055197615610749033938316348e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.578
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.077
y[1] (closed_form) = -0.88394150762595340437859573600547
y[1] (numeric) = -0.88394150762595340437449021363901
absolute error = 4.10552236646e-21
relative error = 4.6445633914017794090303533530851e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.577
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.076
y[1] (closed_form) = -0.8861265835660359945314207045795
y[1] (numeric) = -0.88612658356603599452713386267075
absolute error = 4.28684190875e-21
relative error = 4.8377308482254055209281528957115e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.576
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.075
y[1] (closed_form) = -0.88831213706615737306580690478765
y[1] (numeric) = -0.8883121370661573730613385054551
absolute error = 4.46839933255e-21
relative error = 5.0302130817528324692359523791959e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.575
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.074
y[1] (closed_form) = -0.8904981683351097771628514094402
y[1] (numeric) = -0.89049816833510977715820121443816
absolute error = 4.65019500204e-21
relative error = 5.2220152352857525902988453728108e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.574
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.073
y[1] (closed_form) = -0.89268467758182240185245898910917
y[1] (numeric) = -0.89268467758182240184762675982712
absolute error = 4.83222928205e-21
relative error = 5.4131424044825544649228532647661e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.573
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.072
y[1] (closed_form) = -0.89487166501536151982338172801583
y[1] (numeric) = -0.89487166501536151981836722547781
absolute error = 5.01450253802e-21
relative error = 5.6035996378697723020211717401050e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.572
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.071
y[1] (closed_form) = -0.89705913084493060136429882637875
y[1] (numeric) = -0.89705913084493060135910181124269
absolute error = 5.19701513606e-21
relative error = 5.7933919374578862670341785169024e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.571
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -0.89924707527987043443610861441433
y[1] (numeric) = -0.89924707527987043443072884697141
absolute error = 5.37976744292e-21
relative error = 5.9825242592484032672995800385260e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.069
y[1] (closed_form) = -0.90143549852965924487560506670685
y[1] (numeric) = -0.90143549852965924487004230688089
absolute error = 5.56275982596e-21
relative error = 6.1710015137339000134533050190816e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.569
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.068
y[1] (closed_form) = -0.90362440080391281673071136965121
y[1] (numeric) = -0.90362440080391281672496537699801
absolute error = 5.74599265320e-21
relative error = 6.3588285664796747586869202810264e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.568
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.067
y[1] (closed_form) = -0.90581378231238461272744335911993
y[1] (numeric) = -0.90581378231238461272151389282659
absolute error = 5.92946629334e-21
relative error = 6.5460102386641839886302478554779e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.567
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.066
y[1] (closed_form) = -0.90800364326496589486877591041808
y[1] (numeric) = -0.90800364326496589486266272930241
absolute error = 6.11318111567e-21
relative error = 6.7325513074908483798459166210789e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.566
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.065
y[1] (closed_form) = -0.91019398387168584516558562796593
y[1] (numeric) = -0.91019398387168584515928849047576
absolute error = 6.29713749017e-21
relative error = 6.9184565068029892619341684787330e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.565
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.064
y[1] (closed_form) = -0.91238480434271168649984344798998
y[1] (numeric) = -0.91238480434271168649336211220254
absolute error = 6.48133578744e-21
relative error = 7.1037305275039067074145544408432e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.564
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.063
y[1] (closed_form) = -0.91457610488834880362023103381066
y[1] (numeric) = -0.91457610488834880361356525743192
absolute error = 6.66577637874e-21
relative error = 7.2883780180915136913487663513986e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.563
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.062
y[1] (closed_form) = -0.91676788571904086427035511008887
y[1] (numeric) = -0.91676788571904086426350465045287
absolute error = 6.85045963600e-21
relative error = 7.4724035851528944733429036859141e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.562
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.061
y[1] (closed_form) = -0.91896014704536994044973414963563
y[1] (numeric) = -0.91896014704536994044269876370385
absolute error = 7.03538593178e-21
relative error = 7.6558117937976871534789490222081e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.561
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -0.92115288907805662980773209410007
y[1] (numeric) = -0.92115288907805662980051153846079
absolute error = 7.22055563928e-21
relative error = 7.8386071681398642848616972753768e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.059
y[1] (closed_form) = -0.92334611202796017717061405803145
y[1] (numeric) = -0.92334611202796017716320808889905
absolute error = 7.40596913240e-21
relative error = 8.0207941918271023957563185341217e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.559
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.058
y[1] (closed_form) = -0.92553981610607859620189923446199
y[1] (numeric) = -0.92553981610607859619430760767633
absolute error = 7.59162678566e-21
relative error = 8.2023773084116603035534652629503e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.558
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.057
y[1] (closed_form) = -0.92773400152354879119618648928038
y[1] (numeric) = -0.92773400152354879118840896030613
absolute error = 7.77752897425e-21
relative error = 8.3833609218564163880425953870137e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.557
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.056
y[1] (closed_form) = -0.92992866849164667900662840126078
y[1] (numeric) = -0.92992866849164667899866472518676
absolute error = 7.96367607402e-21
relative error = 8.5637493969695114820730777258784e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.556
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.055
y[1] (closed_form) = -0.93212381722178731110622977468109
y[1] (numeric) = -0.93212381722178731109807970621961
absolute error = 8.15006846148e-21
relative error = 8.7435470598438664378280205974291e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.555
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.054
y[1] (closed_form) = -0.93431944792552499578314692200727
y[1] (numeric) = -0.93431944792552499577481021549347
absolute error = 8.33670651380e-21
relative error = 8.9227581982907867871371406138379e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.554
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.053
y[1] (closed_form) = -0.93651556081455342047016428513893
y[1] (numeric) = -0.93651556081455342046164069453012
absolute error = 8.52359060881e-21
relative error = 9.1013870622677470915773214798020e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.553
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.052
y[1] (closed_form) = -0.93871215610070577420852523520612
y[1] (numeric) = -0.93871215610070577419981451408111
absolute error = 8.71072112501e-21
relative error = 9.2794378643110988174469180449843e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.552
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.051
y[1] (closed_form) = -0.940909233995954870246294162879
y[1] (numeric) = -0.94090923399595487023739606443744
absolute error = 8.89809844156e-21
relative error = 9.4569147799417328785133410570557e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.551
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -0.9431067947124132687714272436023
y[1] (numeric) = -0.94310679471241326876234152066401
absolute error = 9.08572293829e-21
relative error = 9.6338219480865466177542394699827e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.049
y[1] (closed_form) = -0.94530483846233339977972953509536
y[1] (numeric) = -0.94530483846233339977045594009966
absolute error = 9.27359499570e-21
relative error = 9.8101634714837181123514135967315e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.549
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.048
y[1] (closed_form) = -0.94750336545810768607787633786774
y[1] (numeric) = -0.94750336545810768606841462287277
absolute error = 9.46171499497e-21
relative error = 9.9859434170931546695782482676478e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.548
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.047
y[1] (closed_form) = -0.94970237591226866642167702339057
y[1] (numeric) = -0.94970237591226866641202694007265
absolute error = 9.65008331792e-21
relative error = 1.0161165816448849895040724409433e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.547
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.046
y[1] (closed_form) = -0.95190187003748911878975980893582
y[1] (numeric) = -0.95190187003748911877992110858876
absolute error = 9.83870034706e-21
relative error = 1.0335834666101158795298108035962e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.546
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.045
y[1] (closed_form) = -0.95410184804658218379285623295052
y[1] (numeric) = -0.95410184804658218378282866648493
absolute error = 1.002756646559e-20
relative error = 1.0509953928000801225228750812923e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.545
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.044
y[1] (closed_form) = -0.95630231015250148821886436017187
y[1] (numeric) = -0.95630231015250148820864767811451
absolute error = 1.021668205736e-20
relative error = 1.0683527529835984765395792581674e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.544
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.043
y[1] (closed_form) = -0.95850325656834126871387002151274
y[1] (numeric) = -0.95850325656834126870346397400583
absolute error = 1.040604750691e-20
relative error = 1.0856559365448591941323045019981e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.543
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.042
y[1] (closed_form) = -0.96070468750733649559930567005636
y[1] (numeric) = -0.96070468750733649558871000685692
absolute error = 1.059566319944e-20
relative error = 1.1029053295172024857051051643116e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.542
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.041
y[1] (closed_form) = -0.96290660318286299682542671129518
y[1] (numeric) = -0.96290660318286299681464118177432
absolute error = 1.078552952086e-20
relative error = 1.1201013146247735481149398128304e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.541
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -0.96510900380843758206128544303242
y[1] (numeric) = -0.9651090038084375820503097961747
absolute error = 1.097564685772e-20
relative error = 1.1372442713111950848604082051670e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.039
y[1] (closed_form) = -0.96731188959771816692138301813779
y[1] (numeric) = -0.96731188959771816691021700254049
absolute error = 1.116601559730e-20
relative error = 1.1543345757844120257144580151279e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.539
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.038
y[1] (closed_form) = -0.96951526076450389732918012161012
y[1] (numeric) = -0.96951526076450389731782348548261
absolute error = 1.135663612751e-20
relative error = 1.1713726010413503767638157686761e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.538
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.037
y[1] (closed_form) = -0.97171911752273527401764733215322
y[1] (numeric) = -0.97171911752273527400609982331623
absolute error = 1.154750883699e-20
relative error = 1.1883587169128452790162653843922e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.537
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.036
y[1] (closed_form) = -0.97392346008649427716703641771468
y[1] (numeric) = -0.97392346008649427715529778359964
absolute error = 1.173863411504e-20
relative error = 1.2052932900905262391968058710886e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.536
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.035
y[1] (closed_form) = -0.97612828867000449118005409417478
y[1] (numeric) = -0.97612828867000449116812408182312
absolute error = 1.193001235166e-20
relative error = 1.2221766841646291195221995152157e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.535
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.034
y[1] (closed_form) = -0.97833360348763122959462005660251
y[1] (numeric) = -0.97833360348763122958249841266499
absolute error = 1.212164393752e-20
relative error = 1.2390092596541635821086279721527e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.534
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.033
y[1] (closed_form) = -0.98053940475388166013439137322086
y[1] (numeric) = -0.98053940475388166012207784395686
absolute error = 1.231352926400e-20
relative error = 1.2557913740438338510191948353284e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.533
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.032
y[1] (closed_form) = -0.98274569268340492989723561344357
y[1] (numeric) = -0.98274569268340492988472994472041
absolute error = 1.250566872316e-20
relative error = 1.2725233818133605692358986518227e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.532
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.031
y[1] (closed_form) = -0.98495246749099229068183536306253
y[1] (numeric) = -0.98495246749099229066913730035478
absolute error = 1.269806270775e-20
relative error = 1.2892056344704906174638830388009e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.531
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -0.98715972939157722445260706187914
y[1] (numeric) = -0.98715972939157722443971635026791
absolute error = 1.289071161123e-20
relative error = 1.3058384805845978672305356492186e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.029
y[1] (closed_form) = -0.9893674786002355689431173817856
y[1] (numeric) = -0.98936747860023556893003376595787
absolute error = 1.308361582773e-20
relative error = 1.3224222658137900899307843411731e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.529
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.028
y[1] (closed_form) = -0.99157571533218564339818064651434
y[1] (numeric) = -0.99157571533218564338490387076223
absolute error = 1.327677575211e-20
relative error = 1.3389573329417588619281885644139e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.528
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.027
y[1] (closed_form) = -0.99378443980278837445482107798619
y[1] (numeric) = -0.9937844398027883744413508862063
absolute error = 1.347019177989e-20
relative error = 1.3554440219010767756583172613242e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.527
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.026
y[1] (closed_form) = -0.99599365222754742216228393840204
y[1] (numeric) = -0.99599365222754742214862007409472
absolute error = 1.366386430732e-20
relative error = 1.3718826698102606330422309168702e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.526
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.025
y[1] (closed_form) = -0.99820335282210930614127992193896
y[1] (numeric) = -0.99820335282210930612742212820763
absolute error = 1.385779373133e-20
relative error = 1.3882736109983402910150769648087e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.525
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.024
y[1] (closed_form) = -1.0004135418022635318826474351317
y[1] (numeric) = -1.0004135418022635318685954546821
absolute error = 1.40519804496e-20
relative error = 1.4046171770411161024098536415577e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.524
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.023
y[1] (closed_form) = -1.0026242193839427171856176907447
y[1] (numeric) = -1.0026242193839427171713712658843
absolute error = 1.42464248604e-20
relative error = 1.4209136967740159230826673979912e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.523
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.022
y[1] (closed_form) = -1.0048353857832227187358678261694
y[1] (numeric) = -1.0048353857832227187214266988066
absolute error = 1.44411273628e-20
relative error = 1.4371634963416230601068736770538e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.522
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.021
y[1] (closed_form) = -1.0070470412163227588235475441176
y[1] (numeric) = -1.0070470412163227588089114557609
absolute error = 1.46360883567e-20
relative error = 1.4533668992286961724720698828459e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.521
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = -1.0092591858996055522014650606254
y[1] (numeric) = -1.0092591858996055521866337523831
absolute error = 1.48313082423e-20
relative error = 1.4695242262353132282706452397158e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.019
y[1] (closed_form) = -1.0114718200495774330836184331345
y[1] (numeric) = -1.0114718200495774330685916457135
absolute error = 1.50267874210e-20
relative error = 1.4856357955937378371622090566225e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.519
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.018
y[1] (closed_form) = -1.013684943882888482284258629678
y[1] (numeric) = -1.0136849438828884822690361033834
absolute error = 1.52225262946e-20
relative error = 1.5017019229160678856342449196767e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.518
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.017
y[1] (closed_form) = -1.0158985576163326544976709889709
y[1] (numeric) = -1.0158985576163326544822524637053
absolute error = 1.54185252656e-20
relative error = 1.5177229212508644238122439450171e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.517
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.016
y[1] (closed_form) = -1.0181126614668479057188620104892
y[1] (numeric) = -1.0181126614668479057032472257517
absolute error = 1.56147847375e-20
relative error = 1.5336991011390592918187165502830e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.516
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.015
y[1] (closed_form) = -1.0203272556515163208053387034154
y[1] (numeric) = -1.0203272556515163207895273983012
absolute error = 1.58113051142e-20
relative error = 1.5496307705809448966884265805822e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.515
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.014
y[1] (closed_form) = -1.0225423403875642411801680136404
y[1] (numeric) = -1.02254234038756424116415992684
absolute error = 1.60080868004e-20
relative error = 1.5655182351014053003997937004556e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.514
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.013
y[1] (closed_form) = -1.0247579158923623926765041388342
y[1] (numeric) = -1.0247579158923623926602990086325
absolute error = 1.62051302017e-20
relative error = 1.5813617977850429215190018761990e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.513
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.012
y[1] (closed_form) = -1.026973982383426013523771832937
y[1] (numeric) = -1.0269739823834260135073693972128
absolute error = 1.64024357242e-20
relative error = 1.5971617592621802503400597959639e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.512
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.011
y[1] (closed_form) = -1.029190540078414982475694093281
y[1] (numeric) = -1.0291905400784149824590940895062
absolute error = 1.66000037748e-20
relative error = 1.6129184177630733280315463844467e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.511
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = -1.0314075891951339470803529159238
y[1] (numeric) = -1.0314075891951339470635550811627
absolute error = 1.67978347611e-20
relative error = 1.6286320691326604113327905439759e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.009
y[1] (closed_form) = -1.0336251299515324520924720976692
y[1] (numeric) = -1.0336251299515324520754761685778
absolute error = 1.69959290914e-20
relative error = 1.6443030068548114099733892429610e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.509
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.008
y[1] (closed_form) = -1.0358431625657050680281113566637
y[1] (numeric) = -1.0358431625657050680109170694888
absolute error = 1.71942871749e-20
relative error = 1.6599315220955895303491013393192e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.508
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.007
y[1] (closed_form) = -1.0380616872558915198619613373874
y[1] (numeric) = -1.038061687255891519844568427966
absolute error = 1.73929094214e-20
relative error = 1.6755179036978071006167871129284e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.507
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.006
y[1] (closed_form) = -1.0402807042404768158674293603164
y[1] (numeric) = -1.0402807042404768158498375640752
absolute error = 1.75917962412e-20
relative error = 1.6910624381948919523839219697793e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.506
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.005
y[1] (closed_form) = -1.0425002137379913765997060715091
y[1] (numeric) = -1.0425002137379913765819151234632
absolute error = 1.77909480459e-20
relative error = 1.7065654099109229092142126277418e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.505
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.004
y[1] (closed_form) = -1.0447202159671111640220034428701
y[1] (numeric) = -1.0447202159671111640040130776229
absolute error = 1.79903652472e-20
relative error = 1.7220271008679662296016213723237e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.504
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.003
y[1] (closed_form) = -1.0469407111466578107751548698749
y[1] (numeric) = -1.046940711146657810756964821617
absolute error = 1.81900482579e-20
relative error = 1.7374477909047417974080306187496e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.503
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.002
y[1] (closed_form) = -1.0491616994955987495907684100868
y[1] (numeric) = -1.0491616994955987495723784125954
absolute error = 1.83899974914e-20
relative error = 1.7528277576508259048258110642372e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.502
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.001
y[1] (closed_form) = -1.0513831812330473428481245028807
y[1] (numeric) = -1.0513831812330473428295342895187
absolute error = 1.85902133620e-20
relative error = 1.7681672765772855885951810213958e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.501
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = -1.0536051565782630122750098083931
y[1] (numeric) = -1.0536051565782630122562191121086
absolute error = 1.87906962845e-20
relative error = 1.7834666209802481447424014899207e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.999
y[1] (closed_form) = -1.0558276257506513687926791018576
y[1] (numeric) = -1.055827625750651368773687655183
absolute error = 1.89914466746e-20
relative error = 1.7987260620404621629844754693337e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.499
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.998
y[1] (closed_form) = -1.0580505889697643425051374581479
y[1] (numeric) = -1.0580505889697643424859449931992
absolute error = 1.91924649487e-20
relative error = 1.8139458688254138347292447554405e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.498
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.997
y[1] (closed_form) = -1.0602740464553003128329352605526
y[1] (numeric) = -1.0602740464553003128135415090286
absolute error = 1.93937515240e-20
relative error = 1.8291263083197249361049409697928e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.497
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.996
y[1] (closed_form) = -1.062497998427104238791668867534
y[1] (numeric) = -1.0624979984271042387720735607157
absolute error = 1.95953068183e-20
relative error = 1.8442676454269474032193142696135e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.496
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.995
y[1] (closed_form) = -1.0647224451051677894153800714882
y[1] (numeric) = -1.064722445105167789395582940238
absolute error = 1.97971312502e-20
relative error = 1.8593701430089173637687266474810e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.495
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.994
y[1] (closed_form) = -1.0669473867096294743250477843212
y[1] (numeric) = -1.066947386709629474305048559082
absolute error = 1.99992252392e-20
relative error = 1.8744340619152576863674059526370e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.494
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.993
y[1] (closed_form) = -1.0691728234607747744423656859905
y[1] (numeric) = -1.0691728234607747744221640967851
absolute error = 2.02015892054e-20
relative error = 1.8894596609751131421119591095707e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.493
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.992
y[1] (closed_form) = -1.0713987555790362728489998740317
y[1] (numeric) = -1.0713987555790362728285956504622
absolute error = 2.04042235695e-20
relative error = 1.9044471970170023141398461201662e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.492
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.991
y[1] (closed_form) = -1.0736251832849937857915208544984
y[1] (numeric) = -1.0736251832849937857709137257451
absolute error = 2.06071287533e-20
relative error = 1.9193969249350066744160646935121e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.491
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = -1.0758521067993744938322045176881
y[1] (numeric) = -1.075852106799374493811394212509
absolute error = 2.08103051791e-20
relative error = 1.9343090976519059248367353581021e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.989
y[1] (closed_form) = -1.0780795263430530731458970455183
y[1] (numeric) = -1.0780795263430530731248832922484
absolute error = 2.10137532699e-20
relative error = 1.9491839661569887287546325542040e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.489
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.988
y[1] (closed_form) = -1.0803074421370518269631390014397
y[1] (numeric) = -1.0803074421370518269419215279899
absolute error = 2.12174734498e-20
relative error = 1.9640217795619214358014606841723e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.488
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.987
y[1] (closed_form) = -1.082535854402540817159744158345
y[1] (numeric) = -1.0825358544025408171383226922017
absolute error = 2.14214661433e-20
relative error = 1.9788227850543258395300326993686e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.487
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.986
y[1] (closed_form) = -1.0847647633608379959930289250468
y[1] (numeric) = -1.0847647633608379959714031932711
absolute error = 2.16257317757e-20
relative error = 1.9935872279533456599087714066677e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.486
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.985
y[1] (closed_form) = -1.0869941692334093379848885375505
y[1] (numeric) = -1.0869941692334093379630582667772
absolute error = 2.18302707733e-20
relative error = 2.0083153517461421113511459947494e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.485
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.984
y[1] (closed_form) = -1.0892240722418689719519164875538
y[1] (numeric) = -1.0892240722418689719298814039907
absolute error = 2.20350835631e-20
relative error = 2.0230073980780487932291500660298e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.484
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.983
y[1] (closed_form) = -1.0914544726079793131827639673516
y[1] (numeric) = -1.0914544726079793131605237967791
absolute error = 2.22401705725e-20
relative error = 2.0376636067428588811306487595737e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.483
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.982
y[1] (closed_form) = -1.0936853705536511957629364176216
y[1] (numeric) = -1.0936853705536511957404908853915
absolute error = 2.24455322301e-20
relative error = 2.0522842157738202074435943354622e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.482
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.981
y[1] (closed_form) = -1.0959167663009440050472245724092
y[1] (numeric) = -1.0959167663009440050245734034442
absolute error = 2.26511689650e-20
relative error = 2.0668694613966586823597236726393e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.481
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = -1.0981486600720658102799677040268
y[1] (numeric) = -1.0981486600720658102571106228194
absolute error = 2.28570812074e-20
relative error = 2.0814195781015666964175160705074e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.979
y[1] (closed_form) = -1.1003810520893734973633470795241
y[1] (numeric) = -1.1003810520893734973402838101364
absolute error = 2.30632693877e-20
relative error = 2.0959347985780102080543102740270e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.479
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.978
y[1] (closed_form) = -1.1026139425753729017739079498883
y[1] (numeric) = -1.1026139425753729017506382159506
absolute error = 2.32697339377e-20
relative error = 2.1104153538407953433191876611183e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.478
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.977
y[1] (closed_form) = -1.1048473317527189416275087031757
y[1] (numeric) = -1.1048473317527189416040322278862
absolute error = 2.34764752895e-20
relative error = 2.1248614731464437242036835535960e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.477
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.976
y[1] (closed_form) = -1.1070812198442157508928961233874
y[1] (numeric) = -1.1070812198442157508692126295111
absolute error = 2.36834938763e-20
relative error = 2.1392733840822131349803410088198e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.476
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.975
y[1] (closed_form) = -1.109315607072816812754106008055
y[1] (numeric) = -1.1093156070728168127302152179233
absolute error = 2.38907901317e-20
relative error = 2.1536513125188348455631899917600e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.475
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.974
y[1] (closed_form) = -1.1115504936616250931218887092228
y[1] (numeric) = -1.1115504936616250930977903447323
absolute error = 2.40983644905e-20
relative error = 2.1679954826987781173802123140392e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.474
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.973
y[1] (closed_form) = -1.1137858798338931742943594747802
y[1] (numeric) = -1.1137858798338931742700532573923
absolute error = 2.43062173879e-20
relative error = 2.1823061171798083324981095566923e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.473
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.972
y[1] (closed_form) = -1.1160217658130233887670737799358
y[1] (numeric) = -1.1160217658130233887425594306757
absolute error = 2.45143492601e-20
relative error = 2.1965834369046792652992138292054e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.472
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.971
y[1] (closed_form) = -1.1182581518225679531927281520108
y[1] (numeric) = -1.1182581518225679531680053914666
absolute error = 2.47227605442e-20
relative error = 2.2108276612074022037320798668335e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.471
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = -1.1204950380862291024906873056827
y[1] (numeric) = -1.1204950380862291024657558540049
absolute error = 2.49314516778e-20
relative error = 2.2250390077926760826505937132436e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.969
y[1] (closed_form) = -1.1227324248278592241065387203267
y[1] (numeric) = -1.1227324248278592240813982972273
absolute error = 2.51404230994e-20
relative error = 2.2392176927868282338338013416050e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.469
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.968
y[1] (closed_form) = -1.1249703122714609924218761061754
y[1] (numeric) = -1.1249703122714609923965264309271
absolute error = 2.53496752483e-20
relative error = 2.2533639307437115647836334724215e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.468
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.967
y[1] (closed_form) = -1.1272087006411875033145135216607
y[1] (numeric) = -1.1272087006411875032889543130962
absolute error = 2.55592085645e-20
relative error = 2.2674779346505411857277803560332e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.467
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.966
y[1] (closed_form) = -1.1294475901613424088693322205088
y[1] (numeric) = -1.1294475901613424088435631970199
absolute error = 2.57690234889e-20
relative error = 2.2815599159602329375719548329335e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.466
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.965
y[1] (closed_form) = -1.1316869810563800522399626239307
y[1] (numeric) = -1.1316869810563800522139835034674
absolute error = 2.59791204633e-20
relative error = 2.2956100846056948529191800477844e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.465
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.964
y[1] (closed_form) = -1.1339268735509056026615041305917
y[1] (numeric) = -1.1339268735509056026353146306617
absolute error = 2.61894999300e-20
relative error = 2.3096286489786829817994119231993e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.464
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.963
y[1] (closed_form) = -1.1361672678696751906144857949549
y[1] (numeric) = -1.1361672678696751905880856326227
absolute error = 2.64001623322e-20
relative error = 2.3236158159793288362032553138592e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.463
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.962
y[1] (closed_form) = -1.1384081642375960431402712230695
y[1] (numeric) = -1.1384081642375960431136601149554
absolute error = 2.66111081141e-20
relative error = 2.3375717910387387136595401012794e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.462
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.961
y[1] (closed_form) = -1.1406495628797266193081113539275
y[1] (numeric) = -1.1406495628797266192812890162072
absolute error = 2.68223377203e-20
relative error = 2.3514967780799671136031123671868e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.461
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = -1.142891464021276745834049114136
y[1] (numeric) = -1.1428914640212767458070152625393
absolute error = 2.70338515967e-20
relative error = 2.3653909796107044660967654148784e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.959
y[1] (closed_form) = -1.1451338678876077528518802538442
y[1] (numeric) = -1.1451338678876077528246346036547
absolute error = 2.72456501895e-20
relative error = 2.3792545966489655606403482046709e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.459
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.958
y[1] (closed_form) = -1.1473767747042326098363749926407
y[1] (numeric) = -1.1473767747042326098089172586946
absolute error = 2.74577339461e-20
relative error = 2.3930878288152532471829258167699e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.458
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.957
y[1] (closed_form) = -1.1496201846968160616789654254767
y[1] (numeric) = -1.1496201846968160616512953221623
absolute error = 2.76701033144e-20
relative error = 2.4068908742844756630421598343249e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.457
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.956
y[1] (closed_form) = -1.1518640980911747649161039605997
y[1] (numeric) = -1.1518640980911747648882212018564
absolute error = 2.78827587433e-20
relative error = 2.4206639298426128524544979807370e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.456
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.955
y[1] (closed_form) = -1.1541085151132774241104983839786
y[1] (numeric) = -1.1541085151132774240824026832962
absolute error = 2.80957006824e-20
relative error = 2.4344071908734133411898320203325e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.455
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.954
y[1] (closed_form) = -1.1563534359892449283854294677845
y[1] (numeric) = -1.1563534359892449283571205382023
absolute error = 2.83089295822e-20
relative error = 2.4481208513884934009724399086545e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.454
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.953
y[1] (closed_form) = -1.1585988609453504881123573641512
y[1] (numeric) = -1.1585988609453504880838349182573
absolute error = 2.85224458939e-20
relative error = 2.4618051040225702822414053541593e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.453
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.952
y[1] (closed_form) = -1.1608447902080197717520233496816
y[1] (numeric) = -1.1608447902080197717232870996119
absolute error = 2.87362500697e-20
relative error = 2.4754601400718310900814104067698e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.452
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.951
y[1] (closed_form) = -1.1630912240038310428492538109912
y[1] (numeric) = -1.1630912240038310428203034684288
absolute error = 2.89503425624e-20
relative error = 2.4890861494716808251885578792948e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.451
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = -1.1653381625595152971816736869888
y[1] (numeric) = -1.1653381625595152971525089631631
absolute error = 2.91647238257e-20
relative error = 2.5026833208348242507752743749271e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.949
y[1] (closed_form) = -1.1675856061019564000625369095887
y[1] (numeric) = -1.1675856061019564000331575152746
absolute error = 2.93793943141e-20
relative error = 2.5162518414546573474926460850055e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.449
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.948
y[1] (closed_form) = -1.1698335548581912237978817111285
y[1] (numeric) = -1.1698335548581912237682873566456
absolute error = 2.95943544829e-20
relative error = 2.5297918973171757695090081333303e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.448
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.947
y[1] (closed_form) = -1.1720820090554097852982189939338
y[1] (numeric) = -1.1720820090554097852684093891454
absolute error = 2.98096047884e-20
relative error = 2.5433036731298177357517182566906e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.447
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.946
y[1] (closed_form) = -1.1743309689209553838449622852288
y[1] (numeric) = -1.1743309689209553838149371395413
absolute error = 3.00251456875e-20
relative error = 2.5567873522988903436238348685618e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.446
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.945
y[1] (closed_form) = -1.1765804346823247390118081289362
y[1] (numeric) = -1.1765804346823247389815671512983
absolute error = 3.02409776379e-20
relative error = 2.5702431169582576417589488986604e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.445
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.944
y[1] (closed_form) = -1.1788304065671681287412760948481
y[1] (numeric) = -1.1788304065671681287108189937498
absolute error = 3.04571010983e-20
relative error = 2.5836711479977078820847071137286e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.444
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.943
y[1] (closed_form) = -1.1810808848032895275766179151779
y[1] (numeric) = -1.1810808848032895275459443986497
absolute error = 3.06735165282e-20
relative error = 2.5970716250571366975280020604078e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.443
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.942
y[1] (closed_form) = -1.1833318696186467450493055886269
y[1] (numeric) = -1.1833318696186467450184153642391
absolute error = 3.08902243878e-20
relative error = 2.6104447265292547164565141180769e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.442
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.941
y[1] (closed_form) = -1.185583361241351564222308622816
y[1] (numeric) = -1.1855833612413515641912013976778
absolute error = 3.11072251382e-20
relative error = 2.6237906295875756874401703512494e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.441
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = -1.1878353598996698803893709172459
y[1] (numeric) = -1.1878353598996698803580463980046
absolute error = 3.13245192413e-20
relative error = 2.6371095101888375444418269756124e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.939
y[1] (closed_form) = -1.1900878658220218399304981208603
y[1] (numeric) = -1.1900878658220218398989560137003
absolute error = 3.15421071600e-20
relative error = 2.6504015431006113544278548181218e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.439
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.938
y[1] (closed_form) = -1.1923408792369819793238666307931
y[1] (numeric) = -1.1923408792369819792921066414354
absolute error = 3.17599893577e-20
relative error = 2.6636669018698963397156161244268e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.438
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.937
y[1] (closed_form) = -1.1945944003732793643143657319919
y[1] (numeric) = -1.1945944003732793642823875656928
absolute error = 3.19781662991e-20
relative error = 2.6769057589009008580552587140103e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.437
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.936
y[1] (closed_form) = -1.1968484294597977292389847111136
y[1] (numeric) = -1.1968484294597977292067880726642
absolute error = 3.21966384494e-20
relative error = 2.6901182853982671860862723712570e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.436
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.935
y[1] (closed_form) = -1.1991029667255756165092571124036
y[1] (numeric) = -1.1991029667255756164768417061291
absolute error = 3.24154062745e-20
relative error = 2.7033046513943391087835988402644e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.435
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.934
y[1] (closed_form) = -1.2013580123998065162509746381804
y[1] (numeric) = -1.2013580123998065162183401679387
absolute error = 3.26344702417e-20
relative error = 2.7164650258177489738256241843983e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.434
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.933
y[1] (closed_form) = -1.2036135667118390061013835320648
y[1] (numeric) = -1.2036135667118390060685297012462
absolute error = 3.28538308186e-20
relative error = 2.7295995764116907190728229010145e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.433
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.932
y[1] (closed_form) = -1.2058696298911768911640766192196
y[1] (numeric) = -1.2058696298911768911310031307459
absolute error = 3.30734884737e-20
relative error = 2.7427084697940937962867607367479e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.432
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.931
y[1] (closed_form) = -1.2081262021674793441217945145929
y[1] (numeric) = -1.2081262021674793440885010709161
absolute error = 3.32934436768e-20
relative error = 2.7557918715005750573274223717793e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.431
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = -1.2103832837705610455073498474964
y[1] (numeric) = -1.2103832837705610454738361505983
absolute error = 3.35136968981e-20
relative error = 2.7688499459195125803958177290498e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.929
y[1] (closed_form) = -1.2126408749303923241328886887999
y[1] (numeric) = -1.2126408749303923240991544401912
absolute error = 3.37342486087e-20
relative error = 2.7818828563433014742840647760764e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.429
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.928
y[1] (closed_form) = -1.2148989758770992976777037055794
y[1] (numeric) = -1.2148989758770992976437486062986
absolute error = 3.39550992808e-20
relative error = 2.7948907649943512981707425008545e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.428
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.927
y[1] (closed_form) = -1.2171575868409640134348139072254
y[1] (numeric) = -1.2171575868409640134006376578381
absolute error = 3.41762493873e-20
relative error = 2.8078738330015051577556858731768e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.427
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.926
y[1] (closed_form) = -1.2194167080524245892165261868024
y[1] (numeric) = -1.2194167080524245891821284874006
absolute error = 3.43976994018e-20
relative error = 2.8208322204095296270094151878113e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.426
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.925
y[1] (closed_form) = -1.2216763397420753544191942018468
y[1] (numeric) = -1.2216763397420753543845747520478
absolute error = 3.46194497990e-20
relative error = 2.8337660862212475306246189840107e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.425
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.924
y[1] (closed_form) = -1.2239364821406669912473904798016
y[1] (numeric) = -1.2239364821406669912125489787472
absolute error = 3.48415010544e-20
relative error = 2.8466755883820176134964711217352e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.424
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.923
y[1] (closed_form) = -1.2261971354791066760977079749178
y[1] (numeric) = -1.2261971354791066760626441212736
absolute error = 3.50638536442e-20
relative error = 2.8595608837807024315652176450072e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.423
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.922
y[1] (closed_form) = -1.2284582999884582211024076456973
y[1] (numeric) = -1.2284582999884582210671211376516
absolute error = 3.52865080457e-20
relative error = 2.8724221282913330156223375475379e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.422
Order of pole (given) = 1
NO POLE (ratio test) for 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=51.4MB, alloc=42.3MB, time=0.48
x[1] = 2.921
y[1] (closed_form) = -1.2307199758999422158331289648199
y[1] (numeric) = -1.230719975899942215797619500083
absolute error = 3.55094647369e-20
relative error = 2.8852594767493175636811167470500e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.421
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = -1.2329821634449361691648806169829
y[1] (numeric) = -1.2329821634449361691291478927862
absolute error = 3.57327241967e-20
relative error = 2.8980730829765803063775101536297e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.919
y[1] (closed_form) = -1.2352448628549746513005289841914
y[1] (numeric) = -1.2352448628549746512645726972865
absolute error = 3.59562869049e-20
relative error = 2.9108630997902388654284996510461e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.419
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.918
y[1] (closed_form) = -1.2375080743617494359560023627676
y[1] (numeric) = -1.2375080743617494359198222094253
absolute error = 3.61801533423e-20
relative error = 2.9236296790192728978272102926904e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.418
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.917
y[1] (closed_form) = -1.2397717981971096427064292017051
y[1] (numeric) = -1.2397717981971096426700248777149
absolute error = 3.64043239902e-20
relative error = 2.9363729714726198125215105770667e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.417
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.916
y[1] (closed_form) = -1.242036034593061879493428997975
y[1] (numeric) = -1.2420360345930618794568001986439
absolute error = 3.66287993311e-20
relative error = 2.9490931270042405929888756885787e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.416
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.915
y[1] (closed_form) = -1.2443007837817703852937748309978
y[1] (numeric) = -1.2443007837817703852569212511496
absolute error = 3.68535798482e-20
relative error = 2.9617902944810411329012188326485e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.415
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.914
y[1] (closed_form) = -1.2465660459955571729496468657338
y[1] (numeric) = -1.246566045995557172912568199708
absolute error = 3.70786660258e-20
relative error = 2.9744646218233470413986834773283e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.414
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.913
y[1] (closed_form) = -1.2488318214669021721606965017086
y[1] (numeric) = -1.2488318214669021721233924433597
absolute error = 3.73040583489e-20
relative error = 2.9871162559808835393104531987129e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.413
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.912
y[1] (closed_form) = -1.2510981104284433726381411937884
y[1] (numeric) = -1.2510981104284433726006114364851
absolute error = 3.75297573033e-20
relative error = 2.9997453429489866212102092247707e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.412
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.911
y[1] (closed_form) = -1.253364913112976967421110319648
y[1] (numeric) = -1.2533649131129769673833545562722
absolute error = 3.77557633758e-20
relative error = 3.0123520277926222776711456456545e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.411
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = -1.2556322297534574963554628186351
y[1] (numeric) = -1.2556322297534574963174807415809
absolute error = 3.79820770542e-20
relative error = 3.0249364546542226037763319093402e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.909
y[1] (closed_form) = -1.2579000605829979897352976771321
y[1] (numeric) = -1.2579000605829979896970889783053
absolute error = 3.82086988268e-20
relative error = 3.0374987667216935542381695631232e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.409
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.908
y[1] (closed_form) = -1.2601684058348701121073786865499
y[1] (numeric) = -1.2601684058348701120689430573666
absolute error = 3.84356291833e-20
relative error = 3.0500391063078696290476031916976e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.408
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.907
y[1] (closed_form) = -1.2624372657425043062386952517541
y[1] (numeric) = -1.2624372657425043062000323831403
absolute error = 3.86628686138e-20
relative error = 3.0625576147786145895517203935456e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.407
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.906
y[1] (closed_form) = -1.2647066405394899372473813800366
y[1] (numeric) = -1.2647066405394899372084909624268
absolute error = 3.88904176098e-20
relative error = 3.0750544326398405539349824767532e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.406
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.905
y[1] (closed_form) = -1.2669765304595754368972153336877
y[1] (numeric) = -1.2669765304595754368580970570246
absolute error = 3.91182766631e-20
relative error = 3.0875296994578480387782175683925e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.405
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.904
y[1] (closed_form) = -1.2692469357366684480559227828197
y[1] (numeric) = -1.2692469357366684480165763365527
absolute error = 3.93464462670e-20
relative error = 3.0999835539617355280862855344263e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.404
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.903
y[1] (closed_form) = -1.2715178566048359693175066493153
y[1] (numeric) = -1.2715178566048359692779317224
absolute error = 3.95749269153e-20
relative error = 3.1124161339716952985438712058167e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.403
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.902
y[1] (closed_form) = -1.2737892932983044997888271876571
y[1] (numeric) = -1.2737892932983044997490234685544
absolute error = 3.98037191027e-20
relative error = 3.1248275764379893189166039273799e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.402
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.901
y[1] (closed_form) = -1.2760612460514601840406562039095
y[1] (numeric) = -1.2760612460514601840006233805844
absolute error = 4.00328233251e-20
relative error = 3.1372180174716772046263090579231e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.401
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = -1.2783337150988489572234296702907
y[1] (numeric) = -1.2783337150988489571831674302117
absolute error = 4.02622400790e-20
relative error = 3.1495875923046170700557921677285e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.899
y[1] (closed_form) = -1.2806067006751766903479233495885
y[1] (numeric) = -1.2806067006751766903074313797267
absolute error = 4.04919698618e-20
relative error = 3.1619364353201761497187332076690e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.399
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.898
y[1] (closed_form) = -1.2828802030153093357310764011348
y[1] (numeric) = -1.2828802030153093356903543879627
absolute error = 4.07220131721e-20
relative error = 3.1742646800836197145005768237062e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.398
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.897
y[1] (closed_form) = -1.2851542223542730726071882981659
y[1] (numeric) = -1.2851542223542730725662359276568
absolute error = 4.09523705091e-20
relative error = 3.1865724593021515076636322178496e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.397
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.896
y[1] (closed_form) = -1.2874287589272544529047147451627
y[1] (numeric) = -1.2874287589272544528635317027897
absolute error = 4.11830423730e-20
relative error = 3.1988599048630564371759813871285e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.396
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.895
y[1] (closed_form) = -1.2897038129696005471888886431807
y[1] (numeric) = -1.2897038129696005471474746139156
absolute error = 4.14140292651e-20
relative error = 3.2111271478481831147392982420330e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.395
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.894
y[1] (closed_form) = -1.2919793847168190907703925112515
y[1] (numeric) = -1.2919793847168190907287471795641
absolute error = 4.16453316874e-20
relative error = 3.2233743185095775117982308731392e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.394
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.893
y[1] (closed_form) = -1.2942554744045786299803091326672
y[1] (numeric) = -1.2942554744045786299384321825244
absolute error = 4.18769501428e-20
relative error = 3.2356015462917368037642306656393e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.393
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.892
y[1] (closed_form) = -1.2965320822687086686115775563408
y[1] (numeric) = -1.2965320822687086685694686712057
absolute error = 4.21088851351e-20
relative error = 3.2478089598382075195707518904179e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.392
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.891
y[1] (closed_form) = -1.2988092085451998145271819454813
y[1] (numeric) = -1.2988092085451998144848408083119
absolute error = 4.23411371694e-20
relative error = 3.2599966870289161138073848075152e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.391
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = -1.3010868534702039264353011285216
y[1] (numeric) = -1.3010868534702039263927274217705
absolute error = 4.25737067511e-20
relative error = 3.2721648549095094401649074479193e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.889
y[1] (closed_form) = -1.3033650172800342608316470706059
y[1] (numeric) = -1.3033650172800342607888404762189
absolute error = 4.28065943870e-20
relative error = 3.2843135897825617883266441643399e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.389
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.888
y[1] (closed_form) = -1.3056437002111656191092208479628
y[1] (numeric) = -1.3056437002111656190661810473781
absolute error = 4.30398005847e-20
relative error = 3.2964430171676274081677336856884e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.388
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.887
y[1] (closed_form) = -1.307922902500234494835715072186
y[1] (numeric) = -1.3079229025002344947924417463334
absolute error = 4.32733258526e-20
relative error = 3.3085532618075889693707828189127e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.387
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.886
y[1] (closed_form) = -1.310202624384039221198792076796
y[1] (numeric) = -1.3102026243840392211552849060959
absolute error = 4.35071707001e-20
relative error = 3.3206444476902087874546640824626e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.386
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.885
y[1] (closed_form) = -1.3124828660995401186194675444788
y[1] (numeric) = -1.3124828660995401185757262088411
absolute error = 4.37413356377e-20
relative error = 3.3327166980618404389515620556815e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.385
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.884
y[1] (closed_form) = -1.3147636278838596425338296200853
y[1] (numeric) = -1.3147636278838596424898537989087
absolute error = 4.39758211766e-20
relative error = 3.3447701354029720688073919547769e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.384
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.883
y[1] (closed_form) = -1.3170449099742825313433239218368
y[1] (numeric) = -1.3170449099742825312991132940078
absolute error = 4.42106278290e-20
relative error = 3.3568048814571771317391539905577e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.383
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.882
y[1] (closed_form) = -1.3193267126082559545338352312071
y[1] (numeric) = -1.319326712608255954489389475099
absolute error = 4.44457561081e-20
relative error = 3.3688210572370299527268317553720e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.382
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.881
y[1] (closed_form) = -1.3216090360233896609637970106553
y[1] (numeric) = -1.3216090360233896609191158041273
absolute error = 4.46812065280e-20
relative error = 3.3808187830223974005010278363238e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.381
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = -1.3238918804574561273215602677567
y[1] (numeric) = -1.323891880457456127276643288153
absolute error = 4.49169796037e-20
relative error = 3.3927981783663056265145349710253e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.879
y[1] (closed_form) = -1.3261752461483907067522536543289
y[1] (numeric) = -1.3261752461483907067071005784778
absolute error = 4.51530758511e-20
relative error = 3.4047593621007501085090509795400e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.379
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.878
y[1] (closed_form) = -1.3284591333342917776543670598744
y[1] (numeric) = -1.3284591333342917776089775640871
absolute error = 4.53894957873e-20
relative error = 3.4167024523650321906310820613794e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.378
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.877
y[1] (closed_form) = -1.3307435422534208926462913300644
y[1] (numeric) = -1.3307435422534208926006650901345
absolute error = 4.56262399299e-20
relative error = 3.4286275665586616399533294346734e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.377
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.876
y[1] (closed_form) = -1.3330284731442029277030471130709
y[1] (numeric) = -1.333028473144202927657183804273
absolute error = 4.58633087979e-20
relative error = 3.4405348214147746909286829126170e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.376
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.875
y[1] (closed_form) = -1.3353139262452262314634362093135
y[1] (numeric) = -1.3353139262452262314173355064025
absolute error = 4.61007029110e-20
relative error = 3.4524243329529800705585340770822e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.375
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.874
y[1] (closed_form) = -1.3375999017952427747078491736342
y[1] (numeric) = -1.3375999017952427746615107508443
absolute error = 4.63384227899e-20
relative error = 3.4642962165074528249196613911516e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.374
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.873
y[1] (closed_form) = -1.3398864000331683000069632930378
y[1] (numeric) = -1.3398864000331682999603868240815
absolute error = 4.65764689563e-20
relative error = 3.4761505867323543208363632894559e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.373
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.872
y[1] (closed_form) = -1.3421734211980824715415654379474
y[1] (numeric) = -1.3421734211980824714947505960146
absolute error = 4.68148419328e-20
relative error = 3.4879875575997498492293666212424e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.372
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.871
y[1] (closed_form) = -1.3444609655292290250937346604222
y[1] (numeric) = -1.3444609655292290250466811181793
absolute error = 4.70535422429e-20
relative error = 3.4998072424049889950401168959258e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.371
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = -1.3467490332660159182096197889687
y[1] (numeric) = -1.3467490332660159181623272185574
absolute error = 4.72925704113e-20
relative error = 3.5116097537943106189336685285717e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.869
y[1] (closed_form) = -1.349037624648015480534047646449
y[1] (numeric) = -1.3490376246480154804865157194857
absolute error = 4.75319269633e-20
relative error = 3.5233952037254561878301548424160e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.369
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.868
y[1] (closed_form) = -1.3513267399149645643171978951555
y[1] (numeric) = -1.3513267399149645642694262827301
absolute error = 4.77716124254e-20
relative error = 3.5351637035174884393530449025818e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.368
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.867
y[1] (closed_form) = -1.3536163793067646950935808913729
y[1] (numeric) = -1.3536163793067646950455692640478
absolute error = 4.80116273251e-20
relative error = 3.5469153638410071202962120192231e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.367
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.866
y[1] (closed_form) = -1.3559065430634822225335553106996
y[1] (numeric) = -1.3559065430634822224853033385088
absolute error = 4.82519721908e-20
relative error = 3.5586502947158423514383370781187e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.366
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.865
y[1] (closed_form) = -1.3581972314253484714676226850408
y[1] (numeric) = -1.3581972314253484714191300374891
absolute error = 4.84926475517e-20
relative error = 3.5703686055087747201207886587274e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.365
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.864
y[1] (closed_form) = -1.3604884446327598930837363725254
y[1] (numeric) = -1.3604884446327598930350027185872
absolute error = 4.87336539382e-20
relative error = 3.5820704049680333143160538229241e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.364
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.863
y[1] (closed_form) = -1.3627801829262782162978628626331
y[1] (numeric) = -1.3627801829262782162488878707514
absolute error = 4.89749918817e-20
relative error = 3.5937558012134214369151539111568e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.363
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.862
y[1] (closed_form) = -1.3650724465466305992980337005531
y[1] (numeric) = -1.3650724465466305992488170386388
absolute error = 4.92166619143e-20
relative error = 3.6054249017192193953705874205086e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.362
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.861
y[1] (closed_form) = -1.3673652357347097812621266972307
y[1] (numeric) = -1.3673652357347097812126680326614
absolute error = 4.94586645693e-20
relative error = 3.6170778133557692440098429464646e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.361
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = -1.3696585507315742342496154746936
y[1] (numeric) = -1.3696585507315742341999144743126
absolute error = 4.97010003810e-20
relative error = 3.6287146423795374870553121415904e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.859
y[1] (closed_form) = -1.3719523917784483152675267800889
y[1] (numeric) = -1.3719523917784483152175831102043
absolute error = 4.99436698846e-20
relative error = 3.6403354944305694696310668688553e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.359
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.858
y[1] (closed_form) = -1.3742467591167224185108453864062
y[1] (numeric) = -1.37424675911672241846065871279
absolute error = 5.01866736162e-20
relative error = 3.6519404745372491546508118086479e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.358
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.857
y[1] (closed_form) = -1.376541652987953127777606783112
y[1] (numeric) = -1.3765416529879531277271767709989
absolute error = 5.04300121131e-20
relative error = 3.6635296871428082198570082852651e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.357
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.856
y[1] (closed_form) = -1.3788370736338633690589182458762
y[1] (numeric) = -1.3788370736338633690082445599628
absolute error = 5.06736859134e-20
relative error = 3.6751032360808061048837836477572e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.356
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.855
y[1] (closed_form) = -1.3811330212963425633041492612405
y[1] (numeric) = -1.3811330212963425632532315656843
absolute error = 5.09176955562e-20
relative error = 3.6866612245943002203186851106465e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.355
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.854
y[1] (closed_form) = -1.3834294962174467793615326694524
y[1] (numeric) = -1.3834294962174467793103706278707
absolute error = 5.11620415817e-20
relative error = 3.6982037553475999502449085338780e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.354
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.853
y[1] (closed_form) = -1.3857264986393988870944182767778
y[1] (numeric) = -1.3857264986393988870430115522467
absolute error = 5.14067245311e-20
relative error = 3.7097309304234739196475190267625e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.353
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.852
y[1] (closed_form) = -1.3880240288045887106734210774074
y[1] (numeric) = -1.388024028804588710621769332461
absolute error = 5.16517449464e-20
relative error = 3.7212428513131834718924912833935e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.352
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.851
y[1] (closed_form) = -1.3903220869555731820447066145882
y[1] (numeric) = -1.3903220869555731819928095112173
absolute error = 5.18971033709e-20
relative error = 3.7327396189569660080685406871263e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.351
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = -1.3926206733350764945746564008429
y[1] (numeric) = -1.3926206733350764945225136004944
absolute error = 5.21428003485e-20
relative error = 3.7442213336979519623954666411002e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.849
y[1] (closed_form) = -1.3949197881859902568711567080932
y[1] (numeric) = -1.3949197881859902568187678716687
absolute error = 5.23888364245e-20
relative error = 3.7556880953440733657575803984904e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.349
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.848
y[1] (closed_form) = -1.3972194317513736467817544301697
y[1] (numeric) = -1.3972194317513736467291192180246
absolute error = 5.26352121451e-20
relative error = 3.7671400031363221700758266863225e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.348
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.847
y[1] (closed_form) = -1.3995196042744535655689241125833
y[1] (numeric) = -1.3995196042744535655160421845261
absolute error = 5.28819280572e-20
relative error = 3.7785771557387602173454180456862e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.347
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.846
y[1] (closed_form) = -1.4018203059986247922626906375464
y[1] (numeric) = -1.4018203059986247922095616528373
absolute error = 5.31289847091e-20
relative error = 3.7899996512928327040832990253307e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.346
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.845
y[1] (closed_form) = -1.4041215371674501381908524460655
y[1] (numeric) = -1.4041215371674501381374760634156
absolute error = 5.33763826499e-20
relative error = 3.8014075873785659155327835005345e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.345
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.844
y[1] (closed_form) = -1.4064232980246606016870505734922
y[1] (numeric) = -1.4064232980246606016334264510623
absolute error = 5.36241224299e-20
relative error = 3.8128010610472509619373142283346e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.344
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.843
y[1] (closed_form) = -1.4087255888141555229769291702044
y[1] (numeric) = -1.4087255888141555229230569656044
absolute error = 5.38722046000e-20
relative error = 3.8241801687828237238824250613721e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.343
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.842
y[1] (closed_form) = -1.4110284097800027392426335751101
y[1] (numeric) = -1.4110284097800027391885129453974
absolute error = 5.41206297127e-20
relative error = 3.8355450065770181019661673364454e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.342
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.841
y[1] (closed_form) = -1.4133317611664387398658924064064
y[1] (numeric) = -1.4133317611664387398115230080854
absolute error = 5.43693983210e-20
relative error = 3.8468956698552021943231077543311e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.341
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = -1.415635643217868821849930531512
y[1] (numeric) = -1.4156356432178688217953120205327
absolute error = 5.46185109793e-20
relative error = 3.8582322535442204067879055505368e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.839
y[1] (closed_form) = -1.4179400561788672454204601762928
y[1] (numeric) = -1.41794005617886724536559220805
absolute error = 5.48679682428e-20
relative error = 3.8695548520337896305352274261556e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.339
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.838
y[1] (closed_form) = -1.4202450002941773898059978326524
y[1] (numeric) = -1.4202450002941773897508800619847
absolute error = 5.51177706677e-20
relative error = 3.8808635591946021200306407612102e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.338
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.837
y[1] (closed_form) = -1.4225504758087119091977550232349
y[1] (numeric) = -1.4225504758087119091423871044235
absolute error = 5.53679188114e-20
relative error = 3.8921584683962550391212336634380e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.337
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.836
y[1] (closed_form) = -1.4248564829675528888893513824071
y[1] (numeric) = -1.424856482967552888833732969175
absolute error = 5.56184132321e-20
relative error = 3.9034396724828989957768023665126e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.336
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.835
y[1] (closed_form) = -1.4271630220159520015965989138431
y[1] (numeric) = -1.4271630220159520015407296593538
absolute error = 5.58692544893e-20
relative error = 3.9147072638121873812657196365320e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.335
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.834
y[1] (closed_form) = -1.4294700931993306639576066869314
y[1] (numeric) = -1.429470093199330663901486243788
absolute error = 5.61204431434e-20
relative error = 3.9259613342308907756742170053296e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.334
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.833
y[1] (closed_form) = -1.4317776967632801932134556368638
y[1] (numeric) = -1.4317776967632801931570836571079
absolute error = 5.63719797559e-20
relative error = 3.9372019750926555261347490232691e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.333
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.832
y[1] (closed_form) = -1.4340858329535619640696935366469
y[1] (numeric) = -1.4340858329535619640130696717579
absolute error = 5.66238648890e-20
relative error = 3.9484292772337548784950970845635e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.332
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.831
y[1] (closed_form) = -1.4363945020161075657389006134063
y[1] (numeric) = -1.4363945020161075656820245142998
absolute error = 5.68760991065e-20
relative error = 3.9596433310395807855456972145587e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.331
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = -1.4387037041970189591645766862237
y[1] (numeric) = -1.4387037041970189591074480032509
absolute error = 5.71286829728e-20
relative error = 3.9708442263784346269496030194838e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.829
y[1] (closed_form) = -1.4410134397425686344266011083746
y[1] (numeric) = -1.441013439742568634369219491321
absolute error = 5.73816170536e-20
relative error = 3.9820320526539294103126100517973e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.329
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.828
y[1] (closed_form) = -1.443323708899199768328517203201
y[1] (numeric) = -1.4433237088991997682708823012855
absolute error = 5.76349019155e-20
relative error = 3.9932068987806782993192386667144e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.328
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.827
y[1] (closed_form) = -1.4456345119135263821668932899794
y[1] (numeric) = -1.4456345119135263821090047518532
absolute error = 5.78885381262e-20
relative error = 4.0043688532017228583392878816330e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.327
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.826
y[1] (closed_form) = -1.4479458490323334996830128040196
y[1] (numeric) = -1.4479458490323334996248702777652
absolute error = 5.81425262544e-20
relative error = 4.0155180038850777836611275301514e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.326
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.825
y[1] (closed_form) = -1.4502577205025773051971464238591
y[1] (numeric) = -1.4502577205025773051387495569893
absolute error = 5.83968668698e-20
relative error = 4.0266544383272063281451681655515e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.325
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.824
y[1] (closed_form) = -1.4525701265713853019256595278056
y[1] (numeric) = -1.4525701265713853018670079672621
absolute error = 5.86515605435e-20
relative error = 4.0377782435840022632965092699848e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.324
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.823
y[1] (closed_form) = -1.454883067486056470481208712221
y[1] (numeric) = -1.4548830674860564704223021043738
absolute error = 5.89066078472e-20
relative error = 4.0488895062189977754678135855337e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.323
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.822
y[1] (closed_form) = -1.4571965434940614275562815148472
y[1] (numeric) = -1.4571965434940614274971195054933
absolute error = 5.91620093539e-20
relative error = 4.0599883123550042477256058259252e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.322
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.821
y[1] (closed_form) = -1.4595105548430425847903338981325
y[1] (numeric) = -1.4595105548430425847309161324948
absolute error = 5.94177656377e-20
relative error = 4.0710747476635997123834587638212e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.321
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = -1.4618251017808143078207804599463
y[1] (numeric) = -1.4618251017808143077611065826727
absolute error = 5.96738772736e-20
relative error = 4.0821488973547183154372538276804e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.819
y[1] (closed_form) = -1.4641401845553630755180927522591
y[1] (numeric) = -1.4641401845553630754581624074212
absolute error = 5.99303448379e-20
relative error = 4.0932108462073204294393490711733e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.319
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.818
y[1] (closed_form) = -1.4664558034148476394052615023168
y[1] (numeric) = -1.4664558034148476393450743334092
absolute error = 6.01871689076e-20
relative error = 4.1042606785315828205750132869637e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.318
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.817
y[1] (closed_form) = -1.4687719586075991832618789455647
y[1] (numeric) = -1.4687719586075991832014345955035
absolute error = 6.04443500612e-20
relative error = 4.1152984782267663676014731213649e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.317
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.816
y[1] (closed_form) = -1.4710886503821214829130978950624
y[1] (numeric) = -1.4710886503821214828523960061844
absolute error = 6.07018888780e-20
relative error = 4.1263243287365739845268924496942e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.316
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.815
y[1] (closed_form) = -1.4734058789870910662037245883952
y[1] (numeric) = -1.4734058789870910661427648024568
absolute error = 6.09597859384e-20
relative error = 4.1373383130728017316240466757810e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.315
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.814
y[1] (closed_form) = -1.4757236446713573731577027701188
y[1] (numeric) = -1.4757236446713573730964847282949
absolute error = 6.12180418239e-20
relative error = 4.1483405138184402564733705384959e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.314
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.813
y[1] (closed_form) = -1.4780419476839429163232468855793
y[1] (numeric) = -1.4780419476839429162617702284621
absolute error = 6.14766571172e-20
relative error = 4.1593310131375148427509432473269e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.313
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.812
y[1] (closed_form) = -1.4803607882740434413038826805326
y[1] (numeric) = -1.4803607882740434412421470481308
absolute error = 6.17356324018e-20
relative error = 4.1703098927510594975897684679986e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.312
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.811
y[1] (closed_form) = -1.4826801666910280874756539203461
y[1] (numeric) = -1.4826801666910280874136589520835
absolute error = 6.19949682626e-20
relative error = 4.1812772339807639875023325553280e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.311
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = -1.4850000831844395488907543626987
y[1] (numeric) = -1.4850000831844395488284996974132
absolute error = 6.22546652855e-20
relative error = 4.1922331177248738341800776469070e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.809
y[1] (closed_form) = -1.4873205380039942353678445386138
y[1] (numeric) = -1.4873205380039942353053298145566
absolute error = 6.25147240572e-20
relative error = 4.2031776244477648161643942471550e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.808
y[1] (closed_form) = -1.4896415313995824337693133183572
y[1] (numeric) = -1.4896415313995824337065381731913
absolute error = 6.27751451659e-20
relative error = 4.2141108342300341898058504566208e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.308
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.807
y[1] (closed_form) = -1.4919630636212684694657446612104
y[1] (numeric) = -1.4919630636212684694027087320097
absolute error = 6.30359292007e-20
relative error = 4.2250328267309928183485513906492e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.307
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.806
y[1] (closed_form) = -1.4942851349192908679878503713982
y[1] (numeric) = -1.4942851349192908679245532946464
absolute error = 6.32970767518e-20
relative error = 4.2359436812050461425238022800032e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.306
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.805
y[1] (closed_form) = -1.4966077455440625168661301064998
y[1] (numeric) = -1.4966077455440625168025715180893
absolute error = 6.35585884105e-20
relative error = 4.2468434765045610862025992103709e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.305
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.804
y[1] (closed_form) = -1.4989308957461708276585203095134
y[1] (numeric) = -1.4989308957461708275946998447441
absolute error = 6.38204647693e-20
relative error = 4.2577322910893796557642036360776e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.304
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.803
y[1] (closed_form) = -1.5012545857763778981662941613732
y[1] (numeric) = -1.5012545857763778981022114549517
absolute error = 6.40827064215e-20
relative error = 4.2686102030029406254911645884665e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.303
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.802
y[1] (closed_form) = -1.5035788158856206748384750771414
y[1] (numeric) = -1.5035788158856206747741297631795
absolute error = 6.43453139619e-20
relative error = 4.2794772899217833383370340861233e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.302
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.801
y[1] (closed_form) = -1.5059035863250111153650266963083
y[1] (numeric) = -1.5059035863250111153004184083221
absolute error = 6.46082879862e-20
relative error = 4.2903336291182680548528748386458e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.301
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -1.508228897345836351459082745647
y[1] (numeric) = -1.5082288973458363513942111165559
absolute error = 6.48716290911e-20
relative error = 4.3011792974700549347660559166361e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.799
y[1] (closed_form) = -1.5105547491995588518284805818721
y[1] (numeric) = -1.5105547491995588517633452439974
absolute error = 6.51353378747e-20
relative error = 4.3120143714893576247051184889912e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.299
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.798
y[1] (closed_form) = -1.5128811421378165853368626509543
y[1] (numeric) = -1.5128811421378165852714632360184
absolute error = 6.53994149359e-20
relative error = 4.3228389272858297681657536595602e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.298
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.797
y[1] (closed_form) = -1.5152080764124231843546105313505
y[1] (numeric) = -1.5152080764124231842889466704755
absolute error = 6.56638608750e-20
relative error = 4.3336530406089922484705652469314e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.297
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.796
y[1] (closed_form) = -1.5175355522753681082998766596082
y[1] (numeric) = -1.5175355522753681082339479833149
absolute error = 6.59286762933e-20
relative error = 4.3444567868243755998815711262718e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.795
y[1] (closed_form) = -1.5198635699788168073699792688146
y[1] (numeric) = -1.5198635699788168073037854070215
absolute error = 6.61938617931e-20
relative error = 4.3552502409162015145907287546024e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.295
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.794
y[1] (closed_form) = -1.5221921297751108864634265031723
y[1] (numeric) = -1.5221921297751108863969670851943
absolute error = 6.64594179780e-20
relative error = 4.3660334775097499672581876831032e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.294
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.793
y[1] (closed_form) = -1.5245212319167682692928361056012
y[1] (numeric) = -1.5245212319167682692261107601486
absolute error = 6.67253454526e-20
relative error = 4.3768065708541664875039795012435e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.293
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.792
y[1] (closed_form) = -1.5268508766564833626890175096957
y[1] (numeric) = -1.5268508766564833626220258648729
absolute error = 6.69916448228e-20
relative error = 4.3875695948447250708092364756209e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.292
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.791
y[1] (closed_form) = -1.5291810642471272210964836026005
y[1] (numeric) = -1.5291810642471272210292252859051
absolute error = 6.72583166954e-20
relative error = 4.3983226229991131728351250784691e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.291
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = -1.5315117949417477112606598614194
y[1] (numeric) = -1.531511794941747711193134499741
absolute error = 6.75253616784e-20
relative error = 4.4090657284796413663181256385378e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.789
y[1] (closed_form) = -1.5338430689935696771070590026313
y[1] (numeric) = -1.5338430689935696770392662222502
absolute error = 6.77927803811e-20
relative error = 4.4197989841022130893037727212954e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.289
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.788
y[1] (closed_form) = -1.536174886655995104812689721665
y[1] (numeric) = -1.5361748866559951047446291482512
absolute error = 6.80605734138e-20
relative error = 4.4305224623191756520851989896308e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.787
y[1] (closed_form) = -1.5385072481826032880699685382782
y[1] (numeric) = -1.5385072481826032880016397968903
absolute error = 6.83287413879e-20
relative error = 4.4412362352283280633279272385765e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.287
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.786
y[1] (closed_form) = -1.5408401538271509935434042026969
y[1] (numeric) = -1.5408401538271509934748069177808
absolute error = 6.85972849161e-20
relative error = 4.4519403745883386879542595735633e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.286
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.785
y[1] (closed_form) = -1.5431736038435726265193245576034
y[1] (numeric) = -1.5431736038435726264504583529914
absolute error = 6.88662046120e-20
relative error = 4.4626349517951437590247785252360e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.285
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.784
y[1] (closed_form) = -1.5455075984859803967489161920157
y[1] (numeric) = -1.5455075984859803966797806909251
absolute error = 6.91355010906e-20
relative error = 4.4733200379167946045829270226273e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.284
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.783
y[1] (closed_form) = -1.547842138008664484484847664876
y[1] (numeric) = -1.5478421380086644844154424899081
absolute error = 6.94051749679e-20
relative error = 4.4839957036698457480522661891734e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.283
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.782
y[1] (closed_form) = -1.5501772226660932067117475187717
y[1] (numeric) = -1.5501772226660932066420722919106
absolute error = 6.96752268611e-20
relative error = 4.4946620194346631693632680418386e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.282
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.781
y[1] (closed_form) = -1.5525128527129131835708087476381
y[1] (numeric) = -1.5525128527129131835008630902496
absolute error = 6.99456573885e-20
relative error = 4.5053190552512725023925192780826e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.281
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = -1.5548490284039495049787918265529
y[1] (numeric) = -1.5548490284039495049085753593832
absolute error = 7.02164671697e-20
relative error = 4.5159668808345406856994663227197e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.779
y[1] (closed_form) = -1.5571857499942058974416988568198
y[1] (numeric) = -1.5571857499942058973712111999946
absolute error = 7.04876568252e-20
relative error = 4.5266055655506914424870491233054e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.778
y[1] (closed_form) = -1.5595230177388648910633918254602
y[1] (numeric) = -1.5595230177388648909926325984833
absolute error = 7.07592269769e-20
relative error = 4.5372351784517433795234991768154e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.278
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.777
y[1] (closed_form) = -1.5618608318932879867494284249861
y[1] (numeric) = -1.5618608318932879866783972467382
absolute error = 7.10311782479e-20
relative error = 4.5478557882648220780396677037843e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.277
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.776
y[1] (closed_form) = -1.5641991927130158236063893269177
y[1] (numeric) = -1.5641991927130158235350858156556
absolute error = 7.13035112621e-20
relative error = 4.5584674633687833839663424056315e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.775
y[1] (closed_form) = -1.56653810045376834653697125094
y[1] (numeric) = -1.5665381004537683464653950242949
absolute error = 7.15762266451e-20
relative error = 4.5690702718540331304610884685481e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.275
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.774
y[1] (closed_form) = -1.5688775553714449740311206208546
y[1] (numeric) = -1.5688775553714449739592712958314
absolute error = 7.18493250232e-20
relative error = 4.5796642814607075693052264994339e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.274
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.773
y[1] (closed_form) = -1.5712175577221247661534830485978
y[1] (numeric) = -1.5712175577221247660813602415737
absolute error = 7.21228070241e-20
relative error = 4.5902495596256038463865206660133e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.273
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.772
y[1] (closed_form) = -1.573558107762066592727444338542
y[1] (numeric) = -1.5735581077620665926550476652654
absolute error = 7.23966732766e-20
relative error = 4.6008261734651430156917444413993e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.272
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.771
y[1] (closed_form) = -1.575899205747709301716039156096
y[1] (numeric) = -1.5758992057477093016433682316852
absolute error = 7.26709244108e-20
relative error = 4.6113941897902141973696590587220e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.271
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = -1.5782408519356718878000039572612
y[1] (numeric) = -1.5782408519356718877270583962033
absolute error = 7.29455610579e-20
relative error = 4.6219536750955433731192824107356e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.769
y[1] (closed_form) = -1.5805830465827536611532512292906
y[1] (numeric) = -1.5805830465827536610800306454404
absolute error = 7.32205838502e-20
relative error = 4.6325046955618116432407479928263e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.768
y[1] (closed_form) = -1.5829257899459344164160425469384
y[1] (numeric) = -1.5829257899459344163425465535171
absolute error = 7.34959934213e-20
relative error = 4.6430473170703909390504899309769e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.268
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.767
y[1] (closed_form) = -1.585269082282374601866138403979
y[1] (numeric) = -1.5852690822823746017923666135731
absolute error = 7.37717904059e-20
relative error = 4.6535816051927181577254283054258e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.267
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.766
y[1] (closed_form) = -1.5876129238494154887882032357212
y[1] (numeric) = -1.5876129238494154887141552602811
absolute error = 7.40479754401e-20
relative error = 4.6641076252112585894908295352607e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.266
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.765
y[1] (closed_form) = -1.5899573149045793410417445051412
y[1] (numeric) = -1.5899573149045793409674199559803
absolute error = 7.43245491609e-20
relative error = 4.6746254420899694656691153359067e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.265
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.764
y[1] (closed_form) = -1.5923022557055695848278651830202
y[1] (numeric) = -1.5923022557055695847532636708136
absolute error = 7.46015122066e-20
relative error = 4.6851351205015477153646767039877e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.264
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.763
y[1] (closed_form) = -1.5946477465102709786551094110848
y[1] (numeric) = -1.5946477465102709785802305458679
absolute error = 7.48788652169e-20
relative error = 4.6956367248356257689836238856374e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.263
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.762
y[1] (closed_form) = -1.5969937875767497835046815966286
y[1] (numeric) = -1.5969937875767497834295249877962
absolute error = 7.51566088324e-20
relative error = 4.7061303191693258336228412777044e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.761
y[1] (closed_form) = -1.5993403791632539331953196474335
y[1] (numeric) = -1.5993403791632539331198849037384
absolute error = 7.54347436951e-20
relative error = 4.7166159673006004258248830341138e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.261
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = -1.6016875215282132049481035170118
y[1] (numeric) = -1.6016875215282132048723902465637
absolute error = 7.57132704481e-20
relative error = 4.7270937327313338475738104248690e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.759
y[1] (closed_form) = -1.6040352149302393901514806922635
y[1] (numeric) = -1.6040352149302393900754885025278
absolute error = 7.59921897357e-20
relative error = 4.7375636786755304068686544188922e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.259
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.758
y[1] (closed_form) = -1.6063834596281264653267907185797
y[1] (numeric) = -1.6063834596281264652505192163761
absolute error = 7.62715022036e-20
relative error = 4.7480258680736573086231750658548e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.258
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.757
y[1] (closed_form) = -1.6087322558808507632945713212325
y[1] (numeric) = -1.6087322558808507632180201127341
absolute error = 7.65512084984e-20
relative error = 4.7584803635633506581447845254914e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.257
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.756
y[1] (closed_form) = -1.6110816039475711445419291465736
y[1] (numeric) = -1.6110816039475711444650978373053
absolute error = 7.68313092683e-20
relative error = 4.7689272275248631020318941097611e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.256
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.755
y[1] (closed_form) = -1.6134315040876291687912586121145
y[1] (numeric) = -1.6134315040876291687141468069521
absolute error = 7.71118051624e-20
relative error = 4.7793665220393440912536710284804e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.255
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.754
y[1] (closed_form) = -1.6157819565605492667705928209935
y[1] (numeric) = -1.6157819565605492666932001241624
absolute error = 7.73926968311e-20
relative error = 4.7897983089155638955274700514906e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.254
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.753
y[1] (closed_form) = -1.6181329616260389121858709636407
y[1] (numeric) = -1.6181329616260389121081969787146
absolute error = 7.76739849261e-20
relative error = 4.8002226496916861420617447410059e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.253
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.752
y[1] (closed_form) = -1.6204845195439887938954070976356
y[1] (numeric) = -1.6204845195439887938174514275353
absolute error = 7.79556701003e-20
relative error = 4.8106396056308551276369177510854e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.252
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.751
y[1] (closed_form) = -1.6228366305744729882868456658223
y[1] (numeric) = -1.6228366305744729882086079128146
absolute error = 7.82377530077e-20
relative error = 4.8210492377168226956590186712778e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.251
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = -1.6251892949777491318568895826941
y[1] (numeric) = -1.6251892949777491317783693483903
absolute error = 7.85202343038e-20
relative error = 4.8314516066803799569945260488799e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.749
y[1] (closed_form) = -1.6275425130142585939940871898941
y[1] (numeric) = -1.6275425130142585939152840752489
absolute error = 7.88031146452e-20
relative error = 4.8418467729764070824505388267932e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.249
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.748
y[1] (closed_form) = -1.6298962849446266499649648534
y[1] (numeric) = -1.6298962849446266498858784587105
absolute error = 7.90863946895e-20
relative error = 4.8522347967795291317289250075745e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.248
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.747
y[1] (closed_form) = -1.6322506110296626541037924475706
y[1] (numeric) = -1.6322506110296626540244223724747
absolute error = 7.93700750959e-20
relative error = 4.8626157380226962655573331731980e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 1
NO POLE (ratio test) for 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=99.3MB, alloc=44.3MB, time=0.86
x[1] = 2.746
y[1] (closed_form) = -1.6346054915303602132062694447292
y[1] (numeric) = -1.6346054915303602131266152882045
absolute error = 7.96541565247e-20
relative error = 4.8729896563681371891932847320504e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.246
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.745
y[1] (closed_form) = -1.6369609267078973601274198033543
y[1] (numeric) = -1.6369609267078973600474811637169
absolute error = 7.99386396374e-20
relative error = 4.8833566112152176968700379727026e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.245
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.744
y[1] (closed_form) = -1.6393169168236367275839843232311
y[1] (numeric) = -1.6393169168236367275037607981343
absolute error = 8.02235250968e-20
relative error = 4.8937166617082326398853626096284e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.743
y[1] (closed_form) = -1.6416734621391257221615996121007
y[1] (numeric) = -1.6416734621391257220810907985338
absolute error = 8.05088135669e-20
relative error = 4.9040698667319492420837938799848e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.243
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.742
y[1] (closed_form) = -1.6440305629160966985270532854241
y[1] (numeric) = -1.644030562916096698446258779711
absolute error = 8.07945057131e-20
relative error = 4.9144162849254376976674598461938e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.242
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.741
y[1] (closed_form) = -1.6463882194164671338459054988569
y[1] (numeric) = -1.6463882194164671337648248966551
absolute error = 8.10806022018e-20
relative error = 4.9247559746593406559981741377083e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.241
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = -1.6487464319023398024057673919133
y[1] (numeric) = -1.6487464319023398023244002882124
absolute error = 8.13671037009e-20
relative error = 4.9350889940679257623441493915644e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.739
y[1] (closed_form) = -1.6511052006360029504455275010823
y[1] (numeric) = -1.6511052006360029503638734902028
absolute error = 8.16540108795e-20
relative error = 4.9454154010324122374301977886947e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.738
y[1] (closed_form) = -1.6534645258799304711908176813504
y[1] (numeric) = -1.6534645258799304711088763569425
absolute error = 8.19413244079e-20
relative error = 4.9557352531825849384764404762117e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.238
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.737
y[1] (closed_form) = -1.6558244078967820800960105566829
y[1] (numeric) = -1.6558244078967820800137815117253
absolute error = 8.22290449576e-20
relative error = 4.9660486078983957141000030998381e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.237
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.736
y[1] (closed_form) = -1.6581848469494034902930410025243
y[1] (numeric) = -1.6581848469494034902105238293228
absolute error = 8.25171732015e-20
relative error = 4.9763555223236135509628895584090e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.236
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.735
y[1] (closed_form) = -1.6605458433008265882473446467965
y[1] (numeric) = -1.6605458433008265881645389369827
absolute error = 8.28057098138e-20
relative error = 4.9866560533612930026794530444778e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.235
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.734
y[1] (closed_form) = -1.6629073972142696096212068602065
y[1] (numeric) = -1.6629073972142696095381122047365
absolute error = 8.30946554700e-20
relative error = 4.9969502576752958054171944600685e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.234
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.733
y[1] (closed_form) = -1.6652695089531373153448161919226
y[1] (numeric) = -1.6652695089531373152614321810759
absolute error = 8.33840108467e-20
relative error = 5.0072381916797905079339820171624e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.233
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.732
y[1] (closed_form) = -1.6676321787810211678953166928436
y[1] (numeric) = -1.6676321787810211678116429162218
absolute error = 8.36737766218e-20
relative error = 5.0175199115528284911404508627863e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.232
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.731
y[1] (closed_form) = -1.6699954069616995077841540557681
y[1] (numeric) = -1.6699954069616995077001901022935
absolute error = 8.39639534746e-20
relative error = 5.0277954732438177546352020100424e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.231
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = -1.6723591937591377302530109897769
y[1] (numeric) = -1.6723591937591377301687564476914
absolute error = 8.42545420855e-20
relative error = 5.0380649324570160223392222768177e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.729
y[1] (closed_form) = -1.6747235394374884621786277350703
y[1] (numeric) = -1.6747235394374884620940821919337
absolute error = 8.45455431366e-20
relative error = 5.0483283446889048568566597830608e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.229
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.728
y[1] (closed_form) = -1.6770884442610917391868041143527
y[1] (numeric) = -1.6770884442610917391019671570419
absolute error = 8.48369573108e-20
relative error = 5.0585857651758078924218250965999e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.228
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.727
y[1] (closed_form) = -1.6794539084944751829758800076405
y[1] (numeric) = -1.6794539084944751828907512223479
absolute error = 8.51287852926e-20
relative error = 5.0688372489431759825669873728592e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.227
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.726
y[1] (closed_form) = -1.6818199324023541788499916290747
y[1] (numeric) = -1.6818199324023541787645706013071
absolute error = 8.54210277676e-20
relative error = 5.0790828507771602449200138995281e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.226
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.725
y[1] (closed_form) = -1.6841865162496320534624014769627
y[1] (numeric) = -1.6841865162496320533766877915397
absolute error = 8.57136854230e-20
relative error = 5.0893226252558015031185146490973e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.225
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.724
y[1] (closed_form) = -1.6865536603014002527692003218439
y[1] (numeric) = -1.686553660301400252683193562897
absolute error = 8.60067589469e-20
relative error = 5.0995566267088070851532319555073e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.723
y[1] (closed_form) = -1.6889213648229385201936800918843
y[1] (numeric) = -1.6889213648229385201073798428553
absolute error = 8.63002490290e-20
relative error = 5.1097849092605599654579991901388e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.223
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.722
y[1] (closed_form) = -1.6912896300797150750016770103473
y[1] (numeric) = -1.6912896300797150749150828539871
absolute error = 8.65941563602e-20
relative error = 5.1200075268077285000507991682289e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.721
y[1] (closed_form) = -1.6936584563373867908881848362733
y[1] (numeric) = -1.6936584563373867908012963546405
absolute error = 8.68884816328e-20
relative error = 5.1302245330324911791213772314766e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = -1.6960278438617993747755385568246
y[1] (numeric) = -1.6960278438617993746883553312845
absolute error = 8.71832255401e-20
relative error = 5.1404359813802747135518560549151e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.719
y[1] (closed_form) = -1.6983977929189875458234693780198
y[1] (numeric) = -1.6983977929189875457359909892426
absolute error = 8.74783887772e-20
relative error = 5.1506419251083342304705623192595e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.219
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.718
y[1] (closed_form) = -1.7007683037751752146513323597928
y[1] (numeric) = -1.7007683037751752145635583877526
absolute error = 8.77739720402e-20
relative error = 5.1608424172398530827008221396452e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.218
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.717
y[1] (closed_form) = -1.7031393766967756627728085414735
y[1] (numeric) = -1.703139376696775662684738565447
absolute error = 8.80699760265e-20
relative error = 5.1710375105830134429000876120370e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.217
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.716
y[1] (closed_form) = -1.7055110119503917222433839048927
y[1] (numeric) = -1.7055110119503917221550175034576
absolute error = 8.83664014351e-20
relative error = 5.1812272577499087768555597030348e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.216
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.715
y[1] (closed_form) = -1.7078832098028159555209080243739
y[1] (numeric) = -1.707883209802815955432244775408
absolute error = 8.86632489659e-20
relative error = 5.1914117111167475894057906563609e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.215
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.714
y[1] (closed_form) = -1.710255970521030835539535755889
y[1] (numeric) = -1.7102559705210308354505752365683
absolute error = 8.89605193207e-20
relative error = 5.2015909228837895740922303109066e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.214
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.713
y[1] (closed_form) = -1.7126292943722089259973558216168
y[1] (numeric) = -1.7126292943722089259080976084148
absolute error = 8.92582132020e-20
relative error = 5.2117649450063269601346237483950e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.712
y[1] (closed_form) = -1.7150031816237130618580106510751
y[1] (numeric) = -1.715003181623713061768454319761
absolute error = 8.95563313141e-20
relative error = 5.2219338292603503121619578477939e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.212
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.711
y[1] (closed_form) = -1.7173776325430965300666123458725
y[1] (numeric) = -1.7173776325430965299767574715101
absolute error = 8.98548743624e-20
relative error = 5.2320976272028596758248514367518e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = -1.7197526473981032504802601419782
y[1] (numeric) = -1.7197526473981032503901062989244
absolute error = 9.01538430538e-20
relative error = 5.2422563901964679989307038716614e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.709
y[1] (closed_form) = -1.7221282264566679570134652512094
y[1] (numeric) = -1.7221282264566679569230120131131
absolute error = 9.04532380963e-20
relative error = 5.2524101693873476867042134921018e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.209
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.708
y[1] (closed_form) = -1.724504369986916378998789472415
y[1] (numeric) = -1.7245043699869163789080364122154
absolute error = 9.07530601996e-20
relative error = 5.2625590157413479489521173573190e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.208
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.707
y[1] (closed_form) = -1.7268810782571654227630044725695
y[1] (numeric) = -1.726881078257165422671951162495
absolute error = 9.10533100745e-20
relative error = 5.2727029800103253601357088690765e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.207
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.706
y[1] (closed_form) = -1.7292583515359233534190791487058
y[1] (numeric) = -1.7292583515359233533277251602725
absolute error = 9.13539884333e-20
relative error = 5.2828421127565811242671627819162e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.206
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.705
y[1] (closed_form) = -1.7316361900918899768743029932927
y[1] (numeric) = -1.7316361900918899767826478973033
absolute error = 9.16550959894e-20
relative error = 5.2929764643308988102728458718995e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.704
y[1] (closed_form) = -1.7340145941939568220548538983224
y[1] (numeric) = -1.7340145941939568219628972648646
absolute error = 9.19566334578e-20
relative error = 5.3031060849026662786856110089264e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.204
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.703
y[1] (closed_form) = -1.7363935641112073233471193469996
y[1] (numeric) = -1.7363935641112073232548607454448
absolute error = 9.22586015548e-20
relative error = 5.3132310244436783684408690198933e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.203
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.702
y[1] (closed_form) = -1.7387731001129170032560804565361
y[1] (numeric) = -1.738773100112917003163519455538
absolute error = 9.25610009981e-20
relative error = 5.3233513327350780387782011093346e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.202
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.701
y[1] (closed_form) = -1.7411532024685536552810688511408
y[1] (numeric) = -1.7411532024685536551882050186342
absolute error = 9.28638325066e-20
relative error = 5.3334670593570114308741333177736e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.201
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = -1.7435338714477775270092068608667
y[1] (numeric) = -1.7435338714477775269160397640659
absolute error = 9.31670968008e-20
relative error = 5.3435782537127813240929660315693e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.699
y[1] (closed_form) = -1.7459151073204415034268420595298
y[1] (numeric) = -1.7459151073204415033333712649274
absolute error = 9.34707946024e-20
relative error = 5.3536849650069825193049791277634e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.199
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.698
y[1] (closed_form) = -1.7482969103565912904492876734563
y[1] (numeric) = -1.7482969103565912903555127468218
absolute error = 9.37749266345e-20
relative error = 5.3637872422581357680188002863303e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.697
y[1] (closed_form) = -1.750679280826465598669180912343
y[1] (numeric) = -1.7506792808264655985751014187212
absolute error = 9.40794936218e-20
relative error = 5.3738851343112193601172148541260e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.197
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.696
y[1] (closed_form) = -1.7530622190004963273237717940346
y[1] (numeric) = -1.7530622190004963272293872977446
absolute error = 9.43844962900e-20
relative error = 5.3839786898044648261657876616096e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.196
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.695
y[1] (closed_form) = -1.7554457251493087484814555565347
y[1] (numeric) = -1.7554457251493087483867656211681
absolute error = 9.46899353666e-20
relative error = 5.3940679572161756605058987263501e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.195
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.694
y[1] (closed_form) = -1.7578297995437216914478622730716
y[1] (numeric) = -1.7578297995437216913528664614916
absolute error = 9.49958115800e-20
relative error = 5.4041529848144557471196166473258e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.194
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.693
y[1] (closed_form) = -1.7602144424547477273918178095464
y[1] (numeric) = -1.760214442454747727296515683886
absolute error = 9.53021256604e-20
relative error = 5.4142338207096073095759700129226e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.193
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.692
y[1] (closed_form) = -1.7625996541535933541914907881887
y[1] (numeric) = -1.7625996541535933540958819098494
absolute error = 9.56088783393e-20
relative error = 5.4243105128266761557861881283902e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.691
y[1] (closed_form) = -1.7649854349116591815010407467533
y[1] (numeric) = -1.7649854349116591814051246764038
absolute error = 9.59160703495e-20
relative error = 5.4343831089065490514247350526360e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.191
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = -1.7673717850005401160380832090943
y[1] (numeric) = -1.767371785000540115941859506669
absolute error = 9.62237024253e-20
relative error = 5.4444516565183591885516865027182e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.689
y[1] (closed_form) = -1.7697587046920255470922879104655
y[1] (numeric) = -1.7697587046920255469957561351632
absolute error = 9.65317753023e-20
relative error = 5.4545162030491900552681984612047e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.189
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.688
y[1] (closed_form) = -1.7721461942580995322554269494176
y[1] (numeric) = -1.7721461942580995321585866597
absolute error = 9.68402897176e-20
relative error = 5.4645767957164347159113264525210e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.188
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.687
y[1] (closed_form) = -1.7745342539709409833731901676881
y[1] (numeric) = -1.7745342539709409832760409212784
absolute error = 9.71492464097e-20
relative error = 5.4746334815631501838377211628343e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.187
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.686
y[1] (closed_form) = -1.7769228841029238527190855900241
y[1] (numeric) = -1.7769228841029238526216269439057
absolute error = 9.74586461184e-20
relative error = 5.4846863074534499350177065604759e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.186
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.685
y[1] (closed_form) = -1.7793120849266173193907432874316
y[1] (numeric) = -1.7793120849266173192929747978466
absolute error = 9.77684895850e-20
relative error = 5.4947353200847946845851858746595e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.185
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.684
y[1] (closed_form) = -1.7817018567147859759289415599166
y[1] (numeric) = -1.7817018567147859758308627823643
absolute error = 9.80787775523e-20
relative error = 5.5047805659889597437029947867962e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.683
y[1] (closed_form) = -1.7840921997403900151596748683726
y[1] (numeric) = -1.7840921997403900150612853576082
absolute error = 9.83895107644e-20
relative error = 5.5148220915217850734267325189379e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.183
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.682
y[1] (closed_form) = -1.7864831142765854172595834798804
y[1] (numeric) = -1.7864831142765854171608827899136
absolute error = 9.87006899668e-20
relative error = 5.5248599428698010673727518508477e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.182
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.681
y[1] (closed_form) = -1.7888746005967241370450653263181
y[1] (numeric) = -1.7888746005967241369460530104115
absolute error = 9.90123159066e-20
relative error = 5.5348941660623919950122007640395e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.181
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = -1.7912666589743542914853911128376
y[1] (numeric) = -1.7912666589743542913860667235054
absolute error = 9.93243893322e-20
relative error = 5.5449248069559494465723856431564e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.679
y[1] (closed_form) = -1.7936592896832203474401442504504
y[1] (numeric) = -1.793659289683220347340507339457
absolute error = 9.96369109934e-20
relative error = 5.5549519112404539974977397583846e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.179
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.678
y[1] (closed_form) = -1.7960524929972633096213077256788
y[1] (numeric) = -1.7960524929972633095213578440374
absolute error = 9.99498816414e-20
relative error = 5.5649755244404371732220825117608e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.677
y[1] (closed_form) = -1.7984462691906209087803205599757
y[1] (numeric) = -1.7984462691906209086800572579466
absolute error = 1.002633020291e-19
relative error = 5.5749956919326174513348401994538e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.177
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.676
y[1] (closed_form) = -1.8008406185376277901204270523961
y[1] (numeric) = -1.8008406185376277900198498794855
absolute error = 1.005771729106e-19
relative error = 5.5850124589189725250390484163710e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.176
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.675
y[1] (closed_form) = -1.8032355413128157019346425408213
y[1] (numeric) = -1.8032355413128157018337510457797
absolute error = 1.008914950416e-19
relative error = 5.5950258704499369974389377772485e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.175
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.674
y[1] (closed_form) = -1.8056310377909136844696599598891
y[1] (numeric) = -1.8056310377909136843684536907102
absolute error = 1.012062691789e-19
relative error = 5.6050359713975720435497624296082e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.174
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.673
y[1] (closed_form) = -1.8080271082468482590160220176816
y[1] (numeric) = -1.8080271082468482589145005216002
absolute error = 1.015214960814e-19
relative error = 5.6150428065119123528717005595937e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.173
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.672
y[1] (closed_form) = -1.8104237529557436172248843581563
y[1] (numeric) = -1.8104237529557436171230471816475
absolute error = 1.018371765088e-19
relative error = 5.6250464203498241483284360430347e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.172
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.671
y[1] (closed_form) = -1.8128209721929218106516956222947
y[1] (numeric) = -1.8128209721929218105495423110722
absolute error = 1.021533112225e-19
relative error = 5.6350468573257859227687499699569e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.171
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = -1.8152187662339029405271208679685
y[1] (numeric) = -1.8152187662339029404246509669829
absolute error = 1.024699009856e-19
relative error = 5.6450441617126866851540397587544e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.669
y[1] (closed_form) = -1.8176171353544053477555353566052
y[1] (numeric) = -1.8176171353544053476527484100429
absolute error = 1.027869465623e-19
relative error = 5.6550383776096081737325657129717e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.169
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.668
y[1] (closed_form) = -1.8200160798303458031414162638691
y[1] (numeric) = -1.8200160798303458030383118151506
absolute error = 1.031044487185e-19
relative error = 5.6650295489757958832493576152824e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.168
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.667
y[1] (closed_form) = -1.8224155999378396978439604217552
y[1] (numeric) = -1.8224155999378396977405380135337
absolute error = 1.034224082215e-19
relative error = 5.6750177196149774048203635277855e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.167
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.666
y[1] (closed_form) = -1.8248156959532012340602567507405
y[1] (numeric) = -1.8248156959532012339565159249005
absolute error = 1.037408258400e-19
relative error = 5.6850029331762450609896929145356e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.665
y[1] (closed_form) = -1.8272163681529436159373425929361
y[1] (numeric) = -1.8272163681529436158332828905918
absolute error = 1.040597023443e-19
relative error = 5.6949852331658777947909891589959e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.165
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.664
y[1] (closed_form) = -1.8296176168137792407134737105454
y[1] (numeric) = -1.8296176168137792406090946720393
absolute error = 1.043790385061e-19
relative error = 5.7049646629372080708572278754118e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.663
y[1] (closed_form) = -1.8320194422126198900889382683608
y[1] (numeric) = -1.8320194422126198899842394332621
absolute error = 1.046988350987e-19
relative error = 5.7149412657024028548609787910256e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.163
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.662
y[1] (closed_form) = -1.8344218446265769218267456745197
y[1] (numeric) = -1.8344218446265769217217265816231
absolute error = 1.050190928966e-19
relative error = 5.7249150845114447561208366053102e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.162
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.661
y[1] (closed_form) = -1.8368248243329614615835217103036
y[1] (numeric) = -1.8368248243329614614781818976274
absolute error = 1.053398126762e-19
relative error = 5.7348861622911646371501891969238e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.161
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = -1.8392283816092845949709419373871
y[1] (numeric) = -1.8392283816092845948652809421721
absolute error = 1.056609952150e-19
relative error = 5.7448545418024128605108452016860e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.659
y[1] (closed_form) = -1.8416325167332575598480359296521
y[1] (numeric) = -1.8416325167332575597420532883598
absolute error = 1.059826412923e-19
relative error = 5.7548202656790159186265035276994e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.159
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.658
y[1] (closed_form) = -1.8440372299827919388446954364522
y[1] (numeric) = -1.8440372299827919387383906847634
absolute error = 1.063047516888e-19
relative error = 5.7647833764067771803545912946418e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.657
y[1] (closed_form) = -1.8464425216359998521167201450709
y[1] (numeric) = -1.8464425216359998520100928178844
absolute error = 1.066273271865e-19
relative error = 5.7747439163188896922122260979326e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.157
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.656
y[1] (closed_form) = -1.8488483919711941503327352720475
y[1] (numeric) = -1.8488483919711941502257849034783
absolute error = 1.069503685692e-19
relative error = 5.7847019276238379929299626229423e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.156
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.655
y[1] (closed_form) = -1.8512548412668886078933157760596
y[1] (numeric) = -1.8512548412668886077860418994374
absolute error = 1.072738766222e-19
relative error = 5.7946574523898689641903494863858e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.155
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.654
y[1] (closed_form) = -1.8536618698017981163826525491502
y[1] (numeric) = -1.8536618698017981162750546970183
absolute error = 1.075978521319e-19
relative error = 5.8046105325241893987987078772464e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.154
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.653
y[1] (closed_form) = -1.8560694778548388782530965082747
y[1] (numeric) = -1.8560694778548388781451742123878
absolute error = 1.079222958869e-19
relative error = 5.8145612098331419400052281757516e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.153
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.652
y[1] (closed_form) = -1.8584776657051286007429170754123
y[1] (numeric) = -1.8584776657051286006346698667357
absolute error = 1.082472086766e-19
relative error = 5.8245095259473950944440981703591e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.152
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.651
y[1] (closed_form) = -1.8608864336319866900276121018595
y[1] (numeric) = -1.8608864336319866899190395105669
absolute error = 1.085725912926e-19
relative error = 5.8344555223981805268426348114706e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = -1.8632957819149344456051068607736
y[1] (numeric) = -1.8632957819149344454962084162461
absolute error = 1.088984445275e-19
relative error = 5.8443992405534018761079165906523e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.649
y[1] (closed_form) = -1.865705710833695254915180301597
y[1] (numeric) = -1.8657057108336952548059555324214
absolute error = 1.092247691756e-19
relative error = 5.8543407216560772168610751031837e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.149
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.648
y[1] (closed_form) = -1.8681162206681947881934573306419
y[1] (numeric) = -1.868116220668194788083905764609
absolute error = 1.095515660329e-19
relative error = 5.8642800068250136294691737693401e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.647
y[1] (closed_form) = -1.8705273116985611935603064538692
y[1] (numeric) = -1.8705273116985611934504276179726
absolute error = 1.098788358966e-19
relative error = 5.8742171370287465776140130049890e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.147
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.646
y[1] (closed_form) = -1.8729389842051252923449826907562
y[1] (numeric) = -1.8729389842051252922347761111905
absolute error = 1.102065795657e-19
relative error = 5.8841521531184123024208600290888e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.146
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.645
y[1] (closed_form) = -1.8753512384684207746453562421051
y[1] (numeric) = -1.8753512384684207745348214442644
absolute error = 1.105347978407e-19
relative error = 5.8940850958123760779973516783336e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.145
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.644
y[1] (closed_form) = -1.8777640747691843951235679697195
y[1] (numeric) = -1.8777640747691843950127044781959
absolute error = 1.108634915236e-19
relative error = 5.9040160056969558465725141958366e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.643
y[1] (closed_form) = -1.8801774933883561690379533220545
y[1] (numeric) = -1.8801774933883561689267606606365
absolute error = 1.111926614180e-19
relative error = 5.9139449232324594185066064438294e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.143
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.642
y[1] (closed_form) = -1.8825914946070795685115769172405
y[1] (numeric) = -1.8825914946070795684000546089115
absolute error = 1.115223083290e-19
relative error = 5.9238718887485520583472204070308e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.142
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.641
y[1] (closed_form) = -1.8850060787067017190377205732888
y[1] (numeric) = -1.8850060787067017189258681402256
absolute error = 1.118524330632e-19
relative error = 5.9337969424449651564218313563513e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.141
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = -1.8874212459687735962226681548149
y[1] (numeric) = -1.887421245968773596110485118386
absolute error = 1.121830364289e-19
relative error = 5.9437201244027964092039550913091e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.639
y[1] (closed_form) = -1.8898369966750502227661311862596
y[1] (numeric) = -1.8898369966750502226536170670237
absolute error = 1.125141192359e-19
relative error = 5.9536414745745579616744717844118e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.638
y[1] (closed_form) = -1.8922533311074908656796597633592
y[1] (numeric) = -1.8922533311074908655668140810636
absolute error = 1.128456822956e-19
relative error = 5.9635610327901553378488413182378e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.138
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.637
y[1] (closed_form) = -1.8946702495482592337433838775074
y[1] (numeric) = -1.8946702495482592336302061510866
absolute error = 1.131777264208e-19
relative error = 5.9734788387469871909548616447770e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.137
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.636
y[1] (closed_form) = -1.8970877522797236752014308516745
y[1] (numeric) = -1.8970877522797236750879205992483
absolute error = 1.135102524262e-19
relative error = 5.9833949320370198560161223542400e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.136
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.635
y[1] (closed_form) = -1.8995058395844573756963651716975
y[1] (numeric) = -1.8995058395844573755825219105698
absolute error = 1.138432611277e-19
relative error = 5.9933093521104812694018917997546e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.135
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.634
y[1] (closed_form) = -1.901924511745238556442997583042
y[1] (numeric) = -1.9019245117452385563288208296989
absolute error = 1.141767533431e-19
relative error = 6.0032221383134419258959985957184e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.134
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.633
y[1] (closed_form) = -1.9043437690450506726419109105488
y[1] (numeric) = -1.9043437690450506725274001806572
absolute error = 1.145107298916e-19
relative error = 6.0131333298620960797778203107899e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.133
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.632
y[1] (closed_form) = -1.9067636117670826121330506472381
y[1] (numeric) = -1.9067636117670826120182054556441
absolute error = 1.148451915940e-19
relative error = 6.0230429658539505601898939473840e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.631
y[1] (closed_form) = -1.9091840401947288942897289479353
y[1] (numeric) = -1.9091840401947288941745488086625
absolute error = 1.151801392728e-19
relative error = 6.0329510852736911135401246447049e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.131
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = -1.9116050546115898691533912543204
y[1] (numeric) = -1.9116050546115898690378756805685
absolute error = 1.155155737519e-19
relative error = 6.0428577269780797689002745761970e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.629
y[1] (closed_form) = -1.914026655301471916809495369984
y[1] (numeric) = -1.914026655301471916693643874127
absolute error = 1.158514958570e-19
relative error = 6.0527629297175393608009061414439e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.129
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.628
y[1] (closed_form) = -1.9164488425483876470048533972002
y[1] (numeric) = -1.916448842548387646888665490785
absolute error = 1.161879064152e-19
relative error = 6.0626667321158309615866049806000e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.128
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.627
y[1] (closed_form) = -1.9188716166365560990067875414074
y[1] (numeric) = -1.9188716166365560988902627351519
absolute error = 1.165248062555e-19
relative error = 6.0725691726967882026763260941196e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.626
y[1] (closed_form) = -1.9212949778504029417044513848133
y[1] (numeric) = -1.9212949778504029415875891886051
absolute error = 1.168621962082e-19
relative error = 6.0824702898535966831284618002031e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.625
y[1] (closed_form) = -1.9237189264745606739526688271306
y[1] (numeric) = -1.9237189264745606738354687500252
absolute error = 1.172000771054e-19
relative error = 6.0923701218754868812855178121598e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.125
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.624
y[1] (closed_form) = -1.9261434627938688251586434891872
y[1] (numeric) = -1.9261434627938688250411050394065
absolute error = 1.175384497807e-19
relative error = 6.1022687069326921770196726435308e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.124
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.623
y[1] (closed_form) = -1.9285685870933741561118919740589
y[1] (numeric) = -1.9285685870933741559940146589895
absolute error = 1.178773150694e-19
relative error = 6.1121660830874466846099165789311e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.123
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.622
y[1] (closed_form) = -1.9309942996583308600577549804344
y[1] (numeric) = -1.9309942996583308599395383066261
absolute error = 1.182166738083e-19
relative error = 6.1220622882841859019008550595020e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.122
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.621
y[1] (closed_form) = -1.9334206007742007640148408641535
y[1] (numeric) = -1.9334206007742007638962843373174
absolute error = 1.185565268361e-19
relative error = 6.1319573603708546017842457547961e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.121
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = -1.9358474907266535303367568462512
y[1] (numeric) = -1.9358474907266535302178599712584
absolute error = 1.188968749928e-19
relative error = 6.1418513370683979052067362622259e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.619
y[1] (closed_form) = -1.9382749698015668585184836694107
y[1] (numeric) = -1.9382749698015668583992459502904
absolute error = 1.192377191203e-19
relative error = 6.1517442560023926524261045368657e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.119
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.618
y[1] (closed_form) = -1.9407030382850266872477501094616
y[1] (numeric) = -1.9407030382850266871281710493997
absolute error = 1.195790600619e-19
relative error = 6.1616361546777612963195825704423e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.118
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.617
y[1] (closed_form) = -1.9431316964633273967017643544768
y[1] (numeric) = -1.9431316964633273965818434558142
absolute error = 1.199208986626e-19
relative error = 6.1715270704948463919005295660922e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.117
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.616
y[1] (closed_form) = -1.9455609446229720110896598711086
y[1] (numeric) = -1.9455609446229720109693966353393
absolute error = 1.202632357693e-19
relative error = 6.1814170407602251881623444485502e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.116
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.615
y[1] (closed_form) = -1.9479907830506724014410139860771
y[1] (numeric) = -1.9479907830506724013204079138469
absolute error = 1.206060722302e-19
relative error = 6.1913061026563756855937836245383e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.614
y[1] (closed_form) = -1.9504212120333494886407980201772
y[1] (numeric) = -1.9504212120333494885198486112818
absolute error = 1.209494088954e-19
relative error = 6.2011942932730949715271592383916e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.114
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.613
y[1] (closed_form) = -1.9528522318581334467111184228075
y[1] (numeric) = -1.9528522318581334465898251761911
absolute error = 1.212932466164e-19
relative error = 6.2110816495823554691884489307521e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.612
y[1] (closed_form) = -1.9552838428123639063401089668532
y[1] (numeric) = -1.9552838428123639062184713806067
absolute error = 1.216375862465e-19
relative error = 6.2209682084593782292189116290844e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.112
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.611
y[1] (closed_form) = -1.9577160451835901586583346767698
y[1] (numeric) = -1.957716045183590158536352248129
absolute error = 1.219824286408e-19
relative error = 6.2308540066831175837536368193665e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.111
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = -1.9601488392595713592630687769252
y[1] (numeric) = -1.9601488392595713591407410022694
absolute error = 1.223277746558e-19
relative error = 6.2407390809163359017556687324369e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.609
y[1] (closed_form) = -1.9625822253282767324908045626643
y[1] (numeric) = -1.9625822253282767323681309375143
absolute error = 1.226736251500e-19
relative error = 6.2506234677367801759139176195213e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.109
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.608
y[1] (closed_form) = -1.965016203677885775938364713162
y[1] (numeric) = -1.9650162036778857758153447321788
absolute error = 1.230199809832e-19
relative error = 6.2605072036019701037134687984864e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.108
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.607
y[1] (closed_form) = -1.9674507745967884652329711829386
y[1] (numeric) = -1.9674507745967884651096043399215
absolute error = 1.233668430171e-19
relative error = 6.2703903248803232225636362192553e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.606
y[1] (closed_form) = -1.9698859383735854590516394279164
y[1] (numeric) = -1.9698859383735854589279252158013
absolute error = 1.237142121151e-19
relative error = 6.2802728678414381257936063811331e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.106
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.605
y[1] (closed_form) = -1.9723216952970883043902613421133
y[1] (numeric) = -1.9723216952970883042661992529713
absolute error = 1.240620891420e-19
relative error = 6.2901548686413798007343753371042e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.105
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.604
y[1] (closed_form) = -1.9747580456563196420827419024932
y[1] (numeric) = -1.9747580456563196419583314275285
absolute error = 1.244104749647e-19
relative error = 6.3000363633587133399383874132643e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.104
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.603
y[1] (closed_form) = -1.9771949897405134125705551421249
y[1] (numeric) = -1.9771949897405134124457957716733
absolute error = 1.247593704516e-19
relative error = 6.3099173879645218653748612987387e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.103
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.602
y[1] (closed_form) = -1.9796325278391150619230856956543
y[1] (numeric) = -1.9796325278391150617979769191816
absolute error = 1.251087764727e-19
relative error = 6.3197979783280062906714924926950e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.601
y[1] (closed_form) = -1.9820706602417817481091227861578
y[1] (numeric) = -1.9820706602417817479836640922581
absolute error = 1.254586938997e-19
relative error = 6.3296781702220441258312962998537e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = -1.9845093872383825475198741487314
y[1] (numeric) = -1.9845093872383825473940650251253
absolute error = 1.258091236061e-19
relative error = 6.3395579993287076419205801740389e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.599
y[1] (closed_form) = -1.9869487091189986617438680136778
y[1] (numeric) = -1.9869487091189986616177079472105
absolute error = 1.261600664673e-19
relative error = 6.3494375012447417104039329488041e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.598
y[1] (closed_form) = -1.9893886261739236245941119008852
y[1] (numeric) = -1.9893886261739236244676003775251
absolute error = 1.265115233601e-19
relative error = 6.3593167114568416093887520034140e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.098
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.597
y[1] (closed_form) = -1.9918291386936635093878776069534
y[1] (numeric) = -1.9918291386936635092610141117905
absolute error = 1.268634951629e-19
relative error = 6.3691956653522564257184271162989e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.097
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.596
y[1] (closed_form) = -1.9942702469689371364794823978116
y[1] (numeric) = -1.9942702469689371363522664150554
absolute error = 1.272159827562e-19
relative error = 6.3790743982443580613775723872288e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.096
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.595
y[1] (closed_form) = -1.9967119512906762810464370519954
y[1] (numeric) = -1.9967119512906762809188680649733
absolute error = 1.275689870221e-19
relative error = 6.3889529453479406344603885356556e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.095
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.594
y[1] (closed_form) = -1.9991542519500258811293320334106
y[1] (numeric) = -1.9991542519500258810014095245663
absolute error = 1.279225088443e-19
relative error = 6.3988313417797117328730545185767e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.094
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.593
y[1] (closed_form) = -2.0015971492383442459258337073075
y[1] (numeric) = -2.0015971492383442457975571581993
absolute error = 1.282765491082e-19
relative error = 6.4087096225637764123595893259997e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.093
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.592
y[1] (closed_form) = -2.0040406434472032643391631493291
y[1] (numeric) = -2.0040406434472032642105320406279
absolute error = 1.286311087012e-19
relative error = 6.4185878226470612418935021730709e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.092
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.591
y[1] (closed_form) = -2.0064847348683886137814307348764
y[1] (numeric) = -2.0064847348683886136524445463641
absolute error = 1.289861885123e-19
relative error = 6.4284659768797390419598938514074e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.091
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.0089294237938999692322003346653
y[1] (numeric) = -2.0089294237938999691028585452333
absolute error = 1.293417894320e-19
relative error = 6.4383441200107301137463421101342e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.589
y[1] (closed_form) = -2.0113747105159512125526575822267
y[1] (numeric) = -2.0113747105159512124229596698738
absolute error = 1.296979123529e-19
relative error = 6.4482222867180386753290526878322e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.089
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.588
y[1] (closed_form) = -2.0138205953269706420557573202303
y[1] (numeric) = -2.0138205953269706419257027620611
absolute error = 1.300545581692e-19
relative error = 6.4581005115842460282648386862626e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.088
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.587
y[1] (closed_form) = -2.0162670785196011823327259748994
y[1] (numeric) = -2.0162670785196011822023142471227
absolute error = 1.304117277767e-19
relative error = 6.4679788290969806496528870567956e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.087
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.586
y[1] (closed_form) = -2.0187141603867005943362952514256
y[1] (numeric) = -2.0187141603867005942055258293523
absolute error = 1.307694220733e-19
relative error = 6.4778572736741534236053070872081e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.086
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.585
y[1] (closed_form) = -2.0211618412213416857210441881939
y[1] (numeric) = -2.0211618412213416855899165462356
absolute error = 1.311276419583e-19
relative error = 6.4877358796296380324794952881791e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.085
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.584
y[1] (closed_form) = -2.0236101213168125214412272537984
y[1] (numeric) = -2.0236101213168125213097408654654
absolute error = 1.314863883330e-19
relative error = 6.4976146812034423055222510657140e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.084
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.583
y[1] (closed_form) = -2.0260590009666166346064668182549
y[1] (numeric) = -2.0260590009666166344746211561545
absolute error = 1.318456621004e-19
relative error = 6.5074937125472399016291452487980e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.083
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.582
y[1] (closed_form) = -2.0285084804644732375956889785231
y[1] (numeric) = -2.0285084804644732374634835143578
absolute error = 1.322054641653e-19
relative error = 6.5173730077297259602686111977617e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.082
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.581
y[1] (closed_form) = -2.0309585601043174334296823684191
y[1] (numeric) = -2.030958560104317433297116572985
absolute error = 1.325657954341e-19
relative error = 6.5272526007271629221941993113999e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.081
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.0334092401803004274026602342473
y[1] (numeric) = -2.0334092401803004272697335774321
absolute error = 1.329266568152e-19
relative error = 6.5371325254435020722511838777702e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.579
y[1] (closed_form) = -2.0358605209867897389732067100029
y[1] (numeric) = -2.0358605209867897388399186607842
absolute error = 1.332880492187e-19
relative error = 6.5470128156959765262038325854184e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.079
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.578
y[1] (closed_form) = -2.0383124028183694139149888798007
y[1] (numeric) = -2.0383124028183694137813389062443
absolute error = 1.336499735564e-19
relative error = 6.5568935052155164706856258945941e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.078
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.577
y[1] (closed_form) = -2.0407648859698402367276168702723
y[1] (numeric) = -2.0407648859698402365936044395301
absolute error = 1.340124307422e-19
relative error = 6.5667746276667621809686122831769e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.077
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.576
y[1] (closed_form) = -2.0432179707362199433080348720425
y[1] (numeric) = -2.0432179707362199431736594503512
absolute error = 1.343754216913e-19
relative error = 6.5766562166092022639422743525568e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.076
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.575
y[1] (closed_form) = -2.0456716574127434338828266470616
y[1] (numeric) = -2.0456716574127434337480876997405
absolute error = 1.347389473211e-19
relative error = 6.5865383055416940561199488440765e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.075
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.574
y[1] (closed_form) = -2.0481259462948629862018197375144
y[1] (numeric) = -2.0481259462948629860667167289638
absolute error = 1.351030085506e-19
relative error = 6.5964209278734266017462301422158e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.074
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.573
y[1] (closed_form) = -2.0505808376782484689933732522796
y[1] (numeric) = -2.0505808376782484688579056459789
absolute error = 1.354676063007e-19
relative error = 6.6063041169389823703797328286547e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.073
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.572
y[1] (closed_form) = -2.0530363318587875556817347684499
y[1] (numeric) = -2.0530363318587875555459020269558
absolute error = 1.358327414941e-19
relative error = 6.6161879059938078418157922935819e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.072
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.571
y[1] (closed_form) = -2.0554924291325859383668525482686
y[1] (numeric) = -2.0554924291325859382306541332133
absolute error = 1.361984150553e-19
relative error = 6.6260723282145818026153548473152e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
memory used=143.3MB, alloc=44.3MB, time=1.28
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.0579491297959675420670299359834
y[1] (numeric) = -2.0579491297959675419304653080728
absolute error = 1.365646279106e-19
relative error = 6.6359574166995812488658249822467e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.569
y[1] (closed_form) = -2.0604064341454747392248094645675
y[1] (numeric) = -2.0604064341454747390878780835794
absolute error = 1.369313809881e-19
relative error = 6.6458432044690449131556602415867e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.069
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.568
y[1] (closed_form) = -2.0628643424778685644764748690185
y[1] (numeric) = -2.0628643424778685643391761938007
absolute error = 1.372986752178e-19
relative error = 6.6557297244703820621006860735019e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.068
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.567
y[1] (closed_form) = -2.0653228550901289296855598710155
y[1] (numeric) = -2.065322855090128929547893359484
absolute error = 1.376665115315e-19
relative error = 6.6656170095736606145450628274191e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.067
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.566
y[1] (closed_form) = -2.0677819722794548392407532690997
y[1] (numeric) = -2.0677819722794548391027183782369
absolute error = 1.380348908628e-19
relative error = 6.6755050925719637706099858068798e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.066
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.565
y[1] (closed_form) = -2.070241694343264605618590539247
y[1] (numeric) = -2.0702416943432646054801867250998
absolute error = 1.384038141472e-19
relative error = 6.6853940061865746884438297859451e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.065
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.564
y[1] (closed_form) = -2.072702021579196065211322822721
y[1] (numeric) = -2.072702021579196065072549540399
absolute error = 1.387732823220e-19
relative error = 6.6952837830624752294662014178536e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.064
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.563
y[1] (closed_form) = -2.0751629542851067944203548514424
y[1] (numeric) = -2.0751629542851067942812115551161
absolute error = 1.391432963263e-19
relative error = 6.7051744557686958423249395144048e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.063
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.562
y[1] (closed_form) = -2.0776244927590743260156440357807
y[1] (numeric) = -2.0776244927590743258761301786795
absolute error = 1.395138571012e-19
relative error = 6.7150660568082895697677976497175e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.062
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.561
y[1] (closed_form) = -2.080086637299396365761453615674
y[1] (numeric) = -2.0800866372993963656215686500846
absolute error = 1.398849655894e-19
relative error = 6.7249586185993904972599355430186e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.061
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.0825493882045910093088534533165
y[1] (numeric) = -2.0825493882045910091685968305808
absolute error = 1.402566227357e-19
relative error = 6.7348521734996230477285500554881e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.559
y[1] (closed_form) = -2.0850127457733969593553627243169
y[1] (numeric) = -2.0850127457733969592147338948302
absolute error = 1.406288294867e-19
relative error = 6.7447467537919694438104442053571e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.059
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.558
y[1] (closed_form) = -2.0874767103047737430721294442389
y[1] (numeric) = -2.087476710304773742931127857448
absolute error = 1.410015867909e-19
relative error = 6.7546423916898993115812960086971e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.058
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.557
y[1] (closed_form) = -2.0899412820979019297990424487775
y[1] (numeric) = -2.089941282097901929657667553179
absolute error = 1.413748955985e-19
relative error = 6.7645391193281087434956285376303e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.057
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.556
y[1] (closed_form) = -2.0924064614521833490081721285159
y[1] (numeric) = -2.0924064614521833488664233716542
absolute error = 1.417487568617e-19
relative error = 6.7744369687772209587979981975433e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.056
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.555
y[1] (closed_form) = -2.0948722486672413085359369032419
y[1] (numeric) = -2.0948722486672413083938137317073
absolute error = 1.421231715346e-19
relative error = 6.7843359720392891416398568254529e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.055
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.554
y[1] (closed_form) = -2.0973386440429208130843931061891
y[1] (numeric) = -2.0973386440429208129418949656159
absolute error = 1.424981405732e-19
relative error = 6.7942361610480991355254072928747e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.054
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.553
y[1] (closed_form) = -2.0998056478792887829920466353052
y[1] (numeric) = -2.0998056478792887828491729703699
absolute error = 1.428736649353e-19
relative error = 6.8041375676647078560874232493573e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.552
y[1] (closed_form) = -2.1022732604766342732745854167451
y[1] (numeric) = -2.1022732604766342731313356711645
absolute error = 1.432497455806e-19
relative error = 6.8140402236825268328444064239710e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.052
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.551
y[1] (closed_form) = -2.1047414821354686929359324152372
y[1] (numeric) = -2.1047414821354686927923060317664
absolute error = 1.436263834708e-19
relative error = 6.8239441608323701978826921025836e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.051
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.1072103131565260245500196167863
y[1] (numeric) = -2.1072103131565260244060160372168
absolute error = 1.440035795695e-19
relative error = 6.8338494107779761608244508485793e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.549
y[1] (closed_form) = -2.1096797538407630441136841013548
y[1] (numeric) = -2.1096797538407630439693027665129
absolute error = 1.443813348419e-19
relative error = 6.8437560051020799970577664446167e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.049
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.548
y[1] (closed_form) = -2.1121498044893595411710880167125
y[1] (numeric) = -2.1121498044893595410263283664569
absolute error = 1.447596502556e-19
relative error = 6.8536639753446645878553980841278e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.048
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.547
y[1] (closed_form) = -2.1146204654037185392100649595587
y[1] (numeric) = -2.114620465403718539064926432779
absolute error = 1.451385267797e-19
relative error = 6.8635733529605503899167262684792e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.047
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.546
y[1] (closed_form) = -2.1170917368854665163307959663167
y[1] (numeric) = -2.1170917368854665161852780009314
absolute error = 1.455179653853e-19
relative error = 6.8734841693434109732487355192249e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.046
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.545
y[1] (closed_form) = -2.1195636192364536261872190136651
y[1] (numeric) = -2.1195636192364536260413210466194
absolute error = 1.458979670457e-19
relative error = 6.8833964558354669266162056590155e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.045
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.544
y[1] (closed_form) = -2.1220361127587539192015766279197
y[1] (numeric) = -2.1220361127587539190552980951839
absolute error = 1.462785327358e-19
relative error = 6.8933102436994125179716524352259e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.044
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.543
y[1] (closed_form) = -2.1245092177546655640525069028128
y[1] (numeric) = -2.1245092177546655639058472393802
absolute error = 1.466596634326e-19
relative error = 6.9032255641423152205862397602388e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.043
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.542
y[1] (closed_form) = -2.1269829345267110694370839270308
y[1] (numeric) = -2.1269829345267110692900425669159
absolute error = 1.470413601149e-19
relative error = 6.9131424483017367490942414646101e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.042
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.541
y[1] (closed_form) = -2.1294572633776375061072143260812
y[1] (numeric) = -2.1294572633776375059597907023176
absolute error = 1.474236237636e-19
relative error = 6.9230609272601271908227006491840e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.1319322046104167291807973276557
y[1] (numeric) = -2.1319322046104167290329908722943
absolute error = 1.478064553614e-19
relative error = 6.9329810320309755942666660931916e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.539
y[1] (closed_form) = -2.1344077585282456007280564656541
y[1] (numeric) = -2.134407758528245600579866609761
absolute error = 1.481898558931e-19
relative error = 6.9429027935731679171550502303004e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.039
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.538
y[1] (closed_form) = -2.1368839254345462126334517454224
y[1] (numeric) = -2.136883925434546212484877919077
absolute error = 1.485738263454e-19
relative error = 6.9528262427818467908127841878820e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.537
y[1] (closed_form) = -2.1393607056329661097335818015572
y[1] (numeric) = -2.1393607056329661095846234338504
absolute error = 1.489583677068e-19
relative error = 6.9627514104840092062287024022513e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.037
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.536
y[1] (closed_form) = -2.1418380994273785132314862898251
y[1] (numeric) = -2.1418380994273785130821428088571
absolute error = 1.493434809680e-19
relative error = 6.9726783274574793634622968590439e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.036
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.535
y[1] (closed_form) = -2.1443161071218825443877594663533
y[1] (numeric) = -2.1443161071218825442380302992319
absolute error = 1.497291671214e-19
relative error = 6.9826070244077787405275214211578e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.035
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.534
y[1] (closed_form) = -2.146794729020803448488886620268
y[1] (numeric) = -2.1467947290208034483387711931064
absolute error = 1.501154271616e-19
relative error = 6.9925375319917375787662479907914e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.034
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.533
y[1] (closed_form) = -2.1492739654286928190932157403863
y[1] (numeric) = -2.1492739654286928189427134783012
absolute error = 1.505022620851e-19
relative error = 7.0024698808037212911490873242561e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.033
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.532
y[1] (closed_form) = -2.1517538166503288225549775124199
y[1] (numeric) = -2.1517538166503288224040878395296
absolute error = 1.508896728903e-19
relative error = 7.0124041013758943404483403365857e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.032
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.531
y[1] (closed_form) = -2.1542342829907164228267674604182
y[1] (numeric) = -2.1542342829907164226754897998405
absolute error = 1.512776605777e-19
relative error = 7.0223402241877665064565970532668e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.1567153647550876065409047648724
y[1] (numeric) = -2.1567153647550876063892385387226
absolute error = 1.516662261498e-19
relative error = 7.0322782796617633894134060442348e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.529
y[1] (closed_form) = -2.1591970622489016083700830100222
y[1] (numeric) = -2.1591970622489016082180276394112
absolute error = 1.520553706110e-19
relative error = 7.0422182981588275887970057958228e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.029
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.528
y[1] (closed_form) = -2.1616793757778451366677288344602
y[1] (numeric) = -2.1616793757778451365152837394926
absolute error = 1.524450949676e-19
relative error = 7.0521603099786763704871373615664e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.028
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.527
y[1] (closed_form) = -2.1641623056478325993884851821102
y[1] (numeric) = -2.1641623056478325992356497818821
absolute error = 1.528354002281e-19
relative error = 7.0621043453739199032873354429587e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.027
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.526
y[1] (closed_form) = -2.1666458521650063302892365750783
y[1] (numeric) = -2.1666458521650063301360102876754
absolute error = 1.532262874029e-19
relative error = 7.0720504345363899878256381468815e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.525
y[1] (closed_form) = -2.1691300156357368154110945557353
y[1] (numeric) = -2.1691300156357368152574767982307
absolute error = 1.536177575046e-19
relative error = 7.0819986076112236907345707542966e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.025
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.524
y[1] (closed_form) = -2.1716147963666229198427621726914
y[1] (numeric) = -2.1716147963666229196887523611439
absolute error = 1.540098115475e-19
relative error = 7.0919488946740115086501575338167e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.024
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.523
y[1] (closed_form) = -2.1741001946644921147656971140758
y[1] (numeric) = -2.1741001946644921146112946635277
absolute error = 1.544024505481e-19
relative error = 7.1019013257540984190686987021942e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.023
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.522
y[1] (closed_form) = -2.1765862108364007047814938217291
y[1] (numeric) = -2.1765862108364007046266981462041
absolute error = 1.547956755250e-19
relative error = 7.1118559308301593471683384168022e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.022
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.521
y[1] (closed_form) = -2.17907284518963405552190565157
y[1] (numeric) = -2.1790728451896340553667161640714
absolute error = 1.551894874986e-19
relative error = 7.1218127398166268128961970441678e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.021
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.1815600980317068215419288785049
y[1] (numeric) = -2.1815600980317068213863449910135
absolute error = 1.555838874914e-19
relative error = 7.1317717825777147968407902162053e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.519
y[1] (closed_form) = -2.1840479696703631744963710788136
y[1] (numeric) = -2.1840479696703631743403922022855
absolute error = 1.559788765281e-19
relative error = 7.1417330889321896276984396822349e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.019
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.518
y[1] (closed_form) = -2.1865364604135770316003271589734
y[1] (numeric) = -2.1865364604135770314439527033381
absolute error = 1.563744556353e-19
relative error = 7.1516966886398146375324819778621e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.018
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.517
y[1] (closed_form) = -2.18902557056955228437398703738
y[1] (numeric) = -2.1890255705695522842172164115384
absolute error = 1.567706258416e-19
relative error = 7.1616626114061603673993848908409e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.017
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.516
y[1] (closed_form) = -2.1915153004467230276721997243832
y[1] (numeric) = -2.1915153004467230275150323362055
absolute error = 1.571673881777e-19
relative error = 7.1716308868873821400481236598021e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.016
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.515
y[1] (closed_form) = -2.1940056503537537889992192864942
y[1] (numeric) = -2.1940056503537537888416545428176
absolute error = 1.575647436766e-19
relative error = 7.1816015446995231039992525127665e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.015
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.514
y[1] (closed_form) = -2.1964966205995397581090589225291
y[1] (numeric) = -2.1964966205995397579510962291562
absolute error = 1.579626933729e-19
relative error = 7.1915746143867797507775365350150e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.014
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.513
y[1] (closed_form) = -2.1989882114932070168918801228459
y[1] (numeric) = -2.1989882114932070167335188845422
absolute error = 1.583612383037e-19
relative error = 7.2015501254627439863174305161192e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.512
y[1] (closed_form) = -2.201480423344112769546844627701
y[1] (numeric) = -2.2014804233441127693880842481932
absolute error = 1.587603795078e-19
relative error = 7.2115281073741445168902001215999e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.012
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.511
y[1] (closed_form) = -2.2039732564618455730418576471121
y[1] (numeric) = -2.2039732564618455728826975290857
absolute error = 1.591601180264e-19
relative error = 7.2215085895328932372673417604886e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.011
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO 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) = -2.2064667111562255678606315524557
y[1] (numeric) = -2.2064667111562255677010710975532
absolute error = 1.595604549025e-19
relative error = 7.2314916012889967947081521600612e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.509
y[1] (closed_form) = -2.2089607877373047090374999993715
y[1] (numeric) = -2.2089607877373047088775386081902
absolute error = 1.599613911813e-19
relative error = 7.2414771719489218713480502392391e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.009
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.508
y[1] (closed_form) = -2.2114554865153669974804131923745
y[1] (numeric) = -2.2114554865153669973200502644644
absolute error = 1.603629279101e-19
relative error = 7.2514653307712267852300426311820e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.008
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.507
y[1] (closed_form) = -2.2139508078009287115825457539113
y[1] (numeric) = -2.213950807800928711421780687773
absolute error = 1.607650661383e-19
relative error = 7.2614561069667395351634480837415e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.007
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.506
y[1] (closed_form) = -2.216446751904738639122949414431
y[1] (numeric) = -2.2164467519047386389617816075137
absolute error = 1.611678069173e-19
relative error = 7.2714495296942230253711329120592e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.006
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.505
y[1] (closed_form) = -2.2189433191377783094566834953819
y[1] (numeric) = -2.218943319137778309295112344081
absolute error = 1.615711513009e-19
relative error = 7.2814456280786029086318320379332e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.005
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.504
y[1] (closed_form) = -2.221440509811262225994856913893
y[1] (numeric) = -2.2214405098112622258328818135483
absolute error = 1.619751003447e-19
relative error = 7.2914444311840567772953215780648e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.503
y[1] (closed_form) = -2.2239383242366380989750161962644
y[1] (numeric) = -2.223938324236638098812636541158
absolute error = 1.623796551064e-19
relative error = 7.3014459680277535009361687340342e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.003
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.502
y[1] (closed_form) = -2.2264367627255870785223147472647
y[1] (numeric) = -2.2264367627255870783595299306188
absolute error = 1.627848166459e-19
relative error = 7.3114502675845172559103449207203e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.002
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.501
y[1] (closed_form) = -2.2289358255900239880018993836327
y[1] (numeric) = -2.2289358255900239878387087976073
absolute error = 1.631905860254e-19
relative error = 7.3214573587914602840483348086468e-18 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 4.001
Order of pole (given) = 1
NO 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 ) = 2.0 / ( 0.2 * x + 0.3 ) ;
Iterations = 600
Total Elapsed Time = 1 Seconds
Elapsed Time(since restart) = 1 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Seconds
Time to Timeout = 2 Minutes 58 Seconds
Percent Done = 0 %
> quit
memory used=161.1MB, alloc=44.3MB, time=1.42